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BEGIN:VEVENT
SUMMARY:Tim Logvinenko (Cardiff)
DTSTART;VALUE=DATE-TIME:20200423T120000Z
DTEND;VALUE=DATE-TIME:20200423T130000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/1
DESCRIPTION:Title: CANCELLED - Skein-triangulated representations of generalised braids\
nby Tim Logvinenko (Cardiff) as part of Online Nottingham algebraic geomet
ry seminar\n\n\nAbstract\nOrdinary braid group $\\mathrm{Br}_n$ is a well-
known algebraic structure which encodes configurations of n non-touching s
trands ("braids") up to continuous transformations ("isotopies"). A classi
cal result of Khovanov and Thomas states that there is a natural categoric
al action of $\\mathrm{Br}_n$ on the derived category of the cotangent bun
dle of the variety of complete flags in $\\mathbb{C}^n$.\nIn this talk\, I
will introduce a new structure: the category $\\mathrm{GBr}_n$ of general
ised braids. These are the braids whose strands are allowed to touch in a
certain way. They have multiple endpoint configurations and can be non-inv
ertible\, thus forming a category rather than a group. In the context of t
riangulated categories\, it is natural to impose certain relations which r
esult in the notion of a skein-triangulated representation of $\\mathrm{GB
r}_n$.\nA decade-old conjecture states that there a skein-triangulated act
ion of $\\mathrm{GBr}_n$ on the cotangent bundles of the varieties of full
and partial flags in $\\mathbb{C}^n$. We prove this conjecture for $n = 3
$. We also show that any categorical action of $\\mathrm{Br}_n$ can be lif
ted to a skein-triangulated action of $\\mathrm{GBr}_n$\, which behaves li
ke a categorical nil Hecke algebra. This is a joint work with Rina Anno an
d Lorenzo De Biase.\n
LOCATION:https://researchseminars.org/talk/notts_ag/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Kohl (Aalto)
DTSTART;VALUE=DATE-TIME:20200430T083000Z
DTEND;VALUE=DATE-TIME:20200430T093000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/2
DESCRIPTION:Title: Unconditional Reflexive Polytopes\nby Florian Kohl (Aalto) as part of
Online Nottingham algebraic geometry seminar\n\n\nAbstract\nA convex body
is unconditional if it is symmetric with respect to reflections in all co
ordinate hyperplanes. In this talk\, we investigate unconditional lattice
polytopes with respect to geometric\, combinatorial\, and algebraic proper
ties. In particular\, we characterize unconditional reflexive polytopes in
terms of perfect graphs. As a prime example\, we study a type-$B$ analogu
e of the Birkhoff polytope. This talk is based on joint work with McCabe O
lsen and Raman Sanyal.\n
LOCATION:https://researchseminars.org/talk/notts_ag/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Livia Campo (Nottingham)
DTSTART;VALUE=DATE-TIME:20200506T090000Z
DTEND;VALUE=DATE-TIME:20200506T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/3
DESCRIPTION:Title: On a high pliability quintic hypersurface\nby Livia Campo (Nottingham
) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nI
n this talk we exhibit an example of a quintic hypersurface with a certain
compound singularity that has pliability at least $2$. We also show that\
, while a non-trivial sequence of birational transformations can be constr
ucted between the two elements of the pliability set\, the Sarkisov link c
onnecting them is not evident. This is done by studying birational links f
or codimension $4$ index $1$ Fano $3$-folds having Picard rank $2$.\n
LOCATION:https://researchseminars.org/talk/notts_ag/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Ducat (Imperial)
DTSTART;VALUE=DATE-TIME:20200513T120000Z
DTEND;VALUE=DATE-TIME:20200513T130000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/4
DESCRIPTION:Title: A Laurent phenomenon for $\\mathrm{OGr}(5\,10)$ and explicit mirror symme
try for the Fano $3$-fold $V_{12}$\nby Tom Ducat (Imperial) as part of
Online Nottingham algebraic geometry seminar\n\n\nAbstract\nThe $5$-perio
dic birational map $(x\, y) -> (y\, (1+y)/x)$ can be interpreted as a muta
tion between five open torus charts in a del Pezzo surface of degree $5$\,
coming from a cluster algebra structure on the Grassmannian $\\mathrm{Gr}
(2\,5)$. This can used to construct a rational elliptic fibration which is
the Landau-Ginzburg mirror to $\\mathrm{dP}_5$. I will briefly recap this
\, and then explain the following $3$-dimensional generalisation: the $8$-
periodic birational map $(x\, y\, z) -> (y\, z\, (1+y+z)/x)$ can be used t
o exhibit a Laurent phenomenon for the orthogonal Grassmannian $\\mathrm{O
Gr}(5\,10)$ and construct a completely explicit $K3$ fibration which is mi
rror to the Fano $3$-fold $V_{12}$\, as well as some other Fano $3$-folds.
\n
LOCATION:https://researchseminars.org/talk/notts_ag/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Thompson (Loughborough)
DTSTART;VALUE=DATE-TIME:20200514T090000Z
DTEND;VALUE=DATE-TIME:20200514T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/5
DESCRIPTION:Title: Threefolds fibred by sextic double planes\nby Alan Thompson (Loughbor
ough) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstrac
t\nI will discuss the theory of threefolds fibred by K3 surfaces mirror to
the sextic double plane. This theory is unexpectedly rich\, in part due t
o the presence of a polarisation-preserving involution on such K3 surfaces
. I will present an explicit birational classification result for such thr
eefolds\, along with computations of several of their basic invariants. Al
ong the way we will uncover several (perhaps) surprising links between thi
s theory and Kodaira's theory of elliptic surfaces. This is joint work wit
h Remkes Kooistra.\n
LOCATION:https://researchseminars.org/talk/notts_ag/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesús Martinez Garcia (Essex)
DTSTART;VALUE=DATE-TIME:20200521T123000Z
DTEND;VALUE=DATE-TIME:20200521T133000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/6
DESCRIPTION:Title: The moduli continuity method for log Fano pairs\nby Jesús Martinez G
arcia (Essex) as part of Online Nottingham algebraic geometry seminar\n\n\
nAbstract\nThe moduli continuity method\, pioneered by Odaka\, Spotti and
Sun\, allows us to explicitly provide algebraic charts of the Gromov-Hausd
orff compactification of (possibly singular) Kähler-Einstein metrics. Ass
uming we can provide a homeomorphism to some 'known' algebraic compactific
ation (customarily\, a GIT one) the method allows us to determine which Fa
no varieties (or more generally log Fano pairs) are K-polystable in a give
n deformation family. In this talk we provide the first examples of compac
tification of the moduli of log Fano pairs for the simplest deformation fa
mily: that of projective space and a hypersurface\, and mention related re
sults for cubic surfaces. This is joint work with Patricio Gallardo and Cr
istiano Spotti.\n
LOCATION:https://researchseminars.org/talk/notts_ag/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Sutherland (Lisbon)
DTSTART;VALUE=DATE-TIME:20200528T090000Z
DTEND;VALUE=DATE-TIME:20200528T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/7
DESCRIPTION:Title: Mirror symmetry for Painlevé surfaces\nby Tom Sutherland (Lisbon) as
part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nThis
talk will survey aspects of mirror symmetry for ten families of non-compac
t hyperkähler manifolds on which the dynamics of one of the Painlevé equ
ations is naturally defined. They each have a pair of natural realisations
: one as the complement of a singular fibre of a rational elliptic surface
and another as the complement of a triangle of lines in a (singular) cubi
c surface. The two realisations relate closely to a space of stability con
ditions and a cluster variety of a quiver respectively\, providing a persp
ective on SYZ mirror symmetry for these manifolds.\n
LOCATION:https://researchseminars.org/talk/notts_ag/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karin Schaller (FU Berlin)
DTSTART;VALUE=DATE-TIME:20200611T090000Z
DTEND;VALUE=DATE-TIME:20200611T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/8
DESCRIPTION:Title: Polyhedral divisors and orbit decompositions of normal affine varieties w
ith torus action\nby Karin Schaller (FU Berlin) as part of Online Nott
ingham algebraic geometry seminar\n\n\nAbstract\nNormal affine varieties o
f dimension $n$ with an effective action of a $k$-dimensional algebraic to
rus can be described completely in terms of proper polyhedral divisors liv
ing on semiprojective varieties of dimension $n−k$. We use the language
of polyhedral divisors to study the collection of $T$-orbits and $T$-orbit
closures of a normal affine $T$-variety in terms of its defining pp-divis
or. This is based on previous work of Klaus Altmann and Jürgen Hausen com
plemented by work in progress with Klaus Altmann.\n
LOCATION:https://researchseminars.org/talk/notts_ag/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuliano Gagliardi (Hannover and MPI Bonn)
DTSTART;VALUE=DATE-TIME:20200604T123000Z
DTEND;VALUE=DATE-TIME:20200604T133000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/9
DESCRIPTION:Title: The Manin-Peyre conjecture for smooth spherical Fano varieties of semisim
ple rank one\nby Giuliano Gagliardi (Hannover and MPI Bonn) as part of
Online Nottingham algebraic geometry seminar\n\n\nAbstract\nThe Manin-Pey
re conjecture is established for a class of smooth spherical Fano varietie
s of semisimple rank one. This includes all smooth spherical Fano threefol
ds of type T as well as some higher-dimensional smooth spherical Fano vari
eties.\n\nJoint work with Valentin Blomer\, Jörg Brüdern\, and Ulrich De
renthal.\n
LOCATION:https://researchseminars.org/talk/notts_ag/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Monin (Bristol)
DTSTART;VALUE=DATE-TIME:20200618T123000Z
DTEND;VALUE=DATE-TIME:20200618T133000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/10
DESCRIPTION:Title: Inversion of matrices\, a $\\C^*$ action on Grassmannians and the space
of complete quadrics\nby Leonid Monin (Bristol) as part of Online Nott
ingham algebraic geometry seminar\n\n\nAbstract\nLet $\\Gamma$ be the clos
ure of the set of pairs $(A\,A^{-1})$ of symmetric matrices of size $n$. I
n other words\, $\\Gamma$ is the graph of the inversion map on the space $
\\mathrm{Sym}_n$ of symmetric matrices of size $n$. What is the cohomology
class of $\\Gamma$ in the product of projective spaces? Equivalently\, wh
at is the degree of the variety $L^{-1}$ obtained as the closure of the se
t of inverses of matrices from a generic linear subspace $L$ of $\\mathrm{
Sym}_n$. This question is interesting in its own right but it is also moti
vated by algebraic statistics. In my talk\, I will explain how to invert a
matrix using a $\\C^*$ action on Grassmannians\, relate the above questio
n to classical enumerative problems about quadrics\, and give several poss
ible answers.\n\nThis is joint work in progress with Laurent Manivel\, Mat
eusz Michalek\, Tim Seynnaeve\, Martin Vodicka\, Andrzej Weber\, and Jaros
law A. Wisniewski.\n
LOCATION:https://researchseminars.org/talk/notts_ag/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Klaus Altmann (FU Berlin)
DTSTART;VALUE=DATE-TIME:20200625T090000Z
DTEND;VALUE=DATE-TIME:20200625T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/11
DESCRIPTION:Title: Displaying the cohomology of toric line bundles\nby Klaus Altmann (F
U Berlin) as part of Online Nottingham algebraic geometry seminar\n\n\nAbs
tract\nLine bundles $L$ on projective toric varieties can be understood as
formal differences $(\\Delta^+ − \\Delta^-)$ of convex polyhedra in the
character lattice. We show how it is possible to use this language for un
derstanding the cohomology of $L$ by studying the set-theoretic difference
$(\\Delta^- \\setminus \\Delta^+)$. Moreover\, when interpreting these co
homology groups as certain Ext-groups\, we demonstrate how the approach vi
a $(\\Delta^-\\setminus \\Delta^+)$ leads to a direct description of the a
ssociated extensions. The first part is joint work with Jarek Buczinski\,
Lars Kastner\, David Ploog\, and Anna-Lena Winz\; the second is work in pr
ogress with Amelie Flatt.\n
LOCATION:https://researchseminars.org/talk/notts_ag/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tim Logvinenko (Cardiff)
DTSTART;VALUE=DATE-TIME:20200519T130000Z
DTEND;VALUE=DATE-TIME:20200519T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/12
DESCRIPTION:Title: Skein-triangulated representations of generalised braids\nby Tim Log
vinenko (Cardiff) as part of Online Nottingham algebraic geometry seminar\
n\n\nAbstract\nOrdinary braid group $\\mathrm{Br}_n$ is a well-known algeb
raic structure which encodes configurations of $n$ non-touching strands ("
braids") up to continuous transformations ("isotopies"). A classical resul
t of Khovanov and Thomas states that there is a natural categorical action
of $\\mathrm{Br}_n$ on the derived category of the cotangent bundle of th
e variety of complete flags in $\\mathbb{C}^n$. In this talk\, I will intr
oduce a new structure: the category $\\mathrm{GBr}_n$ of generalised braid
s. These are the braids whose strands are allowed to touch in a certain wa
y. They have multiple endpoint configurations and can be non-invertible\,
thus forming a category rather than a group. In the context of triangulate
d categories\, it is natural to impose certain relations which result in t
he notion of a skein-triangulated representation of $\\mathrm{GBr}_n$. A d
ecade-old conjecture states that there a skein-triangulated action of $\\m
athrm{GBr}_n$ on the cotangent bundles of the varieties of full and partia
l flags in $\\mathbb{C}^n$. We prove this conjecture for $n = 3$. We also
show that any categorical action of $\\mathrm{Br}_n$ can be lifted to a sk
ein-triangulated action of $\\mathrm{GBr}_n$\, which behaves like a catego
rical nil Hecke algebra. This is a joint work with Rina Anno and Lorenzo D
e Biase.\n
LOCATION:https://researchseminars.org/talk/notts_ag/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gregory Smith (Queen's University)
DTSTART;VALUE=DATE-TIME:20200702T123000Z
DTEND;VALUE=DATE-TIME:20200702T133000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/13
DESCRIPTION:Title: Geometry of smooth Hilbert schemes\nby Gregory Smith (Queen's Univer
sity) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstrac
t\nHow can we understand the subvarieties of a fixed projective space? Hil
bert schemes provide the geometric answer to this question. After surveyi
ng some features of these natural parameter spaces\, we will classify the
smooth Hilbert schemes. Time permitting\, we will also describe the geomet
ry of nonsingular Hilbert schemes by interpreting them as suitable general
izations of partial flag varieties. This talk is based on joint work with
Roy Skjelnes (KTH).\n
LOCATION:https://researchseminars.org/talk/notts_ag/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ed Segal (University College London)
DTSTART;VALUE=DATE-TIME:20200708T123000Z
DTEND;VALUE=DATE-TIME:20200708T133000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/14
DESCRIPTION:Title: Semi-orthogonal decompositions and discriminants\nby Ed Segal (Unive
rsity College London) as part of Online Nottingham algebraic geometry semi
nar\n\n\nAbstract\nThe derived category of a toric variety can usually be
decomposed into smaller pieces\, by passing through different birational m
odels and applying the "windows" theory relating VGIT and derived categori
es. There are many choices involved and the decompositions are not unique.
We prove a Jordan-Hölder result\, that the multiplicities of the pieces
are independent of choices. If the toric variety is Calabi-Yau then there
are no decompositions\, instead the theory produces symmetries of the deri
ved category. Physics predicts that these all these symmetries form an act
ion of the fundamental group of the "FI parameter space". I'll explain why
our Jordan-Hölder result is necessary for this prediction to work\, and
state a conjecture (based on earlier work of Aspinwall-Plesser-Wang) relat
ing our multiplicities to the geometry of the FI parameter space. This is
joint work with Alex Kite.\n
LOCATION:https://researchseminars.org/talk/notts_ag/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Lazda (Warwick)
DTSTART;VALUE=DATE-TIME:20200715T090000Z
DTEND;VALUE=DATE-TIME:20200715T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/15
DESCRIPTION:Title: A Neron-Ogg-Shafarevich criterion for $K3$ surfaces\nby Chris Lazda
(Warwick) as part of Online Nottingham algebraic geometry seminar\n\n\nAbs
tract\nThe naive analogue of the Néron-Ogg-Shafarevich criterion fails fo
r $K3$ surfaces\, that is\, there exist $K3$ surfaces over Henselian\, dis
cretely valued fields $\\mathbb{K}$\, with unramified étale cohomology gr
oups\, but which do not admit good reduction over $\\mathbb{K}$. Assuming
potential semi-stable reduction\, I will show how to correct this by provi
ng that a $K3$ surface has good reduction if and only if is second cohomol
ogy is unramified\, and the associated Galois representation over the resi
due field coincides with the second cohomology of a certain "canonical red
uction" of $X$. This is joint work with B. Chiarellotto and C. Liedtke.\n
LOCATION:https://researchseminars.org/talk/notts_ag/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hendrik Süß (Manchester)
DTSTART;VALUE=DATE-TIME:20200716T123000Z
DTEND;VALUE=DATE-TIME:20200716T133000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/16
DESCRIPTION:Title: Normalised volumes of singularities\nby Hendrik Süß (Manchester) a
s part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nThe
notion of the normalised volume of a singularity has been introduced relat
ively recently\, but plays a crucial role in the context of Einstein metri
cs and $K$-stability. After introducing this invariant my plan is to speci
alise quickly to the case of toric singularities and show that even in thi
s relatively simple setting interesting phenomena occur.\n
LOCATION:https://researchseminars.org/talk/notts_ag/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elana Kalashnikov (Harvard)
DTSTART;VALUE=DATE-TIME:20200724T150000Z
DTEND;VALUE=DATE-TIME:20200724T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/17
DESCRIPTION:Title: Constructing Laurent polynomial mirrors for quiver flag zero loci\nb
y Elana Kalashnikov (Harvard) as part of Online Nottingham algebraic geome
try seminar\n\n\nAbstract\nAll smooth Fano varieties of dimension at most
three can be constructed as either toric complete intersections (subvariet
ies of toric varieties) or quiver ﬂag zero loci (subvarieties of quiver
ﬂag varieties). Conjecturally\, Fano varieties are expected to mirror ce
rtain Laurent polynomials. The construction of mirrors of Fano toric compl
ete intersections is well-understood. In this talk\, I'll discuss evidence
for this conjecture by proposing a method of constructing mirrors for Fan
o quiver flag zero loci. A key step of the construction is via ﬁnding to
ric degenerations of the ambient quiver ﬂag varieties. These degeneratio
ns generalise the Gelfand-Cetlin degeneration of flag varieties\, which in
the Grassmannian case has an important role in the cluster structure of i
ts coordinate ring.\n
LOCATION:https://researchseminars.org/talk/notts_ag/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Braun (University of Kentucky)
DTSTART;VALUE=DATE-TIME:20200730T140000Z
DTEND;VALUE=DATE-TIME:20200730T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/18
DESCRIPTION:Title: The integer decomposition property and Ehrhart unimodality for weighted
projective space simplices\nby Benjamin Braun (University of Kentucky)
as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nWe
consider lattice simplices corresponding to weighted projective spaces wh
ere one of the weights is $1$. We study the integer decomposition property
and Ehrhart unimodality for such simplices by focusing on restrictions re
garding the multiplicity of each weight. We introduce a necessary conditio
n for when a simplex satisfies the integer decomposition property\, and cl
assify those simplices that satisfy it in the case where there are no more
than three distinct weights. We also introduce the notion of reflexive st
abilizations of a simpex of this type\, and show that higher-order reflexi
ve stabilizations fail to be Ehrhart unimodal and fail to have the integer
decomposition property. This is joint work with Robert Davis\, Morgan Lan
e\, and Liam Solus.\n
LOCATION:https://researchseminars.org/talk/notts_ag/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yang-Hui He (City and Oxford)
DTSTART;VALUE=DATE-TIME:20200806T090000Z
DTEND;VALUE=DATE-TIME:20200806T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/19
DESCRIPTION:Title: Universes as Big Data: Superstrings\, Calabi-Yau Manifolds and Machine-L
earning\nby Yang-Hui He (City and Oxford) as part of Online Nottingham
algebraic geometry seminar\n\n\nAbstract\nWe review how historically the
problem of string phenomenology lead theoretical physics first to algebrai
c/diffenretial geometry\, and then to computational geometry\, and now to
data science and AI. With the concrete playground of the Calabi-Yau landsc
ape\, accumulated by the collaboration of physicists\, mathematicians and
computer scientists over the last 4 decades\, we show how the latest techn
iques in machine-learning can help explore problems of physical and mathem
atical interest.\n
LOCATION:https://researchseminars.org/talk/notts_ag/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Ilten (Simon Fraser)
DTSTART;VALUE=DATE-TIME:20200813T150000Z
DTEND;VALUE=DATE-TIME:20200813T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/20
DESCRIPTION:Title: Type D associahedra are unobstructed\nby Nathan Ilten (Simon Fraser)
as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nGe
neralized associahedra associated to any root system were introduced by Fo
min and Zelevinsky in their study of cluster algebras. For type $\\mathsf{
A}$ root systems\, one recovers the classical associahedron parametrizing
triangulations of a regular $n$-gon. For type $\\mathsf{D}$ root systems\,
one obtains a polytope parametrizing centrally symmetric triangulations o
f a $2n$-gon. In previous work\, Jan Christophersen and I showed that the
Stanley-Reisner ring of the simplicial complex dual to the boundary of the
classical associahedron is unobstructed\, that is\, has vanishing second
cotangent cohomology. This could be used to find toric degenerations of th
e Grassmannian $\\mathrm{Gr}(2\,n)$. In this talk\, I will describe work-i
n-progress that generalizes this unobstructedness result to the type $\\ma
thsf{D}$ associahedron.\n
LOCATION:https://researchseminars.org/talk/notts_ag/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Man-Wai "Mandy" Cheung (Harvard)
DTSTART;VALUE=DATE-TIME:20200820T130000Z
DTEND;VALUE=DATE-TIME:20200820T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/21
DESCRIPTION:Title: Polytopes\, wall crossings\, and cluster varieties\nby Man-Wai "Mand
y" Cheung (Harvard) as part of Online Nottingham algebraic geometry semina
r\n\n\nAbstract\nCluster varieties are log Calabi-Yau varieties which are
a union of algebraic tori glued by birational "mutation" maps. Partial com
pactifications of the varieties\, studied by Gross\, Hacking\, Keel\, and
Kontsevich\, generalize the polytope construction of toric varieties. Howe
ver\, it is not clear from the definitions how to characterize the polytop
es giving compactifications of cluster varieties. We will show how to desc
ribe the compactifications easily by broken line convexity. As an applicat
ion\, we will see the non-integral vertex in the Newton Okounkov body of $
\\mathrm{Gr}(3\,6)$ comes from broken line convexity. Further\, we will al
so see certain positive polytopes will give us hints about the Batyrev mir
ror in the cluster setting. The mutations of the polytopes will be related
to the almost toric fibration from the symplectic point of view. Finally\
, we can see how to extend the idea of gluing of tori in Floer theory whic
h then ended up with the Family Floer Mirror for the del Pezzo surfaces of
degree $5$ and $6$. The talk will be based on a series of joint works wit
h Bossinger\, Lin\, Magee\, Najera-Chavez\, and Vienna.\n
LOCATION:https://researchseminars.org/talk/notts_ag/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Petracci (FU Berlin)
DTSTART;VALUE=DATE-TIME:20200827T123000Z
DTEND;VALUE=DATE-TIME:20200827T133000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/22
DESCRIPTION:Title: $K$-moduli stacks and $K$-moduli spaces are singular\nby Andrea Petr
acci (FU Berlin) as part of Online Nottingham algebraic geometry seminar\n
\n\nAbstract\nOnly recently a separated moduli space for (some) Fano varie
ties has been constructed by several algebraic geometers: this is the $K$-
moduli stack which parametrises $K$-semistable Fano varieties and has a se
parated good moduli space. A natural question is: are these stacks and spa
ces smooth? This question makes sense because deformations of smooth Fano
varieties are unobstructed\, so moduli stacks of smooth Fano varieties are
smooth. In this talk I will explain how to use toric geometry to construc
t examples of non-smooth points in the $K$-moduli stack and the $K$-moduli
space of Fano $3$-folds. This is joint work with Anne-Sophie Kaloghiros.\
n
LOCATION:https://researchseminars.org/talk/notts_ag/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Harder (Lehigh)
DTSTART;VALUE=DATE-TIME:20200904T140000Z
DTEND;VALUE=DATE-TIME:20200904T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/23
DESCRIPTION:Title: Log symplectic pairs and mixed Hodge structures\nby Andrew Harder (L
ehigh) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstra
ct\nA log symplectic pair is a pair $(X\,Y)$ consisting of a smooth projec
tive variety $X$ and a divisor $Y$ in $X$ so that there is a non-degenerat
e log $2$-form on $X$ with poles along $Y$. I will discuss the relationshi
p between log symplectic pairs and degenerations of hyperkaehler varieties
\, and how this naturally leads to a class of log symplectic pairs called
log symplectic pairs of "pure weight". I will discuss results which show t
hat the classification of log symplectic pairs of pure weight is analogous
to the classification of log Calabi-Yau surfaces. Time permitting\, I'll
discuss two classes of log symplectic pairs which are related to real hype
rplane arrangements and which admit cluster type structures.\n
LOCATION:https://researchseminars.org/talk/notts_ag/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lara Bossinger (Oaxaca)
DTSTART;VALUE=DATE-TIME:20200910T150000Z
DTEND;VALUE=DATE-TIME:20200910T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/24
DESCRIPTION:Title: Families of Gröbner degenerations\, Grassmannians\, and universal clust
er algebras\nby Lara Bossinger (Oaxaca) as part of Online Nottingham a
lgebraic geometry seminar\n\n\nAbstract\nLet $V$ be the weighted projectiv
e variety defined by a weighted homogeneous ideal $J$ and $C$ a maximal co
ne in the Gröbner fan of $J$ with m rays. We construct a flat family over
affine $m$-space that assembles the Gröbner degenerations of $V$ associa
ted with all faces of $C$. This is a multi-parameter generalization of the
classical one-parameter Gröbner degeneration associated to a weight. We
show that our family can be constructed from Kaveh-Manon's recent work on
the classification of toric flat families over toric varieties: it is the
pullback of a toric family defined by a Rees algebra with base $X_C$ (the
toric variety associated to $C$) along the universal torsor $\\mathbb{A}^m
\\to X_C$. If time permits I will explain how to apply this construction
to the Grassmannians $\\mathrm{Gr}(2\,n)$ (with Plücker embedding) and $\
\mathrm{Gr}(3\,6)$ (with "cluster embedding"). In each case there exists a
unique maximal Gröbner cone whose associated initial ideal is the Stanle
y-Reisner ideal of the cluster complex. We show that the corresponding clu
ster algebra with universal coefficients arises as the algebra defining th
e flat family associated to this cone. Further\, for $\\mathrm{Gr}(2\,n)$
we show how Escobar-Harada's mutation of Newton-Okounkov bodies can be rec
overed as tropicalized cluster mutation. This is joint work with Fatemeh M
ohammadi and Alfredo Nájera Chávez.\n
LOCATION:https://researchseminars.org/talk/notts_ag/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ronan Terpereau (Bourgogne)
DTSTART;VALUE=DATE-TIME:20200917T090000Z
DTEND;VALUE=DATE-TIME:20200917T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/25
DESCRIPTION:Title: Actions of connected algebraic groups on rational 3-dimensional Mori fib
rations\nby Ronan Terpereau (Bourgogne) as part of Online Nottingham a
lgebraic geometry seminar\n\n\nAbstract\nIn this talk we will study the co
nnected algebraic groups acting on Mori fibrations $X \\to Y$ with $X$ a r
ational threefold and $Y$ a curve or a surface. We will see how these grou
ps can be classified\, using the minimal model program (MMP) and the Sarki
sov program\, and how our results make possible to recover most of the cla
ssification of the connected algebraic subgroups of the Cremona group $\\m
athrm{Bir}(\\mathbb{P}^3)$ obtained by Hiroshi Umemura in the 1980's when
the base field is the field of complex numbers.\n
LOCATION:https://researchseminars.org/talk/notts_ag/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renato Vianna (Rio de Janeiro)
DTSTART;VALUE=DATE-TIME:20200903T140000Z
DTEND;VALUE=DATE-TIME:20200903T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/26
DESCRIPTION:Title: Sharp ellipsoid embeddings and almost-toric mutations\nby Renato Via
nna (Rio de Janeiro) as part of Online Nottingham algebraic geometry semin
ar\n\n\nAbstract\nWe will show how to construct volume filling ellipsoid e
mbeddings in some $4$-dimensional toric domain using mutations of almost t
oric compactifications of those. In particular we recover the results of M
cDuff-Schlenk for the ball\, Fenkel-Müller for product of symplectic disk
s and Cristofaro-Gardiner for $E(2\,3)$\, giving a more explicit geometric
perspective for these results. To be able to represent certain divisors\,
we develop the idea of symplectic tropical curves in almost toric fibrati
ons\, inspired by Mikhalkin's work for tropical curves. This is joint work
with Roger Casals.\n
LOCATION:https://researchseminars.org/talk/notts_ag/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Navid Nabijou (Cambridge)
DTSTART;VALUE=DATE-TIME:20200924T140000Z
DTEND;VALUE=DATE-TIME:20200924T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/27
DESCRIPTION:Title: Degenerating tangent curves\nby Navid Nabijou (Cambridge) as part of
Online Nottingham algebraic geometry seminar\n\n\nAbstract\nIt is well-kn
own that a smooth plane cubic $E$ supports $9$ flex lines. In higher degre
es we may ask an analogous question: "How many degree $d$ curves intersect
$E$ in a single point?" The problem of calculating such numbers has fasci
nated enumerative geometers for decades. Despite being an extremely classi
cal and concrete problem\, it was not until the advent of Gromov-Witten in
variants in the 1990s that a general method was discovered. The resulting
theory is incredibly rich\, and the curve counts satisfy a suite of remark
able properties\, some proven and some still conjectural. In this talk I w
ill discuss joint work with Lawrence Barrott\, in which we study the behav
iour of these tangent curves as the cubic $E$ degenerates to a cycle of li
nes. Using the machinery of logarithmic Gromov-Witten theory\, we obtain d
etailed information concerning how the tangent curves degenerate along wit
h $E$. The theorems we obtain are purely classical\, with no reference to
Gromov-Witten theory\, but they do not appear to admit a classical proof.
No prior knowledge of Gromov-Witten theory will be assumed.\n
LOCATION:https://researchseminars.org/talk/notts_ag/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Smirnov (Augsburg)
DTSTART;VALUE=DATE-TIME:20201001T140000Z
DTEND;VALUE=DATE-TIME:20201001T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/28
DESCRIPTION:Title: Residual categories of Grassmannians\nby Maxim Smirnov (Augsburg) as
part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nExcep
tional collections in derived categories of coherent sheaves have a long h
istory going back to the pioneering work of A. Beilinson. After recalling
the general setup\, I will concentrate on some recent developments inspire
d by the homological mirror symmetry. Namely\, I will define residual cate
gories of Lefschetz decompositions and discuss a conjectural relation betw
een the structure of quantum cohomology and residual categories. I will il
lustrate this relationship in the case of some isotropic Grassmannians. Th
is is a joint work with Alexander Kuznetsov.\n
LOCATION:https://researchseminars.org/talk/notts_ag/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiroshi Iritani (Kyoto)
DTSTART;VALUE=DATE-TIME:20201007T130000Z
DTEND;VALUE=DATE-TIME:20201007T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/29
DESCRIPTION:Title: Quantum cohomology of blow-ups: a conjecture\nby Hiroshi Iritani (Ky
oto) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract
\nIn this talk\, I discuss a conjecture that a semiorthogonal decompositio
n of topological $K$-groups (or derived categories) due to Orlov should in
duce a relationship between quantum cohomology under blowups. The relation
ship between quantum cohomology can be described in terms of solutions to
a Riemann-Hilbert problem.\n
LOCATION:https://researchseminars.org/talk/notts_ag/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Kaplan (Birmingham)
DTSTART;VALUE=DATE-TIME:20201015T120000Z
DTEND;VALUE=DATE-TIME:20201015T130000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/30
DESCRIPTION:Title: Exceptional collections for invertible polynomials using VGIT\nby Da
niel Kaplan (Birmingham) as part of Online Nottingham algebraic geometry s
eminar\n\n\nAbstract\nA sum of n monomials in n variables is said to be in
vertible if it is quasi-homogeneous and quasi-smooth (i.e. it has a unique
singularity at the origin). To an invertible polynomial w\, one can assoc
iate a maximal symmetry group\, and consider the derived category of equiv
ariant matrix factorizations of w. Joint with David Favero and Tyler Kelly
\, we prove this category has a full exceptional collection\, using a vari
ation of GIT result of Ballard—Favero—Katzarkov. Our proof additionall
y utilizes the Kreuzer-Skarke classification of invertible polynomials as
Thom—Sebastiani sums of Fermat\, chain\, and loop polynomials. I’ll pr
esent a friendly\, example-oriented illustration of our approach\, review
related literature\, and discuss applications to mirror symmetry.\n
LOCATION:https://researchseminars.org/talk/notts_ag/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tyler Kelly (Birmingham)
DTSTART;VALUE=DATE-TIME:20201022T140000Z
DTEND;VALUE=DATE-TIME:20201022T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/31
DESCRIPTION:Title: What is an exoflop?\nby Tyler Kelly (Birmingham) as part of Online N
ottingham algebraic geometry seminar\n\n\nAbstract\nAspinwall stated in 20
14 that an exoflop "occurs in the gauged linear sigma-model by varying the
Kähler form so that a subspace appears to shrink to a point and then ree
merge 'outside' the original manifold." This description may be intangible
at first for us to sink our hands into but it turns out to be a great con
crete technique that relates to many things we care about as algebraic geo
meters! We will interpret it in this talk. I will explain in toric geometr
y concretely what this means for us. Afterwards\, I will explain why it’
s yet another reason we should listen to our string theoretic friends. Nam
ely\, I hope to have enough time to explain how it gives us applications i
n mirror symmetry and derived categories. Exoflops are a recurring charact
er in my joint work with David Favero (Alberta)\, Chuck Doran (Alberta)\,
and Dan Kaplan (Birmingham).\n
LOCATION:https://researchseminars.org/talk/notts_ag/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catherine Cannizzo (Simons Center)
DTSTART;VALUE=DATE-TIME:20201029T150000Z
DTEND;VALUE=DATE-TIME:20201029T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/32
DESCRIPTION:Title: Towards global homological mirror symmetry for genus 2 curves\nby Ca
therine Cannizzo (Simons Center) as part of Online Nottingham algebraic ge
ometry seminar\n\n\nAbstract\nThe first part of the talk will discuss work
in arXiv:1908.04227 [math.SG] on constructing a Donaldson-Fukaya-Seidel t
ype category for the generalized SYZ mirror of a genus $2$ curve. We will
explain the categorical mirror correspondence on the cohomological level.
The key idea uses that a $4$-torus is SYZ mirror to a $4$-torus. So if we
view the complex genus $2$ curve as a hypersurface of a $4$-torus $V$\, a
mirror can be constructed as a symplectic fibration with fiber given by th
e dual $4$-torus $V^\\vee$. Hence on categories\, line bundles on $V$ are
restricted to the genus $2$ curve while fiber Lagrangians of $V^\\vee$ are
parallel transported over $U$-shapes in the base of the mirror. Next we d
escribe ongoing work with H. Azam\, H. Lee\, and C-C. M. Liu on extending
the result to a global statement\, namely allowing the complex and symplec
tic structures to vary in their real six-dimensional families. The mirror
statement for this more general result relies on work of A. Kanazawa and S
-C. Lau.\n
LOCATION:https://researchseminars.org/talk/notts_ag/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Barbacovi (UCL)
DTSTART;VALUE=DATE-TIME:20201105T133000Z
DTEND;VALUE=DATE-TIME:20201105T143000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/33
DESCRIPTION:Title: Understanding the flop-flop autoequivalence using spherical functors
\nby Federico Barbacovi (UCL) as part of Online Nottingham algebraic geome
try seminar\n\n\nAbstract\nThe homological interpretation of the Minimal M
odel Program conjectures that flips should correspond to embeddings of der
ived categories\, and flops to equivalences. Even if the conjecture doesn
’t provide us with a preferred functor\, there is an obvious choice: the
pull-push via the fibre product. When this approach work\, we obtain an i
nteresting autoequivalence of either side of the flop\, known as the “fl
op-flop autoequivalence”. Understanding the structure of this functor (e
.g. does it split as the composition of simpler functors?) is an interesti
ng problem\, and it has been extensively studied. In this talk I will expl
ain that there is a natural\, i.e. arising from the geometry\, way to real
ise the “flop-flop autoequivalence” as the inverse of a spherical twis
t\, and that this presentation can help us shed light on the structure of
the autoequivalence itself.\n
LOCATION:https://researchseminars.org/talk/notts_ag/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arkadij Bojko (Oxford)
DTSTART;VALUE=DATE-TIME:20201112T133000Z
DTEND;VALUE=DATE-TIME:20201112T143000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/34
DESCRIPTION:Title: Orientations for DT invariants on quasi-projective Calabi-Yau $4$-folds<
/a>\nby Arkadij Bojko (Oxford) as part of Online Nottingham algebraic geom
etry seminar\n\n\nAbstract\nDonaldson-Thomas type invariants in complex di
mension $4$ have attracted a lot of attention in the past few years. I wil
l give a brief overview of how one can count coherent sheaves on Calabi-Ya
u $4$-folds. Inherent to the definition of DT4 invariants is the notion of
orientations on moduli spaces of sheaves/ perfect complexes. For virtual
fundamental classes and virtual structure sheaves to be well-defined\, one
needs to prove orientability. The result of Cao-Gross-Joyce does this for
projective CY $4$-folds. However\, computations are more feasible in the
non-compact setting using localization formulae\, where the fixed point lo
ci inherit orientations from global ones\, and orientations of the virtual
normal bundles come into play. I will explain how to use real determinant
line bundles of Dirac operators on the double of the original Calabi-Yau
manifold to construct orientations on the moduli stack of compactly suppor
ted perfect complexes\, moduli schemes of stable pairs and Hilbert schemes
. These are controlled by choices of orientations in K-theory and satisfy
compatibility under direct sums. If time allows\, I will discuss the conne
ction between the sings obtained from comparing orientations and universal
wall-crossing formulae of Joyce using vertex algebras.\n
LOCATION:https://researchseminars.org/talk/notts_ag/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrico Fatighenti (Toulouse)
DTSTART;VALUE=DATE-TIME:20201111T100000Z
DTEND;VALUE=DATE-TIME:20201111T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/35
DESCRIPTION:Title: Fano varieties from homogeneous vector bundles\nby Enrico Fatighenti
(Toulouse) as part of Online Nottingham algebraic geometry seminar\n\n\nA
bstract\nThe idea of classifying Fano varieties using homogeneous vector b
undles was behind Mukai's classification of prime Fano 3-folds. In this ta
lk\, we give a survey of some recent progress along the same lines\, inclu
ding a biregular rework of the non-prime Mori-Mukai 3-folds classification
and some examples of higher-dimensional Fano varieties with special Hodge
-theoretical properties.\n
LOCATION:https://researchseminars.org/talk/notts_ag/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naoki Fujita (University of Tokyo)
DTSTART;VALUE=DATE-TIME:20201119T100000Z
DTEND;VALUE=DATE-TIME:20201119T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/36
DESCRIPTION:Title: Newton-Okounkov bodies arising from cluster structures\nby Naoki Fuj
ita (University of Tokyo) as part of Online Nottingham algebraic geometry
seminar\n\n\nAbstract\nA toric degeneration is a flat degeneration from a
projective variety to a toric variety\, which can be used to apply the the
ory of toric varieties to other projective varieties. In this talk\, we di
scuss relations among the following three constructions of toric degenerat
ions: representation theory\, Newton-Okounkov bodies\, and cluster algebra
s. More precisely\, we construct Newton-Okounkov bodies using cluster stru
ctures\, and realize representation-theoretic and cluster-theoretic toric
degenerations from this framework. As an application\, we connect two kind
s of representation-theoretic polytopes (string polytopes and Nakashima-Ze
levinsky polytopes) by tropicalized cluster mutations. We also discuss rel
ations with combinatorial mutations which was introduced in the context of
mirror symmetry for Fano varieties. More precisely\, we relate dual polyt
opes of these representation-theoretic polytopes by combinatorial mutation
s. This talk is based on joint works with Hironori Oya and Akihiro Higashi
tani.\n
LOCATION:https://researchseminars.org/talk/notts_ag/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Peón-Nieto (Birmingham/Côte d'Azur)
DTSTART;VALUE=DATE-TIME:20201120T100000Z
DTEND;VALUE=DATE-TIME:20201120T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/37
DESCRIPTION:Title: Pure codimensionality of wobbly bundles\nby Ana Peón-Nieto (Birming
ham/Côte d'Azur) as part of Online Nottingham algebraic geometry seminar\
n\n\nAbstract\nHiggs bundles on smooth projective curves were introduced b
y Hitchin as solutions to gauge equations motivated by physics. They can b
e seen as points of $T^*N$\, where N is the moduli space of vector bundles
on the curve. The topology of the moduli space of Higgs bundles is determ
ined by the nilpotent cone\, which is a reducible scheme containing the ze
ro section of $T^*N\\dashrightarrow N$. Inside this section\, wobbly bundl
es are particularly important\, as this is the locus where any other compo
nent intersects $N$. In fact\, this implies that the geometry of the nilpo
tent cone can be described in terms of wobbly bundles. In this talk I will
explain an inductive method to prove pure codimensionality of the wobbly
locus\, as announced in a paper by Laumon from the 80's. We expect our met
hod to yield moreover a description of the irreducible components of the n
ilpotent cone in arbitrary rank.\n
LOCATION:https://researchseminars.org/talk/notts_ag/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Okke van Garderen (Glasgow)
DTSTART;VALUE=DATE-TIME:20201126T133000Z
DTEND;VALUE=DATE-TIME:20201126T143000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/38
DESCRIPTION:Title: Refined Donaldson-Thomas theory of threefold flops\nby Okke van Gard
eren (Glasgow) as part of Online Nottingham algebraic geometry seminar\n\n
\nAbstract\nDT invariants are virtual counts of semistable objects in the
derived category of a Calabi-Yau variety\, which can be calculated at vari
ous levels of refinement. An interesting family of CY variety which are of
particular interest to the MMP are threefold flopping curves\, and in thi
s talk I will explain how to understand their DT theory. The key point is
that the stability conditions on the derived categories can be understood
via tilting equivalences\, which can be seen as the analogue of cluster mu
tations in this setting. I will show that these equivalences induce wall-c
rossing formulas\, and use this to reduce the DT theory of a flop to a com
prehensible set of curve-counting invariants\, which can be computed for s
everal examples. These computations produce new evidence for a conjecture
of Pandharipande-Thomas\, and show that refined DT invariants are not enou
gh to completely classify flops.\n
LOCATION:https://researchseminars.org/talk/notts_ag/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timothy Magee (Birmingham)
DTSTART;VALUE=DATE-TIME:20201203T133000Z
DTEND;VALUE=DATE-TIME:20201203T143000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/39
DESCRIPTION:Title: Convexity in tropical spaces and compactifications of cluster varieties<
/a>\nby Timothy Magee (Birmingham) as part of Online Nottingham algebraic
geometry seminar\n\n\nAbstract\nCluster varieties are a relatively new\, b
roadly interesting class of geometric objects that generalize toric variet
ies. Convexity is a key notion in toric geometry. For instance\, projectiv
e toric varieties are defined by convex lattice polytopes. In this talk\,
I'll explain how convexity generalizes to the cluster world\, where "polyt
opes" live in a tropical space rather than a vector space and "convex poly
topes" define projective compactifications of cluster varieties. Time perm
itting\, I'll conclude with two exciting applications of this more general
notion of convexity: 1) an intrinsic version of Newton-Okounkov bodies an
d 2) a possible cluster version of a classic toric mirror symmetry constru
ction due to Batyrev. Based on joint work with Man-Wai Cheung and Alfredo
Nájera Chávez.\n
LOCATION:https://researchseminars.org/talk/notts_ag/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Eur (Stanford)
DTSTART;VALUE=DATE-TIME:20201210T163000Z
DTEND;VALUE=DATE-TIME:20201210T173000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/40
DESCRIPTION:Title: Tautological bundles of matroids\nby Christopher Eur (Stanford) as p
art of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nRecent
advances in matroid theory via tropical geometry broadly fall into two the
mes: One concerns the K-theory of Grassmannians\, and the other concerns t
he intersection theory of wonderful compactifications. How do these two t
hemes talk to each other? We introduce the notion of tautological bundles
of matroids to unite these two themes. As a result\, we give a geometric
interpretation of the Tutte polynomial of a matroid that unifies several
previous works as its corollaries\, deduce new log-concavity statements\,
and answer few conjectures in the literature. This is an ongoing project
with Andrew Berget\, Hunter Spink\, and Dennis Tseng.\n
LOCATION:https://researchseminars.org/talk/notts_ag/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lawrence Barrott (Boston College)
DTSTART;VALUE=DATE-TIME:20210114T150000Z
DTEND;VALUE=DATE-TIME:20210114T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/41
DESCRIPTION:Title: Log geometry and Chow theory\nby Lawrence Barrott (Boston College) a
s part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nLog
geometry has become a central tool in enumerative geometry over the past y
ears\, providing means to study many degenerations situations. Unfortunate
ly much of the theory is complicated by the fact that products of log sche
mes differ from products of schemes.\n\nIn this talk I will introduce a ga
dget which replaces Chow theory for log schemes\, reproducing many familia
r tools such as virtual pullback in the context of log geometry.\n
LOCATION:https://researchseminars.org/talk/notts_ag/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michel Van Garrel (Birmingham)
DTSTART;VALUE=DATE-TIME:20210121T100000Z
DTEND;VALUE=DATE-TIME:20210121T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/42
DESCRIPTION:Title: Stable maps to Looijenga pairs\nby Michel Van Garrel (Birmingham) as
part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nStart
with a rational surface $Y$ admitting a decomposition of its anticanonica
l divisor into at least 2 smooth nef components. We associate 5 curve coun
ting theories to this Looijenga pair: 1) all genus stable log maps with ma
ximal tangency to each boundary component\; 2) genus 0 stable maps to the
local Calabi-Yau surface obtained by twisting $Y$ by the sum of the line b
undles dual to the components of the boundary\; 3) the all genus open Grom
ov-Witten theory of a toric Calabi-Yau threefold associated to the Looijen
ga pair\; 4) the Donaldson-Thomas theory of a symmetric quiver specified b
y the Looijenga pair and 5) BPS invariants associated to the various curve
counting theories. In this joint work with Pierrick Bousseau and Andrea B
rini\, we provide closed-form solutions to essentially all of the associat
ed invariants and show that the theories are equivalent. I will start by d
escribing the geometric transitions from one geometry to the other\, then
give an overview of the curve counting theories and their relations. I wil
l end by describing how the scattering diagrams of Gross and Siebert are a
natural place to count stable log maps.\n
LOCATION:https://researchseminars.org/talk/notts_ag/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matej Filip (Ljubljana)
DTSTART;VALUE=DATE-TIME:20210128T100000Z
DTEND;VALUE=DATE-TIME:20210128T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/43
DESCRIPTION:Title: The miniversal deformation of an affine toric Gorenstein threefold\n
by Matej Filip (Ljubljana) as part of Online Nottingham algebraic geometry
seminar\n\n\nAbstract\nWe are going to describe the reduced miniversal de
formation of an affine toric Gorenstein threefold. The reduced deformation
components correspond to special Laurent polynomials. There is canonical
bijective map between the set of the smoothing components and the set of t
he corresponding Laurent polynomials\, which we are going to analyse in mo
re details.\n
LOCATION:https://researchseminars.org/talk/notts_ag/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pieter Belmans (Bonn)
DTSTART;VALUE=DATE-TIME:20210204T100000Z
DTEND;VALUE=DATE-TIME:20210204T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/44
DESCRIPTION:Title: Hochschild cohomology of partial flag varieties and Fano 3-folds\nby
Pieter Belmans (Bonn) as part of Online Nottingham algebraic geometry sem
inar\n\n\nAbstract\nThe Hochschild-Kostant-Rosenberg decomposition gives a
description of the Hochschild cohomology of a smooth projective variety i
n terms of the sheaf cohomology of exterior powers of the tangent bundle.
In all but a few cases it is a non-trivial task to compute this decomposit
ion\, and understand the extra algebraic structure which exists on Hochsch
ild cohomology. I will give a general introduction to Hochschild cohomolog
y and this decomposition\, and explain what it looks like for partial flag
varieties (joint work with Maxim Smirnov) and Fano 3-folds (joint work wi
th Enrico Fatighenti and Fabio Tanturri).\n
LOCATION:https://researchseminars.org/talk/notts_ag/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrica Mazzon (Bonn)
DTSTART;VALUE=DATE-TIME:20210211T110000Z
DTEND;VALUE=DATE-TIME:20210211T120000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/45
DESCRIPTION:Title: Non-archimedean approach to mirror symmetry and to degenerations of vari
eties\nby Enrica Mazzon (Bonn) as part of Online Nottingham algebraic
geometry seminar\n\n\nAbstract\nMirror symmetry is a fast-moving research
area at the boundary between mathematics and theoretical physics. Originat
ed from observations in string theory\, it suggests that complex Calabi-Ya
u manifolds should come in mirror pairs\, in the sense that geometrical in
formation of a Calabi-Yau manifold can be read through invariants of its m
irror.\n\nIn the first part of the talk\, I will introduce some geometrica
l ideas inspired by mirror symmetry. In particular\, I will go through the
main steps which relate mirror symmetry to non-archimedean geometry and t
he theory of Berkovich spaces.\n\nIn the second part\, I will describe a c
ombinatorial object\, the so-called dual complex of a degeneration of vari
eties. This emerges in many contexts of algebraic geometry\, including mir
ror symmetry where moreover it comes equipped with an integral affine stru
cture. I will show how the techniques of Berkovich geometry give a new ins
ight into the study of dual complexes and their integral affine structure.
This is based on a joint work with Morgan Brown and a work in progress wi
th Léonard Pille-Schneider.\n
LOCATION:https://researchseminars.org/talk/notts_ag/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Zucconi (Udine)
DTSTART;VALUE=DATE-TIME:20210218T100000Z
DTEND;VALUE=DATE-TIME:20210218T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/46
DESCRIPTION:Title: Fujita decomposition and Massey product for fibered varieties\nby Fr
ancesco Zucconi (Udine) as part of Online Nottingham algebraic geometry se
minar\n\n\nAbstract\nLet $f\\colon X \\to B$ be a semistable fibration whe
re $X$ is a smooth variety of dimension $n ≥ 2$ and $B$ is a smooth curv
e. We give an interpretation of the second Fujita decomposition of $f_∗\
\omega_{X/B}$ in terms of local systems of the relative 1-forms and of the
relative top forms. We show the existence of higher irrational pencils un
der natural hypothesis on local subsystems.\n
LOCATION:https://researchseminars.org/talk/notts_ag/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fatemeh Rezaee (Loughborough)
DTSTART;VALUE=DATE-TIME:20210304T100000Z
DTEND;VALUE=DATE-TIME:20210304T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/47
DESCRIPTION:Title: Wall-crossing does not induce MMP\nby Fatemeh Rezaee (Loughborough)
as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nI w
ill describe a new wall-crossing phenomenon of sheaves on the projective 3
-space that induces singularities that are not allowed in the sense of the
Minimal Model Program (MMP). Therefore\, it cannot be detected as an oper
ation in the MMP of the moduli space\, unlike the case for many surfaces.\
n
LOCATION:https://researchseminars.org/talk/notts_ag/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diane Maclagan (Warwick)
DTSTART;VALUE=DATE-TIME:20210311T130000Z
DTEND;VALUE=DATE-TIME:20210311T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/48
DESCRIPTION:Title: Toric and tropical Bertini theorems in arbitrary characteristic\nby
Diane Maclagan (Warwick) as part of Online Nottingham algebraic geometry s
eminar\n\n\nAbstract\nThe classical Bertini theorem on irreducibility when
intersecting by hyperplanes is a standard part of the algebraic geometry
toolkit. This was generalised recently\, in characteristic zero\, by Fuchs
\, Mantova\, and Zannier to a toric Bertini theorem for subvarieties of an
algebraic torus\, with hyperplanes replaced by subtori. I will discuss jo
int work with Gandini\, Hering\, Mohammadi\, Rajchgot\, Wheeler\, and Yu i
n which we give a different proof of this theorem that removes the charact
eristic assumption. An application is a tropical Bertini theorem.\n
LOCATION:https://researchseminars.org/talk/notts_ag/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Taro Sano (Kobe)
DTSTART;VALUE=DATE-TIME:20210318T100000Z
DTEND;VALUE=DATE-TIME:20210318T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/49
DESCRIPTION:Title: Construction of non-Kähler Calabi-Yau manifolds by log deformations
\nby Taro Sano (Kobe) as part of Online Nottingham algebraic geometry semi
nar\n\n\nAbstract\nCalabi-Yau manifolds (in the strict sense) form an impo
rtant class in the classification of algebraic varieties. One can also con
sider its generalisation by removing the projectivity assumption. It was p
reviously known that there are infinitely many topological types of non-K
ähler Calabi-Yau 3-folds. In this talk\, I will present construction of s
uch examples in higher dimensions by smoothing normal crossing varieties.
The key tools of the construction are some isomorphisms between general ra
tional elliptic surfaces which induce isomorphisms between Calabi-Yau mani
folds of Schoen type.\n
LOCATION:https://researchseminars.org/talk/notts_ag/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michał Kapustka (IMPAN and Stavanger)
DTSTART;VALUE=DATE-TIME:20210325T100000Z
DTEND;VALUE=DATE-TIME:20210325T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/50
DESCRIPTION:Title: Nikulin orbifolds\nby Michał Kapustka (IMPAN and Stavanger) as part
of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nThe theory
of K3 surfaces with symplectic involutions and their quotients is now a w
ell understood classical subject thanks to foundational works of Nikulin\,
and van Geemen and Sarti. In this talk we will try to develop an analogou
s theory in the context of hyperkahler fourfolds of K3${}^{[2]}$ type. Fir
st\, we will present a latttice theoretic classification of such fourfolds
which admit a symplectic involution. Then we will investigate the associa
ted quotients that we call Nikulin orbifolds. These are orbifolds which ad
mit a symplectic form on the smooth locus and hence are special cases of s
o called hyperkahler orbifolds. Finally\, we shall discuss families of Nik
ulin orbifolds and their deformations called hyperkahler orbifolds of Niku
lin type. As an application\, we will provide a description of the first k
nown example of a complete family of projective hyperkahler orbifolds. Thi
s is joint work with A. Garbagnati\, C. Camere and G. Kapustka.\n
LOCATION:https://researchseminars.org/talk/notts_ag/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiarui Fei (Shanghai Jiao Tong)
DTSTART;VALUE=DATE-TIME:20210401T120000Z
DTEND;VALUE=DATE-TIME:20210401T130000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/51
DESCRIPTION:Title: Tropical $F$-polynomials and Cluster Algebras\nby Jiarui Fei (Shangh
ai Jiao Tong) as part of Online Nottingham algebraic geometry seminar\n\n\
nAbstract\nThe representation-theoretic interpretations of $g$-vectors and
$F$-polynomials are two fundamental ingredients in the (additive) categor
ification of cluster algebras. We knew that the $g$-vectors are related to
the presentation spaces. We introduce the tropical $F$-polynomial $f_M$ o
f a quiver representation $M$\, and explain its interplay with the general
presentation for any finite-dimensional basic algebra. As a consequence\,
we give a presentation of the Newton polytope $N(M)$ of $M$. We propose a
n algorithm to determine the generic Newton polytopes\, and show it works
for path algebras. As an application\, we give a representation-theoretic
interpretation of Fock-Goncharov's cluster duality pairing. We also study
many combinatorial aspects of $N(M)$\, such as faces\, the dual fan and $1
$-skeleton. We conjecture that the coefficients of a cluster monomial corr
esponding to vertices are all $1$\, and the coefficients inside the Newton
polytope are saturated. We show the conjecture holds for acyclic cluster
algebras. We specialize the above general results to the cluster-finite al
gebras and the preprojective algebras of Dynkin type.\n
LOCATION:https://researchseminars.org/talk/notts_ag/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tim Gräfnitz (Hamburg)
DTSTART;VALUE=DATE-TIME:20210408T090000Z
DTEND;VALUE=DATE-TIME:20210408T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/52
DESCRIPTION:Title: Tropical correspondence for smooth del Pezzo log Calabi-Yau pairs\nb
y Tim Gräfnitz (Hamburg) as part of Online Nottingham algebraic geometry
seminar\n\n\nAbstract\nIn this talk I will present the main results of my
thesis\, a tropical correspondence theorem for log Calabi-Yau pairs $(X\,D
)$ consisting of a smooth del Pezzo surface $X$ of degree $\\ge3$ and a sm
ooth anticanonical divisor $D$. The easiest example of such a pair is $(\\
mathbb{P}^2\,E)$\, where $E$ is an elliptic curve. I will explain how the
genus zero logarithmic Gromov-Witten invariants of $X$ with maximal tangen
cy to $D$ are related to tropical curves in the dual intersection complex
of $(X\,D)$ and how they can be read off from the consistent wall structur
e appearing in the Gross-Siebert program. The novelty in this corresponden
ce is that $D$ is smooth but non-toric\, leading to log singularities in t
he toric degeneration that have to be resolved.\n
LOCATION:https://researchseminars.org/talk/notts_ag/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Nordstrom (Bath)
DTSTART;VALUE=DATE-TIME:20210415T120000Z
DTEND;VALUE=DATE-TIME:20210415T130000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/53
DESCRIPTION:Title: Extra-twisted connected sum $G_2$-manifolds\nby Johannes Nordstrom (
Bath) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstrac
t\nThe twisted connected sum construction of Kovalev produces many example
s of closed Riemannian $7$-manifolds with holonomy group $G_2$ (a special
class of Ricci-flat manifolds)\, starting from complex algebraic geometry
data like Fano $3$-folds. If the pieces admit automorphisms\, then adding
an extra twist to the construction yields examples with a wider variety of
topological features. I will describe the constructions and outline how o
ne can use them to produce example of e.g. closed $7$-manifolds with disco
nnected moduli space of holonomy $G_2$ metrics\, or pairs of $G_2$-manifol
ds that homeomorphic but not diffeomorphic. This is joint work with Diarmu
id Crowley and Sebastian Goette.\n
LOCATION:https://researchseminars.org/talk/notts_ag/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Wormleighton (Washington)
DTSTART;VALUE=DATE-TIME:20210422T120000Z
DTEND;VALUE=DATE-TIME:20210422T130000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/54
DESCRIPTION:Title: A tale of two widths: lattice and Gromov\nby Ben Wormleighton (Washi
ngton) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstra
ct\nTo a polytope $P$ whose facet normals are rational one can associate t
wo geometric objects: a symplectic toric domain $X_P$ and a polarised tori
c algebraic variety $Y_P$\, which can also be viewed as a potentially sing
ular symplectic space. A basic invariant of a symplectic manifold $X$ is i
ts Gromov width: essentially the size of the largest ball that can be 'sym
plectically' embedded in $X$. A conjecture of Averkov-Hofscheier-Nill prop
osed a combinatorial bound for the Gromov width of $Y_P$\, which I recentl
y verified in dimension two with Julian Chaidez. I’ll discuss the proof\
, which goes via various symplectic and algebraic invariants with winsome
combinatorial interpretations in the toric case. If there’s time\, I’l
l discuss ongoing work and new challenges for a similar result in higher d
imensions.\n
LOCATION:https://researchseminars.org/talk/notts_ag/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Wemyss (Glasgow)
DTSTART;VALUE=DATE-TIME:20210429T090000Z
DTEND;VALUE=DATE-TIME:20210429T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/55
DESCRIPTION:Title: Jacobi algebras on the two-loop quiver and applications\nby Michael
Wemyss (Glasgow) as part of Online Nottingham algebraic geometry seminar\n
\n\nAbstract\nI will explain recent progress on classifying finite dimensi
onal Jacobi algebras on the two loop quiver. This is a purely algebraic pr
oblem\, which at first sight is both seemingly hopeless and seemingly deta
ched from any form of reality or wider motivation. There are two surprises
: first\, the problem is not hopeless\, and parts of the answer are in fac
t very beautiful. Second\, this has immediate and surprising consequences
to both 3-fold flops and 3-fold divisor-to-curve contractions\, their curv
e invariants and their conjectural classification. This is joint work with
Gavin Brown.\n
LOCATION:https://researchseminars.org/talk/notts_ag/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Travis Mandel (Oklahoma)
DTSTART;VALUE=DATE-TIME:20210505T140000Z
DTEND;VALUE=DATE-TIME:20210505T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/56
DESCRIPTION:Title: Quantum theta bases for quantum cluster algebras\nby Travis Mandel (
Oklahoma) as part of Online Nottingham algebraic geometry seminar\n\n\nAbs
tract\nOne of the central goals in the study of cluster algebras is to bet
ter understand various canonical bases and positivity properties of the cl
uster algebras and their quantizations. Gross-Hacking-Keel-Kontsevich (GHK
K) applied ideas from mirror symmetry to construct so-called "theta bases"
for cluster algebras which satisfy all the desired positivity properties\
, thus proving several conjectures regarding cluster algebras. I will disc
uss joint work with Ben Davison in which we combine the techniques used by
GHKK with ideas from the DT theory of quiver representations to quantize
the GHKK construction\, thus producing quantum theta bases and proving the
desired quantum positivity properties.\n
LOCATION:https://researchseminars.org/talk/notts_ag/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roger Casals (UC Davis)
DTSTART;VALUE=DATE-TIME:20210513T150000Z
DTEND;VALUE=DATE-TIME:20210513T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/57
DESCRIPTION:Title: Positroid links and braid varieties\nby Roger Casals (UC Davis) as p
art of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nI will
discuss a class of affine algebraic varieties associated to positive braid
s\, their relation to open positroid strata in Grassmannians and their clu
ster structures. First\, I will introduce the objects of interest\, with t
he necessary ingredients\, and motivate the problem at hand. Then we will
discuss in detail how the study of a DG-algebra associated to certain link
s may allow us to better understand the algebraic (and cluster) geometry o
f Richardson and positroid varieties. Explicit examples of this interplay
between topology and algebraic geometry will be illustrated. At a more con
ceptual level\, the talk brings to bear insight from symplectic topology t
o better understand positroid varieties. This is joint work with E. Gorsky
\, M. Gorsky and J. Simental.\n
LOCATION:https://researchseminars.org/talk/notts_ag/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Markwig (Tübingen)
DTSTART;VALUE=DATE-TIME:20210520T090000Z
DTEND;VALUE=DATE-TIME:20210520T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/58
DESCRIPTION:Title: Counting bitangents of plane quartics - tropical\, real and arithmetic\nby Hannah Markwig (Tübingen) as part of Online Nottingham algebraic g
eometry seminar\n\n\nAbstract\nA smooth plane quartic defined over the com
plex numbers has precisely 28 bitangents. This result goes back to Pluecke
r. In the tropical world\,the situation is different. One can define equiv
alence classes of tropical bitangents of which there are 7\, and each has
4 lifts over the complex numbers. Over the reals\, we can have 4\, 8\, 16
or 28 bitangents. The avoidance locus of a real quartic is the set in the
dual plane consisting of all lines which do not meet the quartic. Every co
nnected component of the avoidance locus has precisely 4 bitangents in its
closure. For any field k of characteristic not equal to 2 and with a non-
Archimedean valuation which allows us to tropicalize\, we show that a trop
ical bitangent class of a quartic either has 0 or 4 lifts over k. This way
of grouping into sets of 4 which exists tropically and over the reals is
intimately connected: roughly\, tropical bitangent classes can be viewed a
s tropicalizations of closures of connected components of the avoidance lo
cus. Arithmetic counts offer a bridge connecting real and complex counts\,
and we investigate how tropical geometry can be used to study this bridge
.\n\nThis talk is based on joint work with Maria Angelica Cueto\, and on j
oint work in progress with Sam Payne and Kristin Shaw.\n
LOCATION:https://researchseminars.org/talk/notts_ag/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Helge Ruddat (Mainz)
DTSTART;VALUE=DATE-TIME:20210527T090000Z
DTEND;VALUE=DATE-TIME:20210527T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/59
DESCRIPTION:Title: Polytopes\, periods\, degenerations\nby Helge Ruddat (Mainz) as part
of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nA lattice
polytope describes a projective toric variety and a regular subdivision of
the polytope describes a flat degeneration of the toric variety. It is in
structive to deform the degenerating family in a way that makes the geomet
ry non-toric and produces a more interesting real torus fibration on the f
ibres of the degeneration. I am going to explain a simple formula that per
mits the easy computation of period integrals for the deformed families. T
his approach to periods doesn't require any differential equations and is
flexible enough to give proofs for strong results about Gross-Siebert's de
generating families obtained from wall structures. The talk is based on jo
int work with Bernd Siebert.\n
LOCATION:https://researchseminars.org/talk/notts_ag/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Ulirsch (Frankfurt)
DTSTART;VALUE=DATE-TIME:20210603T120000Z
DTEND;VALUE=DATE-TIME:20210603T130000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/60
DESCRIPTION:Title: Parabolic Higgs bundles on toric varieties\nby Martin Ulirsch (Frank
furt) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstrac
t\nIn this talk I will explain a version of Simpson’s non-abelian Hodge
correspondence on a toric variety X. There is a natural 1-1 correspondence
between stable parabolic Higgs bundles on X and irreducible representatio
ns of the fundamental group of the big torus. This correspondence reduces
to a correspondence between toric vector bundles and integral unitary repr
esentations in a suitable sense. In this story the spherical Tits building
will have a surprise appearance. The main result suggests (at least to me
) that there is a yet-to-be-discovered logarithmic incarnation of the non-
abelian Hodge correspondence.\n
LOCATION:https://researchseminars.org/talk/notts_ag/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yusuke Nakajima (Kyoto)
DTSTART;VALUE=DATE-TIME:20210624T090000Z
DTEND;VALUE=DATE-TIME:20210624T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/61
DESCRIPTION:Title: Combinatorial mutations and deformations of dimer models\nby Yusuke
Nakajima (Kyoto) as part of Online Nottingham algebraic geometry seminar\n
\n\nAbstract\nThe combinatorial mutation of a polytope was introduced in t
he context of the mirror symmetry of Fano manifolds for achieving the clas
sification problem. This operation makes a given polytope another one whil
e keeping some properties. In my talk\, I will consider the combinatorial
mutation of a polygon associated to a dimer model. A dimer model is a bipa
rtite graph on the real two-torus\, and the combinatorics of a dimer model
gives rise to a certain lattice polygon. Also\, a dimer model enjoys rich
information regarding toric geometry associated to that polygon. It is kn
own that for any lattice polygon P there is a dimer model whose associated
polygon coincides with P. Thus\, there also exists a dimer model giving t
he lattice polygon obtained as the combinatorial mutation of P. I will obs
erve the relationship between a dimer model giving a lattice polygon P and
the one giving the combinatorial mutation of P. In particular\, I introdu
ce the operation which I call the deformation of a dimer model\, and show
that this operation induces the combinatorial mutation of a polygon associ
ated to a dimer model. This talk is based on a joint work with A. Higashit
ani.\n
LOCATION:https://researchseminars.org/talk/notts_ag/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Escobar (Washington)
DTSTART;VALUE=DATE-TIME:20210617T120000Z
DTEND;VALUE=DATE-TIME:20210617T130000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/62
DESCRIPTION:Title: Wall-crossing phenomenon for Newton-Okounkov bodies\nby Laura Escoba
r (Washington) as part of Online Nottingham algebraic geometry seminar\n\n
\nAbstract\nA Newton-Okounkov body is a convex set associated to a project
ive variety\, equipped with a valuation. These bodies generalize the theor
y of Newton polytopes and the correspondence between polytopes and project
ive toric varieties. Work of Kaveh-Manon gives an explicit link between tr
opical geometry and Newton-Okounkov bodies. We use this link to describe a
wall-crossing phenomenon for Newton-Okounkov bodies. As an example\, we d
escribe wall-crossing formula in the case of the Grassmannian Gr(2\,m). Th
is is joint work with Megumi Harada.\n
LOCATION:https://researchseminars.org/talk/notts_ag/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne Lonjou (Paris-Saclay)
DTSTART;VALUE=DATE-TIME:20210610T090000Z
DTEND;VALUE=DATE-TIME:20210610T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/63
DESCRIPTION:Title: Action of Cremona groups on CAT(0) cube complexes\nby Anne Lonjou (P
aris-Saclay) as part of Online Nottingham algebraic geometry seminar\n\n\n
Abstract\nA key tool to study the plane Cremona group is its action on a h
yperbolic space. Sadly\, in higher rank such an action is not available. R
ecently\, in geometric group theory\, actions on CAT(0) cube complexes tur
ned out to be a powerful tool to study a large class of groups. In this ta
lk\, based on a common work with Christian Urech\, we will construct such
complexes on which Cremona groups of rank n act. Then\, we will see which
kind of results on these groups we can obtain.\n
LOCATION:https://researchseminars.org/talk/notts_ag/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro Montero (Valparaíso)
DTSTART;VALUE=DATE-TIME:20210701T130000Z
DTEND;VALUE=DATE-TIME:20210701T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/64
DESCRIPTION:Title: On the liftability of the automorphism group of smooth hypersurfaces of
the projective space\nby Pedro Montero (Valparaíso) as part of Online
Nottingham algebraic geometry seminar\n\n\nAbstract\nSmooth hypersurfaces
are classical objects in algebraic geometry since they are the simplest v
arieties one can define as they are given by only one equation. As such\,
they have been intensively studied and their geometry has shaped the devel
opment of classic and modern algebraic geometry. In this talk\, I will fir
st recall some fundamental results concerning the automorphism group of sm
ooth hypersurfaces of the projective space and then I will present some ne
w results obtained in a joint work with Victor Gonzalez-Aguilera and Alvar
o Liendo\, which are inspired by the classification groups which faithfull
y act on smooth cubic and quintic threefolds by Oguiso\, Wei and Yu. Final
ly\, I will discuss some perspectives and open problems that arise from th
is.\n
LOCATION:https://researchseminars.org/talk/notts_ag/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Galkin (PUC-Rio and HSE)
DTSTART;VALUE=DATE-TIME:20210715T120000Z
DTEND;VALUE=DATE-TIME:20210715T130000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/65
DESCRIPTION:Title: Graph potentials and combinatorial non-abelian Torelli\nby Sergey Ga
lkin (PUC-Rio and HSE) as part of Online Nottingham algebraic geometry sem
inar\n\n\nAbstract\nI will introduce graph potentials and discuss some of
their combinatorial aspects\, such as small resolution conjecture and comb
inatorial non-abelian Torelli theorem. The talk is based on the joint work
s with Pieter Belmans and Swarnava Mukhopadhyay.\n
LOCATION:https://researchseminars.org/talk/notts_ag/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ollie Clarke (Ghent and Bristol)
DTSTART;VALUE=DATE-TIME:20210812T090000Z
DTEND;VALUE=DATE-TIME:20210812T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/66
DESCRIPTION:Title: Combinatorial mutations and block diagonal polytopes\nby Ollie Clark
e (Ghent and Bristol) as part of Online Nottingham algebraic geometry semi
nar\n\n\nAbstract\nMatching fields were introduced by Sturmfels and Zelevi
nsky to study certain Newton polytopes and more recently have been shown t
o give rise to toric degenerations of various families of varieties. Whene
ver a matching field gives rise to a toric degeneration of the Grassmannia
n\, the polytope of the associated toric variety coincides with the matchi
ng field polytope. In this talk I will describe combinatorial mutations of
matching field polytopes. We will explore properties of polytopes which a
re preserved by mutation\, and we will see that property of giving rise to
a toric degeneration is preserved by mutations. This gives us an easy way
to generate new families of toric degenerations of the Grassmannian from
old. This talk is based on joint work with Akihiro Higashitani and Fatemeh
Mohammadi.\n
LOCATION:https://researchseminars.org/talk/notts_ag/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:DongSeon Hwang (Ajou)
DTSTART;VALUE=DATE-TIME:20210826T090000Z
DTEND;VALUE=DATE-TIME:20210826T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/67
DESCRIPTION:Title: Cascades of singular rational surfaces of Picard number one\nby Dong
Seon Hwang (Ajou) as part of Online Nottingham algebraic geometry seminar\
n\n\nAbstract\nI will introduce the notion of cascades of singular rationa
l surfaces of Picard number one\, which consists of a sequence of special
birational morphisms\, and then discuss some applications in the toric cas
e\, Fano case\, and (log) general type case. The latter application is clo
sely related to algebraic Montgomery-Yang problem\, conjectured by Kollár
.\n
LOCATION:https://researchseminars.org/talk/notts_ag/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chengxi Wang (UCLA)
DTSTART;VALUE=DATE-TIME:20210708T140000Z
DTEND;VALUE=DATE-TIME:20210708T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/68
DESCRIPTION:Title: Varieties of general type with small volume\nby Chengxi Wang (UCLA)
as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nBy
Hacon-McKernan\, Takayama\, and Tsuji\, there is a constant r_n such that
for every r at least r_n\, the r-canonical map of every n-dimensional vari
ety of general type is birational. In this talk\, we show that r_n must gr
ow faster than any polynomial in n\, by giving examples of general type wi
th small volume in high dimensions. In particular\, we construct a klt n-f
old with ample canonical class whose volume is less than 1/2^(2^n). The kl
t examples should be close to optimal. This is joint work with Burt Totaro
.\n
LOCATION:https://researchseminars.org/talk/notts_ag/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kristin DeVleming (UCSD)
DTSTART;VALUE=DATE-TIME:20210722T150000Z
DTEND;VALUE=DATE-TIME:20210722T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/69
DESCRIPTION:Title: K moduli of quartic K3 surfaces\nby Kristin DeVleming (UCSD) as part
of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nWe will di
scuss a family of compactifications of moduli spaces of log Fano pairs com
ing from K-stability\, and discuss an application to moduli of quartic K3
surfaces\, with a focus on the locus of hyperelliptic K3s that arise as do
uble covers of $\\mathbb{P}^1\\times\\mathbb{P}^1$ branched over a $(4\,4)
$ curve. We will show that K-stability provides a natural way to interpol
ate between the GIT moduli space and the Baily-Borel compactification and
will relate this interpolation to VGIT wall crossings. This is joint work
with Kenny Ascher and Yuchen Liu.\n
LOCATION:https://researchseminars.org/talk/notts_ag/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthias Nickel (Frankfurt)
DTSTART;VALUE=DATE-TIME:20210729T130000Z
DTEND;VALUE=DATE-TIME:20210729T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/70
DESCRIPTION:Title: Local positivity and effective Diophantine approximation\nby Matthia
s Nickel (Frankfurt) as part of Online Nottingham algebraic geometry semin
ar\n\n\nAbstract\nIn this talk I will discuss a new approach to prove effe
ctive results in Diophantine approximation relying on lower bounds of Sesh
adri constants. I will then show how to use it to prove an effective theor
em on the simultaneous approximation of two algebraic numbers satisfying a
n algebraic equation.\n
LOCATION:https://researchseminars.org/talk/notts_ag/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dhruv Ranganathan (Cambridge)
DTSTART;VALUE=DATE-TIME:20210805T120000Z
DTEND;VALUE=DATE-TIME:20210805T130000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/71
DESCRIPTION:Title: Toric contact cycles in the moduli space of curves\nby Dhruv Rangana
than (Cambridge) as part of Online Nottingham algebraic geometry seminar\n
\n\nAbstract\nThe toric contact cycles are loci in the moduli space of cur
ves that parameterize those curves that admit a morphism to a fixed toric
variety\, with prescribed tangency data with the toric boundary. The cycle
s are the fundamental building blocks in higher genus logarithmic Gromov-W
itten theory and are higher dimensional analogues of the double ramificati
on cycles\, which have been studied intensely in the last decade. In recen
t work\, Sam Molcho (ETH) and I proved that these cycles lie in the tautol
ogical part of the Chow ring of the moduli space of curves. A lesson I lea
rned from this project\, and earlier work with Navid Nabijou (Cambridge)\,
is that it can be quite profitable to blend Fulton’s analysis of blowup
s and strict transforms with logarithmic Gromov-Witten theory and its virt
ual class. I’ll try to give a sense of the basic geometric phenomena\, a
nd point to some other places where they come up.\n
LOCATION:https://researchseminars.org/talk/notts_ag/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Addington (Oregon)
DTSTART;VALUE=DATE-TIME:20210923T150000Z
DTEND;VALUE=DATE-TIME:20210923T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/73
DESCRIPTION:Title: Hodge number are not derived invariants in positive characteristic\n
by Nicolas Addington (Oregon) as part of Online Nottingham algebraic geome
try seminar\n\n\nAbstract\nDerived categories of coherent sheaves behave a
lot like cohomology\, so it's natural to ask which cohomological invarian
ts are preserved by derived equivalences. After discussing the motivation
and previous results\, I'll present a derived equivalence between Calabi-Y
au 3-folds in characteristic 3 with different Hodge numbers\; this couldn'
t happen in characteristic 0. The project has a substantial computer algeb
ra component which I'll spend some time on.\n
LOCATION:https://researchseminars.org/talk/notts_ag/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julius Giesler (Tübingen)
DTSTART;VALUE=DATE-TIME:20210930T090000Z
DTEND;VALUE=DATE-TIME:20210930T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/74
DESCRIPTION:Title: Kanev and Todorov type surfaces in toric 3-folds\nby Julius Giesler
(Tübingen) as part of Online Nottingham algebraic geometry seminar\n\n\nA
bstract\nIn this talk we show at the example of some surfaces of general t
ype\, so called Kanev and Todorov type surfaces\, how to construct minimal
and canonical models of hypersurfaces in toric varieties. We relate the p
lurigenera and the Kodaira dimension of the hypersurfaces to a special pol
ytope\, known as the Fine interior. Then we study singularities of the can
onical models of Kanev/Todorov type surfaces via toric geometry\, degenera
tions of these surfaces and investigate some Hodge theoretic consequences.
\n
LOCATION:https://researchseminars.org/talk/notts_ag/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Sophie Kaloghiros (Brunel)
DTSTART;VALUE=DATE-TIME:20211021T090000Z
DTEND;VALUE=DATE-TIME:20211021T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/76
DESCRIPTION:Title: The Calabi problem for Fano 3-folds\nby Anne-Sophie Kaloghiros (Brun
el) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\
nI will discuss progress on the Calabi problem for Fano 3-folds. The 105 d
eformation families of smooth Fano 3-folds\, were classified by Iskovskikh
\, Mori and Mukai. We determine whether or not the general member of each
of these 105 families admits a Kähler-Einstein metric. In some cases\, it
is known that while the general member of the family admits a Kähler-Ein
stein metric\, some other member does not. This leads to the problem of de
termining which members of a deformation family admit a Kähler-Einstein m
etric when the general member does. This is accomplished for most of the f
amilies\, and I will present a conjectural picture for some of the remaini
ng families. This is a joint project with Carolina Araujo\, Ana-Maria Cast
ravet\, Ivan Cheltsov\, Kento Fujita\, Jesus Martinez-Garcia\, Constantin
Shramov\, Hendrik Süss and Nivedita Viswanathan.\n
LOCATION:https://researchseminars.org/talk/notts_ag/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hunter Spink (Stanford)
DTSTART;VALUE=DATE-TIME:20210902T150000Z
DTEND;VALUE=DATE-TIME:20210902T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/77
DESCRIPTION:Title: Log-concavity of matroid h-vectors and mixed Eulerian numbers\nby Hu
nter Spink (Stanford) as part of Online Nottingham algebraic geometry semi
nar\n\n\nAbstract\n(Joint with Andrew Berget and Dennis Tseng) For any mat
roid $M$\, we compute the Tutte polynomial using the mixed intersection nu
mbers of certain tautological classes in the combinatorial Chow ring arisi
ng from Grassmannians. Using mixed Hodge-Riemann relations\, we deduce a s
trengthening of the log-concavity of the h-vector of a matroid complex\, i
mproving on an old conjecture of Dawson that was resolved contemporaneousl
y by Ardila\, Denham\, and Huh.\n
LOCATION:https://researchseminars.org/talk/notts_ag/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Nikolaev (Sheffield)
DTSTART;VALUE=DATE-TIME:20210916T130000Z
DTEND;VALUE=DATE-TIME:20210916T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/78
DESCRIPTION:Title: Abelianisation of Meromorphic Connections\nby Nikita Nikolaev (Sheff
ield) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstrac
t\nThere is a natural 1-1 correspondence between Higgs bundles on a compac
t complex curve and line bundles on an appropriate branched cover. This ab
elianisation process goes through the direct image functor and it has been
fruitful in addressing a variety of problems relating to bundles on curve
s. We extend this abelianisation correspondence from Higgs bundles to flat
bundles. This generalisation involves choosing a certain graph which tran
slates to cohomology as a natural cocycle that exhibits a local deformatio
n of the direct image functor. Furthermore\, our abelianisation correspond
ence extends to lambda-connections and recovers the abelianisation of Higg
s bundles as lambda goes to 0. Based in part on joint work in progress wit
h Marco Gualtieri.\n
LOCATION:https://researchseminars.org/talk/notts_ag/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Brini (Sheffield)
DTSTART;VALUE=DATE-TIME:20211028T090000Z
DTEND;VALUE=DATE-TIME:20211028T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/79
DESCRIPTION:Title: Quantum geometry of log-Calabi Yau surfaces\nby Andrea Brini (Sheffi
eld) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract
\nA log-Calabi Yau surface with maximal boundary\, or Looijenga pair\, is
a pair (X\,D) with X a smooth complex projective surface and D a singular
anticanonical divisor in X. I will introduce a series of physics-motivated
correspondences relating five different classes of enumerative invariants
of the pair (X\,D):\n * the log Gromov--Witten theory of (X\,D)\,\n * the
Gromov--Witten theory of X twisted by the sum of the dual line bundles to
the irreducible components of D\,\n * the open Gromov--Witten theory of s
pecial Lagrangians in a toric Calabi--Yau 3-fold determined by (X\,D)\,\n
* the Donaldson--Thomas theory of a symmetric quiver specified by (X\,D)\,
and\n * a class of BPS invariants considered in different contexts by Kle
mm--Pandharipande\, Ionel--Parker\, and Labastida--Marino--Ooguri--Vafa.\n
I will also show how the problem of computing all these invariants is clos
ed-form solvable. Based on joint works with P. Bousseau\, M. van Garrel\,
and Y. Schueler.\n
LOCATION:https://researchseminars.org/talk/notts_ag/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diana Torres Valencia (University of Pamplona)
DTSTART;VALUE=DATE-TIME:20211111T130000Z
DTEND;VALUE=DATE-TIME:20211111T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/80
DESCRIPTION:Title: CANCELLED - On accumulation points of volumes of stable surfaces with on
e cyclic quotient singularity\nby Diana Torres Valencia (University of
Pamplona) as part of Online Nottingham algebraic geometry seminar\n\n\nAb
stract\nThe set of volumes of stable surfaces does have accumulation point
s. I will introduce this phenomenon for surfaces with one cyclic quotient
singularity towards answering the question under which conditions we can s
till have boundedness. Effective bounds allow listing singularities that m
ight appear on a stable surface after fixing its invariants. I will show o
ptimal inequalities for stable surfaces with one cyclic quotient singulari
ty\, which can be used to prove boundedness under certain conditions. I al
so will introduce the notion of generalized T-singularity\, which is a nat
ural generalization of the well-known T-singularities. I will show how the
accumulation points of volumes of stable surfaces with one generalized T-
singularity are formed.\n
LOCATION:https://researchseminars.org/talk/notts_ag/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Ros Camacho (Cardiff)
DTSTART;VALUE=DATE-TIME:20211125T100000Z
DTEND;VALUE=DATE-TIME:20211125T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/81
DESCRIPTION:Title: Computational aspects in orbifold equivalence\nby Ana Ros Camacho (C
ardiff) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstr
act\nLandau-Ginzburg models are a family of physical theories described by
some polynomial (or "potential") characterized by having an isolated sing
ularity at the origin. Often appearing in mirror-symmetric phenomena\, the
y can be collected in higher categories with nice properties that allow di
rect computations. In this context\, it is possible to introduce an equiva
lence relation between two different potentials called "orbifold equivalen
ce". We will present some recent examples of this equivalence\, and discus
s the computational challenges posed by the search of new ones. Joint work
with Timo Kluck.\n
LOCATION:https://researchseminars.org/talk/notts_ag/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eleonore Faber (Leeds)
DTSTART;VALUE=DATE-TIME:20211208T140000Z
DTEND;VALUE=DATE-TIME:20211208T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/82
DESCRIPTION:Title: Matrix factorizations for discriminants of pseudo-reflection groups\
nby Eleonore Faber (Leeds) as part of Online Nottingham algebraic geometry
seminar\n\n\nAbstract\nIn this talk we will give an introduction to the M
cKay correspondence for complex reflection groups (joint work with Ragnar
Buchweitz and Colin Ingalls)\, and then show how this allows to identify c
ertain matrix factorizations of the discriminants of these reflection grou
ps. We will in particular consider the family of pseudo-reflection groups
G(r\,p\,n)\, for which one can explicitly determine matrix factorizations\
, using higher Specht polynomials (work in progress with Colin Ingalls\, S
imon May\, and Marco Talarico).\n
LOCATION:https://researchseminars.org/talk/notts_ag/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arina Voorhaar (Geneva)
DTSTART;VALUE=DATE-TIME:20220113T130000Z
DTEND;VALUE=DATE-TIME:20220113T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/83
DESCRIPTION:Title: On the Newton Polytope of the Morse Discriminant\nby Arina Voorhaar
(Geneva) as part of Online Nottingham algebraic geometry seminar\n\n\nAbst
ract\nA famous classical result by Gelfand\, Kapranov and Zelevinsky provi
des a combinatorial description of the vertices of the Newton polytope of
the $A$-discriminant (the closure of the set of all non-smooth hypersurfac
es defined by polynomials with the given support $A$). Namely\, it gives a
surjection from the set of all convex triangulations of the convex hull o
f the set $A$ with vertices in $A$ (or\, equivalently\, the set of all pos
sible combinatorial types of smooth tropical hypersurfaces defined by trop
ical polynomials with support $A$) onto the set of vertices of this Newton
polytope. In my talk\, I will discuss a similar problem for the Morse dis
criminant — the closure of the set of all polynomials with the given sup
port $A$ which are non-Morse if viewed as polynomial maps. Namely\, for a
$1$-dimensional support set $A$\, there is a surjection from the set of al
l possible combinatorial types of so-called Morse tropical polynomials ont
o the vertices of the Newton polytope of the Morse discriminant.\n
LOCATION:https://researchseminars.org/talk/notts_ag/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alastair Craw (Bath)
DTSTART;VALUE=DATE-TIME:20211014T100000Z
DTEND;VALUE=DATE-TIME:20211014T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/84
DESCRIPTION:Title: Hyperpolygon spaces: beyond the movable cone\nby Alastair Craw (Bath
) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nF
or $n\\geq 4$\, the hyperpolygon spaces are a collection of Nakajima quive
r varieties in dimension $2n-6$ that have been a useful testing ground for
conjectures on conical symplectic varieties. I'll describe joint work in
progress with Gwyn Bellamy\, Steven Rayan\, Travis Schedler and Hartmut We
iss in which we describe completely the birational geometry of these space
s. The case $n=5$ recovers a well-known finite quotient singularity in dim
ension four\, and allows us to provide a uniform construction of all 81 pr
ojective crepant resolutions studied in previous work of Donten-Bury--Wi\\
'{s}niewski. I'll also explain the title of the talk by giving a geometric
interpretation of the components of the stability parameter even when it
doesn't lie in the positive orthant.\n
LOCATION:https://researchseminars.org/talk/notts_ag/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Coates (Imperial)
DTSTART;VALUE=DATE-TIME:20211007T090000Z
DTEND;VALUE=DATE-TIME:20211007T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/85
DESCRIPTION:Title: Rigid maximally mutable Laurent polynomials\nby Tom Coates (Imperial
) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nI
will describe a class of Laurent polynomials which conjecturally correspo
nds under mirror symmetry to Fano varieties\, in any dimension\, with mild
singularities. This is joint work with Alexander Kasprzyk\, Giuseppe Pitt
on\, and Ketil Tveiten.\n
LOCATION:https://researchseminars.org/talk/notts_ag/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fatemeh Mohammadi (Ghent)
DTSTART;VALUE=DATE-TIME:20211104T100000Z
DTEND;VALUE=DATE-TIME:20211104T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/86
DESCRIPTION:Title: CANCELLED - Matroid stratifications of hypergraph determinantal varietie
s and their realization spaces\nby Fatemeh Mohammadi (Ghent) as part o
f Online Nottingham algebraic geometry seminar\n\n\nAbstract\nI will provi
de an introductory talk to hypergraph determinantal varieties from project
ive geometry and matroid theory perspectives. I describe their decompositi
ons into matroid varieties. Matroids varieties in general can be reducible
with arbitrary singularities by the Mnëv-Sturmfels universality theorem.
Our goal is to provide families of matroids whose corresponding varieties
are irreducible\, and use them to find minimal irreducible decompositions
for hypergraph varieties. The main themes of the talk are:\n1) giving a d
ecomposition for each hypergraph variety\;\n2) identifying each component
in the decomposition as a matroid variety\; and\n3) understanding the irre
ducibility of these matroid varieties and their realizability.\nI will not
assume any prior knowledge of algebraic\, polyhedral\, or incidence geome
try\, and I will try to make the talk accessible to people with a broad ra
nge of backgrounds. The talk is based on joint work with Oliver Clarke\, K
evin Grace\, and Harshit Motwani.\n
LOCATION:https://researchseminars.org/talk/notts_ag/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Anderson (Queen Mary)
DTSTART;VALUE=DATE-TIME:20211118T130000Z
DTEND;VALUE=DATE-TIME:20211118T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/87
DESCRIPTION:Title: Paving tropical ideals\nby Nicholas Anderson (Queen Mary) as part of
Online Nottingham algebraic geometry seminar\n\n\nAbstract\nTropical geom
etry is a powerful tool in algebraic geometry\, which offers a multitude o
f combinatorial approaches to studying algebraic varieties. This talk will
focus on the recent development of tropical commutative algebra by Diane
Maclagan and Felipe Rincon. The central object of study is the “tropical
Ideal\,” which generalizes the structure of polynomial ideals over fiel
ds to be suitable for study in the setting of tropical geometry\, that is\
, in polynomial semirings over semifields. All polynomial ideals over a fi
eld can be associated to a “realizable” tropical ideal\, and it is a n
on-trivial fact that “non-realizable” tropical ideals exist. In this t
alk\, I will demonstrate how the combinatorics of matroid theory allows us
to easily generate a subclass of tropical ideals\, called paving tropical
ideals\, which in turn allows us to prove that most zero-dimensional trop
ical ideals are not realizable.\n
LOCATION:https://researchseminars.org/talk/notts_ag/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florin Ambro (Simion Stoilow)
DTSTART;VALUE=DATE-TIME:20220127T100000Z
DTEND;VALUE=DATE-TIME:20220127T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/88
DESCRIPTION:Title: On Seshadri constants\nby Florin Ambro (Simion Stoilow) as part of O
nline Nottingham algebraic geometry seminar\n\n\nAbstract\nThe Seshadri co
nstant of a polarized variety $(X\,L)$ at a point $x$ measures how positiv
e is the polarization $L$ at $x$. If $x$ is very general\, the Seshadri co
nstant does not depend on $x$\, and captures global information on $X$. In
spired by ideas from the Geometry of Numbers\, we introduce in this talk s
uccessive Seshadri minima\, such that the first one is the Seshadri consta
nt at a point\, and the last one is the width of the polarization at the p
oint. Assuming the point is very general\, we obtain two results: a) the
product of the successive Seshadri minima is proportional to the volume of
the polarization\; b) if $X$ is toric\, the $i$-th successive Seshadri co
nstant is proportional to the $i$-th successive minima of a suitable $0$-s
ymmetric convex body. Based on joint work with Atsushi Ito.\n
LOCATION:https://researchseminars.org/talk/notts_ag/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marvin Hahn (Sorbonne)
DTSTART;VALUE=DATE-TIME:20220120T100000Z
DTEND;VALUE=DATE-TIME:20220120T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/89
DESCRIPTION:Title: The tropical geometry of monotone Hurwitz numbers\nby Marvin Hahn (S
orbonne) as part of Online Nottingham algebraic geometry seminar\n\n\nAbst
ract\nHurwitz numbers are important enumerative invariants in algebraic ge
ometry. They count branched maps between Riemann surfaces. Equivalently\,
they enumerate factorizations in the symmetric group. Hurwitz numbers were
introduced in the 1890s by Adolf Hurwitz and became central objects of en
umerative algebraic geometry in the 1990s through close connections with t
he so-called Gromov-Witten theory. This interplay between Hurwitz and Grom
ov-Witten theory is an active field of research and led to\, among other t
hings\, the celebrated ELSV formula. In the last decade\, many variants of
Hurwitz numbers have been introduced and studied. In particular\, the que
stion of connections between these variants of Hurwitz numbers and Gromov-
Witten theory is of great interest. So-called monotone Hurwitz numbers \,
which originate from the theory of random matrices\, are among the most st
udied variants of Hurwitz numbers. This talk is a progress report of our l
arger program in which we study the connections between monotone Hurwitz n
umbers and Gromov-Witten theory by combinatorial methods of tropical geome
try\, and whose long-term goal is a proof of the still open conjecture of
an ELSV - type formula for double monotone Hurwitz numbers. The talk is ba
sed in part on joint work with Reinier Kramer and Danilo Lewanski.\n
LOCATION:https://researchseminars.org/talk/notts_ag/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wendelin Lutz (Imperial)
DTSTART;VALUE=DATE-TIME:20220203T100000Z
DTEND;VALUE=DATE-TIME:20220203T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/90
DESCRIPTION:Title: A geometric proof of the classification of T-polygons\nby Wendelin L
utz (Imperial) as part of Online Nottingham algebraic geometry seminar\n\n
\nAbstract\nOne formulation of mirror symmetry predicts (omitting a few ad
jectives) a one-to-one correspondence between equivalence classes of latti
ce polygons and deformation families of del Pezzo surfaces. Lattice polygo
ns that correspond to smooth Del Pezzo surfaces are called T-polygons and
have been classified by Kasprzyk-Nill-Prince using combinatorial methods\,
thereby verifying the conjecture in the smooth case. I will give a new ge
ometric proof of their classification result.\n
LOCATION:https://researchseminars.org/talk/notts_ag/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qaasim Shafi (Imperial)
DTSTART;VALUE=DATE-TIME:20220303T100000Z
DTEND;VALUE=DATE-TIME:20220303T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/91
DESCRIPTION:Title: Logarithmic Toric Quasimaps\nby Qaasim Shafi (Imperial) as part of O
nline Nottingham algebraic geometry seminar\n\n\nAbstract\nQuasimaps provi
de an alternate curve counting system to Gromov-Witten theory\, related by
wall-crossing formulas. Relative (or logarithmic) Gromov-Witten theory ha
s proved useful for constructions in mirror symmetry\, as well as for dete
rmining ordinary Gromov-Witten invariants via the degeneration formula. I
’ll discuss how to build a theory of logarithmic quasimaps in the toric
case\, some restrictions\, and why one might want to do so.\n
LOCATION:https://researchseminars.org/talk/notts_ag/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ananyo Dan (Sheffield)
DTSTART;VALUE=DATE-TIME:20220210T100000Z
DTEND;VALUE=DATE-TIME:20220210T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/92
DESCRIPTION:Title: McKay correspondence for isolated Gorenstein singularities\nby Anany
o Dan (Sheffield) as part of Online Nottingham algebraic geometry seminar\
n\n\nAbstract\nThe McKay correspondence is a (natural) correspondence betw
een the (non-trivial) irreducible representations of a finite subgroup G o
f SL(2\,C) and the irreducible components of the exceptional divisor of a
minimal resolution of the associated quotient singularity C^2//G. A geomet
ric construction for this correspondence was given by González-Sprinberg
and Verdier\, who showed that the two sets also correspond bijectively to
the set of indecomposable reflexive modules on the quotient singularity. T
his was generalised to higher dimensional quotient singularities (i.e.\, q
uotient of C^n by a finite subgroup of SL(n\,C)) by Ito-Reid\, where the a
bove sets were substituted by certain smaller subsets. It was further gene
ralised to more general quotient singularities by Bridgeland-King-Reid\, I
yama-Wemyss and others\, using the language of derived categories. In this
talk\, I will survey past results and discuss what happens for the isolat
ed Gorenstein singularities case (not necessarily a quotient singularity).
If time permits\, I will discuss applications to Matrix factorization. Th
is is joint work in progress with J. F. de Bobadilla and A. Romano-Velazqu
ez.\n
LOCATION:https://researchseminars.org/talk/notts_ag/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jarosław Buczyński (Polish Academy of Sciences)
DTSTART;VALUE=DATE-TIME:20220224T100000Z
DTEND;VALUE=DATE-TIME:20220224T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/93
DESCRIPTION:Title: Fujita vanishing\, sufficiently ample line bundles\, and cactus varietie
s\nby Jarosław Buczyński (Polish Academy of Sciences) as part of Onl
ine Nottingham algebraic geometry seminar\n\n\nAbstract\nFor a fixed proje
ctive manifold X\, we say that a property P(L) (where L is a line bundle o
n X) is satisfied by sufficiently ample line bundles if there exists a lin
e bundle M on X such that P(L) hold for any L with L-M ample. I will discu
ss which properties of line bundles are satisfied by the sufficiently ampl
e line bundles - for example\, can you figure out before the talk\, whethe
r a sufficiently ample line bundle must be very ample? A basic ingredient
used to study this concept is Fujita's vanishing theorem\, which is an ana
logue of Serre's vanishing for sufficiently ample line bundles. At the end
of the talk I will define cactus varieties (an analogue of secant varieti
es) and sketch a proof that cactus varieties to sufficiently ample embeddi
ngs of X are (set-theoretically) defined by minors of matrices with linear
entries. The topic is closely related to conjectures of Eisenbud-Koh-Stil
lman (for curves) and Sidman-Smith (for any varieties). The new ingredient
s are based on a joint work in preparation with Weronika Buczyńska and Ł
ucja Farnik.\n
LOCATION:https://researchseminars.org/talk/notts_ag/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessio Borzì (Warwick)
DTSTART;VALUE=DATE-TIME:20220317T100000Z
DTEND;VALUE=DATE-TIME:20220317T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/94
DESCRIPTION:Title: Weierstrass sets on finite graphs\nby Alessio Borzì (Warwick) as pa
rt of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nWeiestra
ss points and Weierstrass semigroups are classical objects of study in Alg
ebraic Geometry. The problem of determining which semigroups arise as Weie
rstrass semigroups of a curve goes back to Hurwitz in 1893. After the adve
nt of tropical geometry\, a divisor theory on graphs was developed by Bake
r and Norine\, and later extended to metric graphs (namely\, abstract trop
ical curves) by Gathmann and Kerber\, and Mikhalkin and Zharkov. In this t
alk we present two natural tropical analogues of Weierstrass semigroups on
graphs\, called rank and functional Weierstrass sets\, first appeared in
a work of Kang\, Matthews and Peachey. We present some results on these tw
o objects and their interplay.\n
LOCATION:https://researchseminars.org/talk/notts_ag/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Egor Yasinsky (École Polytechnique)
DTSTART;VALUE=DATE-TIME:20220324T110000Z
DTEND;VALUE=DATE-TIME:20220324T120000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/95
DESCRIPTION:Title: Birational involutions of the projective plane\nby Egor Yasinsky (É
cole Polytechnique) as part of Online Nottingham algebraic geometry semina
r\n\n\nAbstract\nBirational involutions of the projective plane (or\, equi
valently\, automorphisms of the field of rational functions in two variabl
es of order 2) were studied already by the Italian school of algebraic geo
metry — Bertini\, Castelnuovo\, and Enriques. However\, their explicit a
nd complete description was obtained by Beauville and Bayle only in 2000 a
nd only in the case of a complex projective plane. It turns out that for p
lanes over algebraically non-closed fields the situation is much more comp
licated. In the first part of the talk\, I will review what is known about
birational involutions of projective planes over various fields. In the s
econd part\, I will talk about the joint work with I. Cheltsov\, F. Mangol
t and S. Zimmerman\, in which we classified birational involutions of the
real projective plane.\n
LOCATION:https://researchseminars.org/talk/notts_ag/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Franco Rota (Glasgow)
DTSTART;VALUE=DATE-TIME:20220331T090000Z
DTEND;VALUE=DATE-TIME:20220331T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/96
DESCRIPTION:Title: Full exceptional collection for anticanonical log del Pezzo surfaces
\nby Franco Rota (Glasgow) as part of Online Nottingham algebraic geometry
seminar\n\n\nAbstract\nThe homological mirror symmetry conjecture predict
s a correspondence between the derived category of coherent sheaves of a v
ariety and the symplectic data (packaged in the Fukaya category) of its mi
rror object. Motivated by this\, we construct exceptional collections for
(the smooth stacks associated with) a family of log del Pezzo surfaces kno
wn as the Johnson-Kollar series. These surfaces have quotient\, non-Gorens
tein\, singularities. Thus\, our computation will include on the one hand
an application of the special McKay correspondence\, and on the other the
study of their minimal resolutions\, which are birational to a degree 2 de
l Pezzo surface. This is all joint work with Giulia Gugiatti.\n
LOCATION:https://researchseminars.org/talk/notts_ag/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Hicks (Edinburgh)
DTSTART;VALUE=DATE-TIME:20220407T083000Z
DTEND;VALUE=DATE-TIME:20220407T090000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/97
DESCRIPTION:Title: Mirror Symmetry and Lagrangian torus fibrations\nby Jeff Hicks (Edin
burgh) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstra
ct\nMirror symmetry is a predicted equivalence between certain aspects of
algebraic geometry and symplectic geometry. The Strominger–Yau–Zaslow
conjecture proposes that this equivalence appears on pairs of algebraic an
d symplectic spaces which have dual torus fibrations. In this pretalk\, we
look at a first example: the complex torus which is fibered by real tori\
, and the cotangent bundle of the real torus. We'll see how both geometrie
s can be related to affine geometry on real n-dimensional space.\n
LOCATION:https://researchseminars.org/talk/notts_ag/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Hicks (Edinburgh)
DTSTART;VALUE=DATE-TIME:20220407T090000Z
DTEND;VALUE=DATE-TIME:20220407T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/98
DESCRIPTION:Title: Realizing tropical curves via mirror symmetry\nby Jeff Hicks (Edinbu
rgh) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract
\nThe tropicalization map associates to each curve in the algebraic n-toru
s a piecewise linear object (tropical curve) in real n-dimensional space.
Given a tropical curve\, a natural question is if it can arise as the trop
icalization of some algebraic curve. If this is the case we say that the t
ropical curve is realizable. Determining good realizability criteria for t
ropical curves remains an important part of tropical geometry since Mikhal
kin provided examples of non-realizable tropical curves. We explore the fo
llowing strategy for realizing tropical curves:\n(1) Produce a Lagrangian
submanifold of the cotangent bundle of the torus whose moment map projecti
on approximates the tropical curve\;\n(2) Use homological mirror symmetry
to obtain a mirror algebraic sheaf\;\n(3) Show that the tropicalization of
the support of this sheaf is the original tropical curve.\nWe will give f
ull answers to (1) and (3)\, and explain why (2) is fairly subtle. As appl
ications\, we will obtain some new and known realizability statements for
tropical curves.\n
LOCATION:https://researchseminars.org/talk/notts_ag/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nivedita Viswanathan (Loughborough)
DTSTART;VALUE=DATE-TIME:20220421T090000Z
DTEND;VALUE=DATE-TIME:20220421T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/99
DESCRIPTION:Title: On K-stability of some singular del Pezzo surfaces\nby Nivedita Visw
anathan (Loughborough) as part of Online Nottingham algebraic geometry sem
inar\n\n\nAbstract\nThere has been a lot of development recently in unders
tanding the existence of Kahler-Einstein metrics on Fano manifolds due to
the Yau-Tian-Donaldson conjecture\, which gives us a way of looking at thi
s problem in terms of the notion of K-stability. In particular\, this prob
lem is solved in totality for smooth del Pezzo surfaces by Tian. For del P
ezzo surfaces with quotient singularities\, there are partial results. In
this talk\, we will consider singular del Pezzo surfaces of indices 2 and
3\, which are quasi-smooth\, well-formed hypersurfaces in weighted project
ive space\, and understand what we can say about their K-stability. This i
s joint work with In-Kyun Kim and Joonyeong Won.\n
LOCATION:https://researchseminars.org/talk/notts_ag/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zakarias Sjöström Dyrefelt (Aarhus-AIAS)
DTSTART;VALUE=DATE-TIME:20220414T090000Z
DTEND;VALUE=DATE-TIME:20220414T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/100
DESCRIPTION:Title: Constant scalar curvature and Kähler manifolds with nef canonical bund
le\nby Zakarias Sjöström Dyrefelt (Aarhus-AIAS) as part of Online No
ttingham algebraic geometry seminar\n\n\nAbstract\nGiven a compact Kähler
manifold it is a classical question\, related to K-stability\, whether it
admits a Kähler metric of constant scalar curvature (cscK metric for sho
rt). In this talk we prove that there always exist cscK metrics on compact
Kähler manifolds with nef canonical bundle\, thus on all smooth minimal
models\, and also on the blowup of any such manifold. This confirms an exp
ectation of Jian-Shi-Song and extends well-known results of Aubin and Yau
to the nef case\, giving a large new class of examples of cscK manifolds.
The tools used are from the variational approach in Kähler geometry\, and
some related results on stability thresholds and Donaldson's J-equation a
re discussed along the way.\n
LOCATION:https://researchseminars.org/talk/notts_ag/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolaos Tsakanikas (Saarbrücken)
DTSTART;VALUE=DATE-TIME:20220428T140000Z
DTEND;VALUE=DATE-TIME:20220428T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/101
DESCRIPTION:Title: On the existence of minimal models for generalized pairs\nby Nikola
os Tsakanikas (Saarbrücken) as part of Online Nottingham algebraic geomet
ry seminar\n\n\nAbstract\nI will discuss recent progress on the existence
of minimal models and Mori fiber spaces for generalized pairs. In particul
ar\, I will explain the close relationship between the existence of minima
l models and the existence of weak Zariski decompositions for generalized
pairs. This is joint work with Vladimir Lazić.\n
LOCATION:https://researchseminars.org/talk/notts_ag/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Veronica Fantini (IHES)
DTSTART;VALUE=DATE-TIME:20220505T090000Z
DTEND;VALUE=DATE-TIME:20220505T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/102
DESCRIPTION:Title: Enumerative geometry in the extended tropical vertex group\nby Vero
nica Fantini (IHES) as part of Online Nottingham algebraic geometry semina
r\n\n\nAbstract\nThe extended tropical vertex group is a pro-nilptotent Li
e group\, which has been introduced in [arxiv:1912.09956] studying the rel
ationship between scattering diagrams and infinitesimal deformations of ho
lomorphic pairs. Scattering diagrams were introduced by Kontsevich and Soi
belman in the context of mirror symmetry. They are defined algebraically\,
in terms of pro-nilpotent Lie groups\, but in many applications they have
a combinatorial structure which encodes enumerative geometric data (as Do
naldson--Thomas invariants\, Gromov--Witten invariants\,...). In particula
r\, Gross\, Pandharipande and Siebert showed how to compute genus zero log
Gromov--Witten invariants for P^2 via scattering diagrams in the so calle
d tropical vertex group. In this talk\, I will discuss a possible generali
zation regarding how to compute genus zero relative Gromov--Witten invaria
nts for toric P^2 using scattering diagrams in the extended tropical verte
x group.\n
LOCATION:https://researchseminars.org/talk/notts_ag/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noah Arbesfeld (Kavli IPMU)
DTSTART;VALUE=DATE-TIME:20220512T090000Z
DTEND;VALUE=DATE-TIME:20220512T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/103
DESCRIPTION:Title: Descendent series for Hilbert schemes of points on surfaces\nby Noa
h Arbesfeld (Kavli IPMU) as part of Online Nottingham algebraic geometry s
eminar\n\n\nAbstract\nStructure often emerges from Hilbert schemes of poin
ts on varieties when the underlying variety is fixed but the number of poi
nts parametrized varies. Some examples of such structure come from integra
ls of tautological bundles\, which arise in geometric and physical computa
tions. When compiled into generating series\, these integrals display inte
resting functional properties. I will give an overview of results on such
series\; the focus will be on K-theoretic descendent series for Hilbert sc
hemes on surfaces\, certain series formed from holomorphic Euler character
istics of tautological bundles. In particular\, I will explain how to see
that the K-theoretic descendent series are expansions of rational function
s.\n
LOCATION:https://researchseminars.org/talk/notts_ag/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kiumars Kaveh (Pittsburgh)
DTSTART;VALUE=DATE-TIME:20220519T130000Z
DTEND;VALUE=DATE-TIME:20220519T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/104
DESCRIPTION:Title: Buildings as classifying spaces for toric principal bundles\nby Kiu
mars Kaveh (Pittsburgh) as part of Online Nottingham algebraic geometry se
minar\n\n\nAbstract\nA building is a certain infinite combinatorial object
(abstract simplicial complex) associated to a (semisimple) linear algebra
ic group which encodes the relative position of maximal tori and parabolic
/parahoric subgroups in it. After an introduction to buildings and discuss
ing some examples from linear algebra\, I will talk about some recent resu
lts on classification of torus equivariant principal G-bundles on toric va
rieties (over a field) and toric schemes (over a discrete valuation ring).
These are extensions of Klyachko's classification of torus equivariant ve
ctor bundles on toric varieties. For this we introduce the notions of "pie
cewise linear map" to the Tits building and "piecewise affine map" to the
Bruhat-Tits building of a linear algebraic group. This is joint work with
Chris Manon (Kentucky) and Boris Tsvelikhovsky (Pittsburgh).\n
LOCATION:https://researchseminars.org/talk/notts_ag/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fei Xie (Edinburgh)
DTSTART;VALUE=DATE-TIME:20220526T090000Z
DTEND;VALUE=DATE-TIME:20220526T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/105
DESCRIPTION:Title: Residual categories of quadric surface bundles\nby Fei Xie (Edinbur
gh) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\
nThe residual category (or the Kuznetsov component) of a quadric surface b
undle is the non-trivial component in the derived category. It is equivale
nt to the twisted derived category of a double cover over the base when th
e quadric surface bundle has simple degeneration (fibers have corank at mo
st 1). I will consider quadric surface bundles with fibers of corank at mo
st 2 and describe their residual categories as (twisted) derived categorie
s of some scheme in two situations: (1) when the bundle has a smooth secti
on\; (2) when the total space is smooth and the base is a smooth surface.
The results can be applied to describe the residual categories of a (parti
al) resolution of nodal quintic del Pezzo threefolds\, cubic fourfolds con
taining a plane and certain complete intersections of quadrics.\n
LOCATION:https://researchseminars.org/talk/notts_ag/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Bäuerle (Eberhard Karl University of Tübingen)
DTSTART;VALUE=DATE-TIME:20220623T090000Z
DTEND;VALUE=DATE-TIME:20220623T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/106
DESCRIPTION:Title: Gorenstein Fano 3-folds of Picard number 1 with a 2-torus action\nb
y Andreas Bäuerle (Eberhard Karl University of Tübingen) as part of Onli
ne Nottingham algebraic geometry seminar\n\n\nAbstract\nWe classify the no
n-toric\, $\\mathbb{Q}$-factorial\, log terminal\, Gorenstein Fano threefo
lds of Picard number one that admit an effective action of a two-dimension
al torus.\n
LOCATION:https://researchseminars.org/talk/notts_ag/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chen Jiang (Shanghai Center for Mathematical Sciences)
DTSTART;VALUE=DATE-TIME:20200630T090000Z
DTEND;VALUE=DATE-TIME:20200630T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/107
DESCRIPTION:Title: Explicit boundedness of canonical Fano 3-folds\nby Chen Jiang (Shan
ghai Center for Mathematical Sciences) as part of Online Nottingham algebr
aic geometry seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/notts_ag/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chen Jiang (Shanghai Center for Mathematical Sciences)
DTSTART;VALUE=DATE-TIME:20220630T090000Z
DTEND;VALUE=DATE-TIME:20220630T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/108
DESCRIPTION:Title: RESCHEDULED TO 8 JULY: Explicit boundedness of canonical Fano 3-folds\nby Chen Jiang (Shanghai Center for Mathematical Sciences) as part of O
nline Nottingham algebraic geometry seminar\n\n\nAbstract\nMotivated by th
e classification of canonical Fano 3-folds\, we are interested in boundedn
ess results on different kinds of canonical Fano 3-folds\, such as antican
onical systems\, indices\, degrees\, and so on. I will summarize known res
ults with recent progress\, such as the explicit upper bound of anitcanoni
cal volumes and the effective birationality of anticanonical systems (base
d on joint works with Yu Zou) and some open problems.\n
LOCATION:https://researchseminars.org/talk/notts_ag/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierrick Bousseau (ETH Zurich)
DTSTART;VALUE=DATE-TIME:20220721T090000Z
DTEND;VALUE=DATE-TIME:20220721T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/109
DESCRIPTION:Title: Fock–Goncharov dual cluster varieties and Gross–Siebert mirrors
\nby Pierrick Bousseau (ETH Zurich) as part of Online Nottingham algebraic
geometry seminar\n\n\nAbstract\nCluster varieties come in pairs: for any
X-cluster variety there is an associated Fock–Goncharov dual A-cluster v
ariety. On the other hand\, in the context of mirror symmetry\, associated
with any log Calabi–Yau variety is its mirror dual\, which can be const
ructed using the enumerative geometry of rational curves in the framework
of the Gross–Siebert program. I will explain how to bridge the theory of
cluster varieties with the algebro-geometric framework of Gross–Siebert
mirror symmetry\, and show that the mirror to the X-cluster variety is a
degeneration of the Fock–Goncharov dual A-cluster variety. To do this\,
we investigate how the cluster scattering diagram of Gross–Hacking–Kee
l–Kontsevich compares with the canonical scattering diagram defined by G
ross–Siebert to construct mirror duals in arbitrary dimensions. This is
joint work with Hülya Argüz.\n
LOCATION:https://researchseminars.org/talk/notts_ag/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Léonard Pille-Schneider (Paris)
DTSTART;VALUE=DATE-TIME:20220714T090000Z
DTEND;VALUE=DATE-TIME:20220714T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/110
DESCRIPTION:Title: Degenerations of Calabi-Yau manifolds and integral affine geometry\
nby Léonard Pille-Schneider (Paris) as part of Online Nottingham algebrai
c geometry seminar\n\n\nAbstract\nLet $X\\rightarrow D^*$ be a maximal deg
eneration of $n$-dimensional Calabi-Yau varieties over the punctured disk.
The SYZ conjecture\, motivated by mirror symmetry\, predicts that the gen
eral fiber $X_t$ admits a Lagrangian torus fibration $f_t : X_t \\rightarr
ow B$ onto a base $B$ of real dimension $n$\, and that as $t\\rightarrow 0
$ the variety $X_t$ endowed with its Ricci-flat Kähler metric collapses t
o the space $B$\, endowed with a $Z$-affine structure. The goal of this ta
lk is to explain how to construct the space $B$ with its extra structures
using non-archimedean geometry. In particular\, in the case of Fermat thre
efolds in $\\mathbb{P}^4$\, using the toric geometry of the ambient space\
, we are able to construct a non-archimedean SYZ fibration inducing on $B$
the affine structure naturally induced by the Gromov-Hausdorff convergenc
e recently proved by Yang Li. This is based on work joint with Enrica Mazz
on.\n
LOCATION:https://researchseminars.org/talk/notts_ag/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elisa Postinghel (Trento)
DTSTART;VALUE=DATE-TIME:20220707T090000Z
DTEND;VALUE=DATE-TIME:20220707T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/111
DESCRIPTION:Title: The geometry of Weyl orbits on blow-ups of projective spaces\nby El
isa Postinghel (Trento) as part of Online Nottingham algebraic geometry se
minar\n\n\nAbstract\nLinear systems of divisors on blow-ups of projective
spaces in points in general positions are connected to certain polynomial
interpolation problems. While for the case of plane curves and of surfaces
in 3-space there are conjectures\, although long standing\, formulated by
M. Nagata\, B. Segre and others\, in the higher dimensional case we are i
n the dark. However\, when the number of points is not too large and the b
low-ups are Mori dream spaces\, an action of the Weyl group on cycles of a
ny codimension governs the birational behaviour of the space on the one ha
nd\, and the stable base locus of divisors on the other hand\, and it yiel
ds a solution to the interpolation problem. Joint work with C. Brambilla\,
O. Dumitrescu and L. Santana Sánchez.\n
LOCATION:https://researchseminars.org/talk/notts_ag/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chen Jiang (Shanghai Center for Mathematical Sciences)
DTSTART;VALUE=DATE-TIME:20220708T090000Z
DTEND;VALUE=DATE-TIME:20220708T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/112
DESCRIPTION:Title: Explicit boundedness of canonical Fano 3-folds\nby Chen Jiang (Shan
ghai Center for Mathematical Sciences) as part of Online Nottingham algebr
aic geometry seminar\n\n\nAbstract\nMotivated by the classification of can
onical Fano 3-folds\, we are interested in boundedness results on differen
t kinds of canonical Fano 3-folds\, such as anticanonical systems\, indice
s\, degrees\, and so on. I will summarize known results with recent progre
ss\, such as the explicit upper bound of anitcanonical volumes and the eff
ective birationality of anticanonical systems (based on joint works with Y
u Zou) and some open problems.\n
LOCATION:https://researchseminars.org/talk/notts_ag/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Schaffler (Roma Tre University)
DTSTART;VALUE=DATE-TIME:20220728T090000Z
DTEND;VALUE=DATE-TIME:20220728T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/113
DESCRIPTION:Title: Boundary divisors in the compactification by stable surfaces of moduli
of Horikawa surfaces\nby Luca Schaffler (Roma Tre University) as part
of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nSmooth mini
mal surfaces of general type with $K^2=1$\, $p_g=2$\, and $q=0$ constitute
a fundamental example in the geography of algebraic surfaces\, and the 28
-dimensional moduli space $\\mathbf{M}$ of their canonical models admits a
modular compactification $\\overline{\\mathbf{M}}$ via the minimal model
program. We describe eight new irreducible boundary divisors in such comp
actification parametrizing reducible stable surfaces. Additionally\, we st
udy the relation with the GIT compactification of $\\mathbf{M}$ and the Ho
dge theory of the degenerate surfaces that the eight divisors parametrize.
This is joint work in progress with Patricio Gallardo\, Gregory Pearlstei
n\, and Zheng Zhang.\n
LOCATION:https://researchseminars.org/talk/notts_ag/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felipe Espreafico (IMPA)
DTSTART;VALUE=DATE-TIME:20220811T130000Z
DTEND;VALUE=DATE-TIME:20220811T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/114
DESCRIPTION:Title: Gauss-Manin Connection in Disguise and Mirror Symmetry\nby Felipe E
spreafico (IMPA) as part of Online Nottingham algebraic geometry seminar\n
\n\nAbstract\nIn this talk\, we aim to explain what the Gauss-Manin Connec
tion in Disguise program is and why it is important. The idea is to constr
uct objects which behave similarly to modular forms using the Gauss-Manin
connection associated to a family of varieties with fixed topological data
. We focus on the applications to Mirror Symmetry\, especially the relatio
ns with Gromov-Witten invariants and the periods of the mirror quintic fam
ily. Among them\, I will explain my results for the open string Mirror Sym
metry and open Gromov-Witten invariants.\n
LOCATION:https://researchseminars.org/talk/notts_ag/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tristan Hübsch (Howard University)
DTSTART;VALUE=DATE-TIME:20220825T090000Z
DTEND;VALUE=DATE-TIME:20220825T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/115
DESCRIPTION:Title: Laurent Smoothing\, Turin Degenerations and Mirror Symmetry\nby Tri
stan Hübsch (Howard University) as part of Online Nottingham algebraic ge
ometry seminar\n\n\nAbstract\nCalabi-Yau hypersurfaces in toric spaces of
general type (encoded by certain non-convex polytopes) are degenerate but
may be smoothed by rational anticanonical sections. Nevertheless\, gauged
linear sigma model phases and an increasing number of their classical and
quantum data are just as computable as for their siblings encoded by refle
xive polytopes\, and they all have transposition mirrors. Showcasing Calab
i-Yau hypersurfaces in Hirzebruch scrolls shows this class of construction
s to be infinitely vast\, yet amenable to several well-founded algebro-geo
metric methods of analysis. This talk will include joint work with Per Be
rglund\, as reported in part: arXiv:1606.07420\, arXiv:1611.10300 and arXi
v:2205.12827.\n
LOCATION:https://researchseminars.org/talk/notts_ag/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Swarnava Mukhopadhyay (Tata Institute)
DTSTART;VALUE=DATE-TIME:20220804T090000Z
DTEND;VALUE=DATE-TIME:20220804T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/116
DESCRIPTION:Title: Graph potentials and mirrors of moduli of rank two bundles on curves\nby Swarnava Mukhopadhyay (Tata Institute) as part of Online Nottingham
algebraic geometry seminar\n\n\nAbstract\nGraph potentials are Laurent pol
ynomials associated to (colored) trivalent graphs that were introduced in
a joint work with Belmans and Galkin. They naturally appear as Newton poly
nomials of natural toric degenerations of the moduli space of rank two bun
dles. In this talk we will first discuss how graph potentials compute quan
tum periods of the moduli space $M$ of rank two bundles with fixed odd deg
ree determinant and hence can be regarded as a partial mirror to $M$. From
the view point of mirror symmetry\, we will show how the critical value d
ecomposition of graph potentials provides evidence for the conjectural sem
iorthogonal decomposition of $D^bCoh(M)$. If time permits we will also dis
cuss a formula to efficiently compute the periods of graph potential via a
TQFT. This is a joint work with Pieter Belmans and Sergey Galkin.\n
LOCATION:https://researchseminars.org/talk/notts_ag/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfredo Nájera Chávez (UNAM)
DTSTART;VALUE=DATE-TIME:20220901T130000Z
DTEND;VALUE=DATE-TIME:20220901T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/117
DESCRIPTION:Title: Newton–Okounkov bodies and minimal models of cluster varieties\nb
y Alfredo Nájera Chávez (UNAM) as part of Online Nottingham algebraic ge
ometry seminar\n\n\nAbstract\nI will explain a general procedure to constr
uct Newton–Okounkov bodies for a certain class of (partial) compactifica
tions of cluster varieties. This class consists of the (partial) minimal m
odels of cluster varieties with enough theta functions. This construction
applies for example to Grassmannians and Flag varieties\, among others. Ou
r construction depends on a choice of torus in the atlas of the cluster va
riety and the associated Newton–Okounkov body lives inside a real vector
space. Time permitting\, I will explain how to compare the Newton–Okoun
kov bodies associated with different tori and elaborate on the "intrinsic
Newton–Okounkov body"\, which is an object that does not depend on the c
hoice of torus and lives inside the real tropicalization of the mirror clu
ster variety. This is based on upcoming work with Lara Bossinger\, Man-Wai
Cheung and Timothy Magee.\n
LOCATION:https://researchseminars.org/talk/notts_ag/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gianluca Occhetta (Trento)
DTSTART;VALUE=DATE-TIME:20220922T090000Z
DTEND;VALUE=DATE-TIME:20220922T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/118
DESCRIPTION:Title: Maximal disjoint Schubert cycles in Rational Homogeneous spaces\nby
Gianluca Occhetta (Trento) as part of Online Nottingham algebraic geometr
y seminar\n\n\nAbstract\nIn 1974 Tango proved that there are no non-consta
nt morphisms from $lmathbb{P}^n$ to the Grassmannian $G(l\,m)$ if $n > m$\
; similar results were later obtained for morphisms from other Fano manifo
lds to Grassmannians. In this talk I will present the following generaliza
tion of these results: if $X$ and $Y$ are rational homogeneous manifold ob
tained as quotients of classical groups $G_X$ and $G_Y$ of the same type a
nd $rk(G_X) > rk(G_Y)$ then there are no non-constant morphisms from $X$ t
o $Y$. The key ingredient of the proof is the determination of the effecti
ve good divisibility of rational homogeneous manifolds of classical type\,
that is\, the greatest integer $s$ such that two effective cycles in the
Chow ring whose sum of codimensions is $s$ have nonzero intersection. This
talk is based on a joint work with R. Muñoz and L.E. Solá Conde.\n
LOCATION:https://researchseminars.org/talk/notts_ag/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Reading (North Carolina)
DTSTART;VALUE=DATE-TIME:20220915T140000Z
DTEND;VALUE=DATE-TIME:20220915T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/119
DESCRIPTION:Title: Scatter\, cluster\, scatter\, model\nby Nathan Reading (North Carol
ina) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract
\nCluster algebras were invented/discovered in order to understand total p
ositivity. But almost immediately\, mathematicians (and later physicists)
started finding connections between the combinatorics/geometry/algebra of
cluster algebras and other areas of mathematics and physics. Most relevant
for this talk are two connections: In one direction\, the theory of scatt
ering diagrams (mirror symmetry/Donaldson-Thomas theory/integrable systems
) has been applied to prove key structural results about cluster algebras.
In the other direction\, certain cluster algebras seem to be relevant to
the computation of scattering amplitudes in physics. The title of this tal
k is also an outline. I will introduce scattering diagrams\, then introduc
e cluster algebras\, and connect the two. Then I will give a brief\, naïv
e summary of the observed connections between cluster algebras and scatter
ing amplitudes\, to motivate the idea that a physicist might be interested
in combinatorial models for cluster algebras/scattering diagrams. I will
conclude with a survey of the state of research on these combinatorial mod
els\, focusing on the models that I have worked most closely with.\n
LOCATION:https://researchseminars.org/talk/notts_ag/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Tasin (Milano)
DTSTART;VALUE=DATE-TIME:20220929T090000Z
DTEND;VALUE=DATE-TIME:20220929T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/120
DESCRIPTION:Title: Sasaki-Einstein metrics on spheres\nby Luca Tasin (Milano) as part
of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nIt is a cla
ssical problem in geometry to construct new metrics on spheres. I will rep
ort on a joint work with Yuchen Liu and Taro Sano in which we construct in
finitely many families of Sasaki-Einstein metrics on odd-dimensional spher
es that bound parallelizable manifolds\, proving in this way conjectures o
f Boyer-Galicki-Kollár and Collins-Székelyhidi. The construction is base
d on showing the K-stability of certain Fano weighted orbifold hypersurfac
es.\n
LOCATION:https://researchseminars.org/talk/notts_ag/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Ugaglia (Palermo)
DTSTART;VALUE=DATE-TIME:20221013T083000Z
DTEND;VALUE=DATE-TIME:20221013T093000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/121
DESCRIPTION:Title: Seshadri constants of toric surfaces\nby Luca Ugaglia (Palermo) as
part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nIn thi
s talk\, after introducing Seshadri constants of projective surfaces and s
ome known results\, I will focus on the case of toric projective surfaces
associated to lattice polygons. I will prove some relations between the ra
tionality of Seshadri constants and the geometry of the polygon\, and I wi
ll present some possible applications to the case of weighted projective p
lanes. This is based on a joint work with Antonio Laface.\n
LOCATION:https://researchseminars.org/talk/notts_ag/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aimeric Malter (Birmingham)
DTSTART;VALUE=DATE-TIME:20221006T090000Z
DTEND;VALUE=DATE-TIME:20221006T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/122
DESCRIPTION:Title: A derived equivalence of the Libgober-Teitelbaum and Batyrev-Borisov mi
rror constructions\nby Aimeric Malter (Birmingham) as part of Online N
ottingham algebraic geometry seminar\n\n\nAbstract\nIn this talk I will de
monstrate how Variations of Geometric Invariant Theory can be used to prov
ide a derived equivalence between complete intersections in toric varietie
s. I will illustrate this by proving the derived equivalence of two mirror
constructions\, due to Libgober-Teitelbaum and Batyrev-Borisov.\n
LOCATION:https://researchseminars.org/talk/notts_ag/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julia Schneider (EPFL)
DTSTART;VALUE=DATE-TIME:20221103T100000Z
DTEND;VALUE=DATE-TIME:20221103T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/123
DESCRIPTION:Title: Birational maps of Severi-Brauer surfaces\, with applications to Cremon
a groups of higher rank\nby Julia Schneider (EPFL) as part of Online N
ottingham algebraic geometry seminar\n\n\nAbstract\nCremona groups are gro
ups of birational transformations of a projective space. Their structure d
epends on the dimension and the field. In this talk\, however\, we will fi
rst focus on birational transformations of (non-trivial) Severi-Brauer sur
faces\, that is\, surfaces that become isomorphic to the projective plane
over the algebraic closure of K. Such surfaces do not contain any K-ration
al point. We will prove that if such a surface contains a point of degree
6\, then its group of birational transformations is not generated by eleme
nts of finite order as it admits a surjective group homomorphism to the in
tegers. As an application\, we use this result to study Mori fiber spaces
over the field of complex numbers\, for which the generic fiber is a non-t
rivial Severi-Brauer surface. We prove that any group of cardinality at mo
st the one of the complex numbers is a quotient of the Cremona group of ra
nk 4 (and higher). This is joint work with Jérémy Blanc and Egor Yasinsk
y.\n
LOCATION:https://researchseminars.org/talk/notts_ag/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Abreu (Fluminense Federal University)
DTSTART;VALUE=DATE-TIME:20221020T090000Z
DTEND;VALUE=DATE-TIME:20221020T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/124
DESCRIPTION:Title: Wall-crossing of Brill-Noether cycles in compactified Jacobians\nby
Alex Abreu (Fluminense Federal University) as part of Online Nottingham a
lgebraic geometry seminar\n\n\nAbstract\nWe will discuss an explicit graph
formula\, in terms of boundary strata classes\, for the wall-crossing of
universal (over the moduli space of curves) Brill-Noether classes. More pr
ecisely\, fix two stability conditions for universal compactified Jacobian
s that are on different sides of a wall in the stability space. Then we ca
n compare the two universal Brill-Noether classes on the two compactified
Jacobians by pulling one of them back along the (rational) identity map. T
he calculation involves constructing a resolution by means of subsequent b
low-ups. This is joint with Nicola Pagani.\n
LOCATION:https://researchseminars.org/talk/notts_ag/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joey Palmer (Illinois)
DTSTART;VALUE=DATE-TIME:20221110T150000Z
DTEND;VALUE=DATE-TIME:20221110T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/125
DESCRIPTION:Title: Integrable systems with S^1-actions and the associated polygons\nby
Joey Palmer (Illinois) as part of Online Nottingham algebraic geometry se
minar\n\n\nAbstract\nSemitoric systems are a type of four-dimensional inte
grable system which admit a global $S^1$-action\; these systems were class
ified by Pelayo and Vu Ngoc in 2011\, generalizing the classification of t
oric integrable systems and making use of an invariant called a `semitoric
polygon'. I will present some results about bifurcations of such systems\
, and show how this can be used to construct explicit examples of such sys
tems associated to certain given semitoric polygon. Time permitting\, I wi
ll also discuss how hypersemitoric systems\, a generalization of semitoric
systems\, appear in this context. Some of the results I will present are
joint with Yohann Le Floch and Sonja Hohloch.\n
LOCATION:https://researchseminars.org/talk/notts_ag/125/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vasiliki Petrotou (Hebrew University of Jerusalem)
DTSTART;VALUE=DATE-TIME:20221117T100000Z
DTEND;VALUE=DATE-TIME:20221117T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/126
DESCRIPTION:Title: Tom & Jerry triples and the 4-intersection unprojection formats\nby
Vasiliki Petrotou (Hebrew University of Jerusalem) as part of Online Nott
ingham algebraic geometry seminar\n\n\nAbstract\nUnprojection is a theory
in Commutative Algebra due to Miles Reid which constructs and analyses mor
e complicated rings from simpler ones. The talk will be about two new form
ats of unprojection which we call Tom & Jerry triples and 4-intersection f
ormat respectively. The motivation is to construct codimension 6 Gorenstei
n rings starting from codimensions 3 and 2 respectively. As an application
we will construct three families of codimension 6 Fano 3-folds in weighte
d projective space which appear in the Graded Ring Database.\n
LOCATION:https://researchseminars.org/talk/notts_ag/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rob Silversmith (Warwick)
DTSTART;VALUE=DATE-TIME:20221128T100000Z
DTEND;VALUE=DATE-TIME:20221128T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/127
DESCRIPTION:Title: Cross-ratios and perfect matchings\nby Rob Silversmith (Warwick) as
part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nGiven
a bipartite graph G (subject to a constraint)\, the "cross-ratio degree"
of G is a non-negative integer invariant of G\, defined via a simple count
ing problem in algebraic geometry. I will discuss some natural contexts in
which cross-ratio degrees arise. I will then present a perhaps-surprising
upper bound on cross-ratio degrees in terms of counting perfect matchings
. Finally\, time permitting\, I may discuss the tropical side of the story
.\n
LOCATION:https://researchseminars.org/talk/notts_ag/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tiago Duarte Guerreiro (Essex)
DTSTART;VALUE=DATE-TIME:20221208T100000Z
DTEND;VALUE=DATE-TIME:20221208T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/128
DESCRIPTION:Title: On toric Sarkisov Links from P^4\nby Tiago Duarte Guerreiro (Essex)
as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nAc
cording to the Sarkisov Program\, a birational map between a Fano variety
of Picard rank one and a Mori fibre space can be decomposed as a finite se
quence of Elementary Sarkisov Links starting with the blowup of a centre.
Hence\, it is natural to try to understand the latter maps explicitly. In
this talk we explain how to describe all possible toric Elementary Sarkiso
v Links starting with the blowup of a point in $\\mathbb{P}^4$.\n
LOCATION:https://researchseminars.org/talk/notts_ag/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucie Devey (Frankfurt and Grenoble)
DTSTART;VALUE=DATE-TIME:20230126T100000Z
DTEND;VALUE=DATE-TIME:20230126T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/129
DESCRIPTION:Title: Stability of toric vector bundles in terms of parliaments of polytopes<
/a>\nby Lucie Devey (Frankfurt and Grenoble) as part of Online Nottingham
algebraic geometry seminar\n\n\nAbstract\nGiven any toric vector bundle\,
we may construct its parliament of polytopes. This is a generalization of
the Newton polytope (or moment polytope) of a toric line bundle. This obje
ct contains a huge amount of information about the original bundle: notabl
y on its global sections and its positivity. We can also easily know if th
e toric bundle is (semi-/poly-)stable with respect to any polarisation. I
will give a combinatorial visualisation of stability of toric vector bundl
es.\n
LOCATION:https://researchseminars.org/talk/notts_ag/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yaoxiong Wen (KIAS)
DTSTART;VALUE=DATE-TIME:20230202T100000Z
DTEND;VALUE=DATE-TIME:20230202T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/130
DESCRIPTION:Title: Mirror symmetry for the parabolic G-Higgs bundle\, from local to global
\nby Yaoxiong Wen (KIAS) as part of Online Nottingham algebraic geomet
ry seminar\n\n\nAbstract\nMotivated by geometric Langlands\, we initiate a
program to study the mirror symmetry for the moduli space of parabolic G-
Higgs bundles. This talk will focus on $G=\\textrm{Sp}_{2n}$ and its Langl
ands dual $\\textrm{SO}_{2n+1}$. Our goal is to prove the SYZ mirror symme
try and topological mirror symmetry (TMS). The parabolic structure of the
parabolic Higgs bundle is related to the nilpotent orbit closure. So we ne
ed to first figure out the mirror pair for nilpotent orbits. Classically\,
there is a famous Springer duality between special orbits. Therefore\, it
is natural to speculate that the mirror symmetry we seek may coincide wit
h Springer duality in the context of special orbits. Unfortunately\, such
a naive statement fails. To remedy the situation\, together with Prof. Rua
n and Prof. Fu (arXiv:2207.10533)\, we propose a conjecture which asserts
the mirror symmetry for certain parabolic/induced covers of special orbits
. Then\, we prove the conjecture for Richardson orbits and obtain certain
partial results in general. After understanding the mirror parabolic struc
tures\, together with W. He\, X. Su\, B. Wang\, X. Wen\, we are working in
progress to prove the SYZ and TMS for the moduli space of parabolic $\\te
xtrm{Sp}_{2n}/\\textrm{SO}_{2n+1}$-Higgs bundles with dual parabolic struc
tures.\n
LOCATION:https://researchseminars.org/talk/notts_ag/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fenglong You (ETH-Zurich)
DTSTART;VALUE=DATE-TIME:20230222T100000Z
DTEND;VALUE=DATE-TIME:20230222T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/131
DESCRIPTION:Title: Relative quantum cohomology under birational transformations\nby Fe
nglong You (ETH-Zurich) as part of Online Nottingham algebraic geometry se
minar\n\n\nAbstract\nI will talk about how relative quantum cohomology\, d
efined by Tseng--You and Fan--Wu--You\, varies under birational transforma
tions. Relation with FJRW theory and extremal transitions of absolute Grom
ov--Witten theory will also be discussed.\n
LOCATION:https://researchseminars.org/talk/notts_ag/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Ducat (Durham)
DTSTART;VALUE=DATE-TIME:20230309T100000Z
DTEND;VALUE=DATE-TIME:20230309T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/132
DESCRIPTION:Title: Quartic surfaces up to volume preserving equivalence\nby Tom Ducat
(Durham) as part of Online Nottingham algebraic geometry seminar\n\n\nAbst
ract\nWe consider log Calabi-Yau pairs of the form $(\\mathbb{P}^3\, D)$\,
where $D$ is a quartic surface\, up to volume-preserving equivalence. The
coregularity of the pair $(\\mathbb{P}^3\, D)$ is a discrete volume-prese
rving invariant $c=0\,1$ or $2$\, and which depends on the nature of the s
ingularities of $D$. We classify all pairs $(\\mathbb{P}^3\,D)$ of coregul
arity $c=0$ or $1$ up to volume preserving equivalence. In particular\, if
$c=0$ then we show that $(\\mathbb{P}^3\, D)$ admits a volume preserving
birational map onto a toric pair.\n
LOCATION:https://researchseminars.org/talk/notts_ag/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iacopo Brivio (NCTS)
DTSTART;VALUE=DATE-TIME:20230209T100000Z
DTEND;VALUE=DATE-TIME:20230209T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/133
DESCRIPTION:Title: Invariance of plurigenera and KSBA moduli in positive and mixed charact
eristic\nby Iacopo Brivio (NCTS) as part of Online Nottingham algebrai
c geometry seminar\n\n\nAbstract\nA famous theorem by Siu states that plur
igenera are invariant under smooth deformations for complex projective man
ifolds\, a result which is a cornerstone of higher dimensional moduli theo
ry. In this talk we will explore some examples showing that Siu's theorem
fails in positive and mixed characteristic\, then discuss the implications
at the level of moduli theory\, as well as some related questions.\n
LOCATION:https://researchseminars.org/talk/notts_ag/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Duc-Khanh Nguyen (Albany)
DTSTART;VALUE=DATE-TIME:20230216T140000Z
DTEND;VALUE=DATE-TIME:20230216T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/134
DESCRIPTION:Title: A generalization of the Murnaghan-Nakayama rule for $K$-$k$-Schur and $
k$-Schur functions\nby Duc-Khanh Nguyen (Albany) as part of Online Not
tingham algebraic geometry seminar\n\n\nAbstract\nWe introduce a generaliz
ation of $K$-$k$-Schur functions and $k$-Schur functions via the Pieri rul
e. Then we obtain the Murnaghan-Nakayama rule for the generalized function
s. The rule are described explicitly in the cases of $K$-$k$-Schur functio
ns and $k$-Schur functions\, with concrete descriptions and algorithms for
coefficients. Our work recovers the result of Bandlow\, Schilling\, and Z
abrocki for $k$-Schur functions\, and explains it as a degeneration of the
rule for $K$-$k$-Schur functions. In particular\, many other special case
s promise to be detailed in the future.\n
LOCATION:https://researchseminars.org/talk/notts_ag/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ayush Kumar Tewari (Ghent)
DTSTART;VALUE=DATE-TIME:20230302T100000Z
DTEND;VALUE=DATE-TIME:20230302T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/135
DESCRIPTION:Title: Forbidden patterns in tropical planar curves and panoptigons\nby Ay
ush Kumar Tewari (Ghent) as part of Online Nottingham algebraic geometry s
eminar\n\n\nAbstract\nTropical curves in $\\mathbb{R}^2$ correspond to met
ric planar graphs but not all planar graphs arise in this way. We describe
several new classes of graphs that cannot occur. For instance\, this yiel
ds a full combinatorial characterization of the tropically planar graphs o
f genus at most six. We also define a special family of lattice polytopes
namely panoptigons and enumerate all possible panoptigons under mild latti
ce width constraints and show how they can be used to find a forbidden pat
tern in tropical planar curves. We also will discuss some possible applica
tions of the classification of panoptigons and ongoing work on suitable ge
neralizations. This talk is based on work in Tewari (2022) and joint work
with Michael Joswig (2020) and Ralph Morrison (2021).\n
LOCATION:https://researchseminars.org/talk/notts_ag/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesca Zaffalon (KU Leuven)
DTSTART;VALUE=DATE-TIME:20230323T100000Z
DTEND;VALUE=DATE-TIME:20230323T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/136
DESCRIPTION:Title: Toric degenerations of partial flag varieties via matching fields and c
ombinatorial mutations\nby Francesca Zaffalon (KU Leuven) as part of O
nline Nottingham algebraic geometry seminar\n\n\nAbstract\nToric degenerat
ions are an important tool that can be used to analyze algebraic varieties
as they allow us to understand a general variety via the geometry of thei
r associated toric varieties. In this talk\, I will show how to produce a
new large family of toric degenerations of Grassmannians and (partial) fla
g varieties\, whose combinatorics is governed by matching fields. Moreover
\, I will study the relations between polytopes associated to different to
ric degenerations of the same variety. This is done using the tool of comb
inatorial mutations\, particular piecewise linear functions on polytopes.
Finally\, I will show how our methods can be used to compute new families
of toric degenerations of small Grassmannians and flag varieties. This tal
k is based on joint work with Oliver Clarke and Fatemeh Mohammadi.\n
LOCATION:https://researchseminars.org/talk/notts_ag/136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Urbinati (Udine)
DTSTART;VALUE=DATE-TIME:20230316T150000Z
DTEND;VALUE=DATE-TIME:20230316T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/137
DESCRIPTION:Title: Mori Dream Pairs and C^*-actions\nby Stefano Urbinati (Udine) as pa
rt of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nThe idea
of the talk is that of giving a connection between 'local' Mori theory an
d $C^*$-actions. In particular\, we construct and characterize a correspon
dence between Mori dream regions arising from small modifications of norma
l projective varieties and $C^*$-actions on polarized pairs which are bord
isms. This is joint work with Lorenzo Barban\, Eleonora A. Romano and Luis
E. Solá Conde.\n
LOCATION:https://researchseminars.org/talk/notts_ag/137/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernd Siebert (Texas)
DTSTART;VALUE=DATE-TIME:20230317T100000Z
DTEND;VALUE=DATE-TIME:20230317T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/138
DESCRIPTION:Title: Toward the logarithmic Hilbert scheme\nby Bernd Siebert (Texas) as
part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nLogari
thmic geometry provides tools to work relative a normal crossings divisor\
, including normal crossings degenerations. I will report on work in progr
ess with Mattia Talpo and Richard Thomas to define a natural logarithmic a
nalogue of the ordinary Hilbert scheme. Immediate applications include ind
uced good degenerations of Hilbert schemes of points. Our point of view al
so suggests a definition of tropical Hilbert schemes. One larger aim is to
develop robust logarithmic methods to deal with coherent sheaves in maxim
al degenerations as they appear in mirror symmetry.\n
LOCATION:https://researchseminars.org/talk/notts_ag/138/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chuyu Zhou (EPFL)
DTSTART;VALUE=DATE-TIME:20230504T090000Z
DTEND;VALUE=DATE-TIME:20230504T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/139
DESCRIPTION:Title: On wall crossing for K-stability with multiple boundaries\nby Chuyu
Zhou (EPFL) as part of Online Nottingham algebraic geometry seminar\n\n\n
Abstract\nIn this talk\, we will focus on a wall-crossing theory for log F
ano pairs with multiple boundaries. As a key ingredient\, we will present
that the K-semistable domains are polytopes. This is based on a recent wor
k https://arxiv.org/abs/2302.13503.\n
LOCATION:https://researchseminars.org/talk/notts_ag/139/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lukas Braun (Freiburg)
DTSTART;VALUE=DATE-TIME:20230420T090000Z
DTEND;VALUE=DATE-TIME:20230420T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/140
DESCRIPTION:Title: Reductive quotients of klt varieties\nby Lukas Braun (Freiburg) as
part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nIn thi
s talk\, I will explain the proof of a recent result\, obtained together w
ith Daniel Greb\, Kevin Langlois\, and Joaquin Moraga\, that reductive quo
tients of klt type varieties are of klt type. This generalizes and extends
a classical result by Boutot\, stating that these kinds of quotients pres
erve rational singularities. The statement was also well known in the case
of finite groups. If time permits\, I will also discuss several applicati
ons of our result\, e.g. on quotients of Fano type varieties\, good moduli
spaces\, and collapsing of homogeneous bundles.\n
LOCATION:https://researchseminars.org/talk/notts_ag/140/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Gioia Cifani (Roma Tre)
DTSTART;VALUE=DATE-TIME:20230412T090000Z
DTEND;VALUE=DATE-TIME:20230412T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/141
DESCRIPTION:Title: Reconstructing curves from their Hodge classes\nby Maria Gioia Cifa
ni (Roma Tre) as part of Online Nottingham algebraic geometry seminar\n\n\
nAbstract\nRecently\, Movasati and Sertöz pose several interesting questi
ons about the reconstruction of a variety from its Hodge class. In particu
lar they give the notion of a perfect class: the Hodge class of a variety
$X$ is perfect if its annihilator is a sum of ideals of varieties whose Ho
dge class is a nonzero rational multiple of that of $X$. I will report on
a joint work with Gian Pietro Pirola and Enrico Schlensiger\, in which we
give an answer to some of these questions for curves: in particular\, we s
how that the Hodge class of a smooth rational quartic on a surface of degr
ee 4 is not perfect\, and that the Hodge class of an arithmetically Cohen-
Macaulay curve is always perfect. Moreover\, I will give some results on t
he problem in higher dimension.\n
LOCATION:https://researchseminars.org/talk/notts_ag/141/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Esser (UCLA)
DTSTART;VALUE=DATE-TIME:20230413T140000Z
DTEND;VALUE=DATE-TIME:20230413T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/142
DESCRIPTION:Title: Automorphisms of weighted projective hypersurfaces\nby Louis Esser
(UCLA) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstra
ct\nAutomorphism groups of smooth hypersurfaces in projective space are we
ll studied in algebraic geometry. In this talk\, I'll work in the more ge
neral setting of automorphism groups of quasismooth hypersurfaces in weigh
ted projective space and consider the following questions: when are these
groups linear? When are they finite\, and if finite\, how large can they
get? What does the automorphism group of a very general hypersurface with
given weights and degree look like? In each case\, I'll generalize analo
gous results for ordinary projective hypersurfaces and explain how unexpec
ted behavior appears in the weighted setting.\n
LOCATION:https://researchseminars.org/talk/notts_ag/142/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aline Zanardini (Leiden)
DTSTART;VALUE=DATE-TIME:20230427T090000Z
DTEND;VALUE=DATE-TIME:20230427T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/143
DESCRIPTION:Title: Pencils of plane cubics revisited\nby Aline Zanardini (Leiden) as p
art of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nIn rece
nt joint work with M. Hattori we have considered the problem of classifyin
g linear systems of hypersurfaces (of a fixed degree) in some projective s
pace up to projective equivalence via geometric invariant theory (GIT). An
d we have obtained a complete and explicit stability criterion. In this ta
lk I will explain how this criterion can be used to recover Miranda’s de
scription of the GIT stability of pencils of plane cubics.\n
LOCATION:https://researchseminars.org/talk/notts_ag/143/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Bates (US Naval Academy)
DTSTART;VALUE=DATE-TIME:20230511T140000Z
DTEND;VALUE=DATE-TIME:20230511T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/144
DESCRIPTION:Title: Numerical methods for working with polynomial systems\nby Daniel Ba
tes (US Naval Academy) as part of Online Nottingham algebraic geometry sem
inar\n\n\nAbstract\nWhether testing conjectures in algebraic geometry or t
rying to solve polynomial systems for some application\, numerical methods
are sometimes a useful alternative to well-known symbolic algorithms. Thi
s talk is intended to introduce some of the main tools of the field of num
erical algebraic geometry\, including homotopy continuation and the numeri
cal irreducible decomposition. In particular\, given a polynomial system\,
we will see how numerical methods can provide floating point approximatio
ns to points on each irreducible component of the corresponding complex va
riety. We will also visit a few recent uses of these methods and consider
the benefits and drawbacks compared to exact\, symbolic methods.\n
LOCATION:https://researchseminars.org/talk/notts_ag/144/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Trusiani (Toulouse)
DTSTART;VALUE=DATE-TIME:20230518T090000Z
DTEND;VALUE=DATE-TIME:20230518T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/145
DESCRIPTION:Title: A relative Yau-Tian-Donaldson conjecture and stability thresholds\n
by Antonio Trusiani (Toulouse) as part of Online Nottingham algebraic geom
etry seminar\n\n\nAbstract\nOn a Fano variety\, the Yau–Tian–Donaldson
correspondence connects the existence of Kähler–Einstein metrics to an
algebro-geometric notion called $K$-stability. In the last decade\, the l
atter has proved to be very valuable in Algebraic Geometry: for instance\,
it is used for the construction of moduli spaces. In the first part of th
e talk\, partly motivated by the study of Kähler–Einstein metrics with
prescribed singularities\, a new relative $K$-stability notion will be int
roduced for a fixed smooth Fano variety. A particular focus will be given
to motivations and intuitions\, making a comparison with the log $K$-stabi
lity/log Kähler–Einstein metrics. The relative $K$-stability and the K
ähler–Einstein metrics with prescribed singularities will then be relat
ed to each other through a Yau–Tian–Donaldson correspondence\, which w
ill be the core of the talk. An important role will be played by algebro-g
eometric valuative criteria\, which will be also used to link the relative
$K$-stability to the genuine $K$-stability.\n
LOCATION:https://researchseminars.org/talk/notts_ag/145/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fei Si (BICMR)
DTSTART;VALUE=DATE-TIME:20230601T090000Z
DTEND;VALUE=DATE-TIME:20230601T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/146
DESCRIPTION:Title: K-moduli space of del Pezzo surface pairs\nby Fei Si (BICMR) as par
t of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nA K3 surf
aces with anti-symplectic involution can be identified with a pair $(X\,C)
$ consisting of a del Pezzo surface $X$ with a curve $C \\sim −2K_X$. Th
eir moduli space has many compactifications from various perspectives. In
this talk\, we will discuss the compactifications from $K$-moduli theoreti
c side and its relation to Baily-Borel compactification from Hodge theoret
ic side. In particular\, we will give an explicit description of $K$-modul
i space $P_c^K$ parametrizing $K$-polystable del Pezzo pairs $(X\,cC)$ und
er the framework of wall-crossing for $K$-moduli space due to Ascher-DeVle
ming-Liu. Moreover\, we will show the $K$-moduli space $P_c^K$ is isomorph
ic to certain log canonical model on Baily-Borel compactification of the m
oduli space of K3 surfaces with anti-symplectic involution. This can be vi
ewed as another example of Hassett-Keel-Looijenga program proposed by Laza
-O'Grady. This is based on joint work with Long Pan and Haoyu Wu.\n
LOCATION:https://researchseminars.org/talk/notts_ag/146/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kelly Jabbusch (Michigan)
DTSTART;VALUE=DATE-TIME:20230525T140000Z
DTEND;VALUE=DATE-TIME:20230525T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/147
DESCRIPTION:Title: The minimal projective bundle dimension and toric 2-Fano manifolds\
nby Kelly Jabbusch (Michigan) as part of Online Nottingham algebraic geome
try seminar\n\n\nAbstract\nIn this talk we will discuss higher Fano manifo
lds\, which are Fano manifolds with positive higher Chern characters. In p
articular we will focus on toric 2-Fano manifolds. Motivated by the proble
m of classifying toric 2-Fano manifolds\, we will introduce a new invarian
t for smooth projective toric varieties\, the minimal projective bundle di
mension\, $m(X)$. This invariant $m(X)$ captures the minimal degree of a d
ominating family of rational curves on $X$ or\, equivalently\, the minimal
length of a centrally symmetric primitive relation for the fan of $X$. We
'll present a classification of smooth projective toric varieties with $m(
X) \\ge \\dim(X)-2$\, and show that projective spaces are the only 2-Fano
manifolds among smooth projective toric varieties with $m(X)$ equal to $1$
\, $\\dim(X)-2$\, $\\dim(X)-1$\, or $\\dim(X)$. This is joint work with Ca
rolina Araujo\, Roya Beheshti\, Ana-Maria Castravet\, Svetlana Makarova\,
Enrica Mazzon\, and Nivedita Viswanathan.\n
LOCATION:https://researchseminars.org/talk/notts_ag/147/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yalong Cao (RIKEN)
DTSTART;VALUE=DATE-TIME:20230831T100000Z
DTEND;VALUE=DATE-TIME:20230831T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/148
DESCRIPTION:Title: From curve counting on Calabi-Yau 4-folds to quasimaps for quivers with
potentials\nby Yalong Cao (RIKEN) as part of Online Nottingham algebr
aic geometry seminar\n\n\nAbstract\nI will start by reviewing an old joint
work with Davesh Maulik and Yukinobu Toda on relating Gromov-Witten\, Gop
akumar-Vafa (in the sense of Klemm-Pandharipande) and stable pair invarian
ts on compact Calabi-Yau 4-folds. For non-compact CY4 like local curves\,
similar invariants can be studied via the perspective of quasimaps to quiv
ers with potentials. In a recent joint work with Gufang Zhao\, we define a
virtual count for such quasimaps and prove a gluing formula. Computations
of examples will also be discussed.\n
LOCATION:https://researchseminars.org/talk/notts_ag/148/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Esterov (LIMS)
DTSTART;VALUE=DATE-TIME:20230622T090000Z
DTEND;VALUE=DATE-TIME:20230622T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/149
DESCRIPTION:Title: Bernstein-Kouchnirenko-Khovanskii with a symmetry\nby Alexander Est
erov (LIMS) as part of Online Nottingham algebraic geometry seminar\n\n\nA
bstract\nA generic polynomial $f(x\,y\,z)$ with a prescribed Newton polyto
pe defines a symmetric spatial curve $f(x\,y\,z)=f(y\,x\,z)=0$. We shall s
tudy its geometry\, and classify the Newton polytopes for which this geome
try is exceptional. As a motivating application\, we shall classify generi
c one-parameter families of complex univariate polynomials\, whose Galois
group differs from the complete symmetric group. We shall see how some of
these results conjecturally extend to higher dimensions and more complicat
ed symmetries. This is based on joint work with Lionel Lang.\n
LOCATION:https://researchseminars.org/talk/notts_ag/149/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junyan Zhao (Illinois)
DTSTART;VALUE=DATE-TIME:20230713T140000Z
DTEND;VALUE=DATE-TIME:20230713T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/150
DESCRIPTION:Title: Moduli of curves of genus 6 and K-stability\nby Junyan Zhao (Illino
is) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\
nIn this talk\, I will describe a way to study moduli of curves of small g
enus (eg. $g=3\,4\,6$) via $K$-stability. For instance\, a general curve
$C$ of genus $6$ can be embedded into the unique quintic del Pezzo surface
$X_5$ as a divisor of class $-2K_{X_5}$. Thus the $K$-moduli spaces of th
e pair $(X_5\, cC)$ are birational to the moduli of DM-stable curves $\\ba
r{M}_6$. On the other hand\, $X_5$ can be embedded in $\\mathbb{P}^1 \\tim
es\\mathbb{P}^2$ as a divisor of class $\\mathcal{O}(1\,2)$\, under which
$-2K_X$ is linearly equivalent to $\\mathcal{O}_X(2\,2)$. One can study th
e VGIT-moduli spaces in this setting. In this talk\, I will compare these
various compactifications of moduli spaces.\n
LOCATION:https://researchseminars.org/talk/notts_ag/150/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruno Suzuki (São Paulo)
DTSTART;VALUE=DATE-TIME:20230706T140000Z
DTEND;VALUE=DATE-TIME:20230706T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/151
DESCRIPTION:Title: Birationally equivalent Landau-Ginzburg models on cotangent bundles and
adjoint orbits\nby Bruno Suzuki (São Paulo) as part of Online Nottin
gham algebraic geometry seminar\n\n\nAbstract\nWe show that the Lie potent
ial on the minimal semisimple adjoint orbit of $\\mathfrak{sl}(n+1\,\\math
bb{C})$ coincides with toric potential on the cotangent bundle of $\\mathb
b{P}^{n}$. We then study the corresponding Landau-Ginzburg models in defor
mation families and give some examples of how the deformations affect the
mirrors.\n
LOCATION:https://researchseminars.org/talk/notts_ag/151/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Massarenti (Ferrara)
DTSTART;VALUE=DATE-TIME:20230803T140000Z
DTEND;VALUE=DATE-TIME:20230803T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/152
DESCRIPTION:Title: On the (uni)rationality problem for quadric bundles and hypersurfaces\nby Alex Massarenti (Ferrara) as part of Online Nottingham algebraic ge
ometry seminar\n\n\nAbstract\nA variety $X$ over a field is unirational if
there is a dominant rational map from a projective space to $X$. We will
discuss the unirationality problem for quartic hypersurfaces and quadric b
undles over a arbitrary field in the the perspective of the relation betwe
en unirationality and rational connectedness. We will prove unirationality
of quadric bundles under certain positivity assumptions on their anti-can
onical divisor. As a consequence we will get the unirationality of any smo
oth 4-fold quadric bundle over the projective plane\, over an algebraicall
y closed field\, and with discriminant of degree at most 12.\n
LOCATION:https://researchseminars.org/talk/notts_ag/152/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nawaz Sultani (Michigan)
DTSTART;VALUE=DATE-TIME:20230810T090000Z
DTEND;VALUE=DATE-TIME:20230810T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/153
DESCRIPTION:Title: Gromov-Witten theory of Non-Convex Complete Intersections\nby Nawaz
Sultani (Michigan) as part of Online Nottingham algebraic geometry semina
r\n\n\nAbstract\nFor a convex complete intersection $X$\, the Quantum Lefs
hetz Hyperplane theorem (QLHT) relates the Gromov-Witten (GW) invariants o
f $X$ to those of the ambient space. This is most notably used in the proo
f of genus 0 mirror symmetry for complete intersections in toric varieties
\, since the invariants of the ambient toric variety are easier to compute
. However\, orbifold complete intersections are rarely convex\, hence QLHT
often fails even in genus 0. In this talk\, I will showcase a method to c
ompute the genus 0 GW invariants for orbifold complete intersections in st
ack quotients of the form $[V /\\!\\!/ G]$\, regardless of convexity condi
tions. The invariants computed by this method include all the invariants o
ne expects of QLHT\, even when QLHT fails. This talk will include results
from joint works with Felix Janda (Notre Dame) and Yang Zhou (Fudan)\, and
with Rachel Webb (Berkeley).\n
LOCATION:https://researchseminars.org/talk/notts_ag/153/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Livia Campo (KIAS)
DTSTART;VALUE=DATE-TIME:20230824T090000Z
DTEND;VALUE=DATE-TIME:20230824T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/154
DESCRIPTION:Title: Flags on Fano 3-fold hypersurfaces\nby Livia Campo (KIAS) as part o
f Online Nottingham algebraic geometry seminar\n\n\nAbstract\nThe existenc
e of Kaehler-Einstein metrics on Fano 3-folds can be determined by studyin
g some positive numbers called stability thresholds. K-stability is ensure
d if appropriate bounds can be found for these thresholds. An effective wa
y to verify such bounds is to construct flags of point-curve-surface insid
e the Fano 3-folds. This approach was initiated by Abban-Zhuang\, and allo
ws us to restrict the computation of bounds for stability thresholds only
on flags. We employ this machinery to prove K-stability of terminal quasi-
smooth Fano 3-fold hypersurfaces. Many of these varieties had been attacke
d by Kim-Okada-Won using log canonical thresholds. In this talk I will tac
kle the remaining Fano hypersurfaces via Abban-Zhuang Theory.\n
LOCATION:https://researchseminars.org/talk/notts_ag/154/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andres Fernandez Herrero (Columbia)
DTSTART;VALUE=DATE-TIME:20230727T090000Z
DTEND;VALUE=DATE-TIME:20230727T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/155
DESCRIPTION:Title: Harder-Narasimhan theory for gauged maps\nby Andres Fernandez Herre
ro (Columbia) as part of Online Nottingham algebraic geometry seminar\n\n\
nAbstract\nIn this talk\, I will discuss recent techniques developed to co
nstruct moduli spaces of decorated principal bundles on a fixed compact Ri
emann surface. Using these techniques\, we construct a Harder-Narasimhan s
tratification\, which can be used to obtain a generalization of the Verlin
de formula in the context of decorated principal bundles. This talk is bas
ed on joint work with Daniel Halpern-Leistner.\n
LOCATION:https://researchseminars.org/talk/notts_ag/155/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mauro Porta (Strasbourg)
DTSTART;VALUE=DATE-TIME:20230907T090000Z
DTEND;VALUE=DATE-TIME:20230907T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/156
DESCRIPTION:Title: Categorified Beauville-Laszlo theorem (and related problems)\nby Ma
uro Porta (Strasbourg) as part of Online Nottingham algebraic geometry sem
inar\n\n\nAbstract\nSheaves of Azumaya algebras were introduced by Grothen
dieck to represent classes in the cohomological Brauer group of schemes\,
i.e. $Br(X) := H^2_{\\text{\\'et}}(X\;G_m)$\, along the same lines every c
lass in $H^1_{\\text{\\'et}}(X\;G_m)$ is representable by a line bundle on
$X$. However\, it turns out that not every class in $Br(X)$ can be repres
ented by a sheaf of Azumaya algebras\, as shown in the case of Mumford's n
ormal surface. In much more recent times\, Toën introduced the notion of
sheaf of derived Azumaya algebra\, and proved that these objects represent
even non-torsion classes in $Br(X)$. In collaboration with Federico Binda
we studied two problems related to derived Azumaya algebras: the Grothend
ieck existence and the Beauville-Laszlo theorems. In this talk\, I will su
rvey both questions and explain how our categorified approach allows to go
beyond a classical injectivity result of Grothendieck. I will finish with
a brief discussion of the consequences of categorified Beauville-Laszlo t
hat will be the object of a future work.\n
LOCATION:https://researchseminars.org/talk/notts_ag/156/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sokratis Zikas (Poitiers)
DTSTART;VALUE=DATE-TIME:20230720T090000Z
DTEND;VALUE=DATE-TIME:20230720T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/157
DESCRIPTION:Title: On connected algebraic subgroups of groups of birational transformation
s\nby Sokratis Zikas (Poitiers) as part of Online Nottingham algebraic
geometry seminar\n\n\nAbstract\nThe problem of understanding the structur
e of the group of birational transformations $\\mathrm{Bir}(X)$ of a proje
ctive variety $X$ is an old one\, with early results dating all the way ba
ck to the 19th century. In general $\\mathrm{Bir}(X)$ does not admit the s
tructure of an algebraic group\; however one may study algebraic subgroups
of it and how they relate to one another. In the last decade there has be
en a resurgence of results in this area\, mainly due to the use of the mod
ern machinery of the Minimal Model Program and the Sarkisov Program. In th
is talk I will present this modern framework as well as various results ar
ound the study of algebraic subgroups of $\\mathrm{Bir}(X)$ for a Mori fib
er space $X$.\n
LOCATION:https://researchseminars.org/talk/notts_ag/157/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Ovcharenko (Steklov)
DTSTART;VALUE=DATE-TIME:20230928T140000Z
DTEND;VALUE=DATE-TIME:20230928T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/158
DESCRIPTION:Title: Modularity of Landau-Ginzburg models\nby Mikhail Ovcharenko (Steklo
v) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\n
In the past decades\, there were proposed many different inter-related app
roaches to Mirror Symmetry for Fano varieties. The goal of this talk is to
show that in the case of Fano threefolds these approaches are in harmony
with each other. General anticanonical sections of a Fano threefold and ge
neral fibres of its Landau-Ginbzurg model are K3 surfaces\, so it is natur
al to consider Mirror Symmetry for K3 surfaces as well. One of its most in
teresting forms is so called Dolgachev-Nikulin duality: for a lattice $L$
it corresponds to a complete family of $L$-polarized K3 surfaces a complet
e family of $L^*$-polarized K3 surfaces\, where $L^*$ is a dual lattice. F
or any smooth Fano threefold $X$ we show that the polarization of its gene
ral anticanonical section by $\\mathrm{Pic}(X)$ is Dolgachev-Nikulin dual
to the polarization of a general fibre $F$ of its tame compactified toric
Landau-Ginzburg model $Z\\rightarrow\\mathbb{P}^1$ by the (explicitly cons
tructed) lattice of monodromy invariants. Moreover\, if the anticanonical
class of $X$ is very ample\, we prove that the deformation space of pairs
$(Z\, F)$ form a complete family of $\\mathrm{Pic}(X)^*$-polarized K3 surf
aces. As a consequence\, we obtain that for any such Fano threefold $X$ th
e corresponding moduli space of $\\mathrm{Pic}(X)^*$-polarized K3 surfaces
is uniruled. This is a joint work with Charles Doran\, Andrew Harder\, Lu
dmil Katzarkov\, and Victor Przyjalkowski.\n
LOCATION:https://researchseminars.org/talk/notts_ag/158/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Deniz Genlik (Ohio)
DTSTART;VALUE=DATE-TIME:20230914T140000Z
DTEND;VALUE=DATE-TIME:20230914T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/159
DESCRIPTION:Title: Higher genus Gromov-Witten theory of C^n/Z_n: Holomorphic anomaly equat
ions and crepant resolution\nby Deniz Genlik (Ohio) as part of Online
Nottingham algebraic geometry seminar\n\n\nAbstract\nIn this talk\, we pre
sent certain results regarding the higher genus Gromov-Witten theory of $\
\mathbb{C}^n/\\mathbb{Z}_n$ obtained by studying its cohomological field t
heory structure in detail. Holomorphic anomaly equations are certain recur
sive partial differential equations predicted by physicists for the Gromov
-Witten potential of a Calabi-Yau threefold. We prove holomorphic anomaly
equations for $\\mathbb{C}^n/\\mathbb{Z}_n$ for any $n\\ge3$. In other wor
ds\, we present a phenomenon of holomorphic anomaly equations in arbitrary
dimensions\, a result beyond the consideration of physicists. The proof o
f this fact relies on showing that the Gromov-Witten potential of $\\mathb
b{C}^n/\\mathbb{Z}_n$ lies in a certain polynomial ring. Moreover\, we pro
ve an arbitrary genera crepant resolution correspondence for $\\mathbb{C}^
n/\\mathbb{Z}_n$ by showing that its cohomological field theory matches wi
th that of $K\\mathbb{P}^{n-1}$\, where $K\\mathbb{P}^{n-1}$ is the total
space of the canonical bundle of $\\mathbb{P}^{n-1}$. More precisely\, we
show that the Gromov-Witten potential of $K\\mathbb{P}^{n-1}$ also lies in
a similar polynomial ring\, and we show that it matches with the Gromov-W
itten potential of $\\mathbb{C}^n/\\mathbb{Z}_n$ under an isomorphism of t
hese polynomial rings. This talk is based on the joint works arXiv:2301.08
389 and arXiv:2308.00780 with Hsian-Hua Tseng.\n
LOCATION:https://researchseminars.org/talk/notts_ag/159/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nawaz Sultani (Michigan)
DTSTART;VALUE=DATE-TIME:20231005T140000Z
DTEND;VALUE=DATE-TIME:20231005T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/160
DESCRIPTION:Title: Gromov-Witten theory of non-convex complete intersections\nby Nawaz
Sultani (Michigan) as part of Online Nottingham algebraic geometry semina
r\n\n\nAbstract\nFor a convex complete intersection $X$\, the Quantum Lefs
hetz Hyperplane theorem (QLHT) relates the Gromov-Witten (GW) invariants o
f $X$ to those of the ambient space. This is most notably used in the proo
f of genus $0$ mirror symmetry for complete intersections in toric varieti
es\, since the invariants of the ambient toric variety are easier to compu
te. However\, orbifold complete intersections are rarely convex\, hence QL
HT often fails even in genus $0$. In this talk\, I will showcase a method
to compute the genus $0$ GW invariants for orbifold complete intersections
in stack quotients of the form $[V/\\!\\!/G]$\, regardless of convexity c
onditions. The invariants computed by this method include all the invarian
ts one expects of QLHT\, even when QLHT fails. This talk will include resu
lts from joint works with Felix Janda (Notre Dame) and Yang Zhou (Fudan)\,
and with Rachel Webb (Berkeley).\n\n(Note: This is a repeat of Nawaz's ta
lk on 10 August\, which had to be abandoned part-way through due to severe
weather causing technical issues.)\n
LOCATION:https://researchseminars.org/talk/notts_ag/160/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lena Ji (Michigan)
DTSTART;VALUE=DATE-TIME:20231110T150000Z
DTEND;VALUE=DATE-TIME:20231110T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/161
DESCRIPTION:Title: Symmetries of Fano varieties\nby Lena Ji (Michigan) as part of Onli
ne Nottingham algebraic geometry seminar\n\n\nAbstract\nProkhorov and Shra
mov showed that the BAB conjecture (later proven by Birkar) implies the Jo
rdan property for automorphism groups of complex Fano varieties. This prop
erty in particular gives an upper bound on the size of semisimple groups a
cting faithfully on $n$-dimensional complex Fano varieties\, and this boun
d only depends on $n$. We investigate the geometric consequences of an act
ion by a large semisimple group - in particular the symmetric group. We gi
ve an effective upper bound on the size of these symmetric group actions\,
and we obtain optimal bounds for certain classes of varieties (toric vari
eties and Fano weighted complete intersections). Finally\, we draw a conne
ction between large symmetric actions and boundedness of varieties\, by sh
owing that the maximally symmetric Fano fourfolds form a bounded family. T
his work is joint with Louis Esser and Joaquín Moraga.\n
LOCATION:https://researchseminars.org/talk/notts_ag/161/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theodoros Papazachariou (Glasgow)
DTSTART;VALUE=DATE-TIME:20230921T090000Z
DTEND;VALUE=DATE-TIME:20230921T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/162
DESCRIPTION:Title: On divisorial stability of finite covers\nby Theodoros Papazachario
u (Glasgow) as part of Online Nottingham algebraic geometry seminar\n\n\nA
bstract\nDivisorial stability of a polarised variety is a stronger - but c
onjecturally equivalent - variant of uniform K-stability introduced by Bou
cksom-Jonsson. Whereas uniform K-stability is defined in terms of test con
figurations\, divisorial stability is defined in terms of convex combinati
ons of divisorial valuations on the variety. In this talk\, I will give a
quick account on divisorial stability\, and then I will describe the behav
iour of divisorial stability under finite group actions. In particular\, I
will show that equivariant divisorial stability of a polarised variety is
equivalent to log divisorial stability of its quotient. I will then use t
his result to give a general construction of equivariantly divisorially st
able polarised varieties. This is joint work with R. Dervan.\n
LOCATION:https://researchseminars.org/talk/notts_ag/162/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuchen Liu (Courant Institute)
DTSTART;VALUE=DATE-TIME:20231012T140000Z
DTEND;VALUE=DATE-TIME:20231012T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/163
DESCRIPTION:Title: Moduli of boundary polarized Calabi-Yau pairs\nby Yuchen Liu (Coura
nt Institute) as part of Online Nottingham algebraic geometry seminar\n\n\
nAbstract\nWhile the theories of KSBA stability and K-stability have been
successful in constructing compact moduli spaces of canonically polarized
varieties and Fano varieties\, respectively\, the case of Calabi-Yau varie
ties remains less well understood. I will discuss a new approach to this p
roblem in the case of boundary polarized Calabi-Yau pairs $(X\,D)$\, i.e.
$X$ is a Fano variety and $D$ is an anticanonical $\\mathbb{Q}$-divisor\,
in which we consider all semi-log-canonical degenerations. One challenge o
f this approach is that the moduli stack can be unbounded. Nevertheless\,
if we consider boundary polarized Calabi-Yau pairs as degenerations of $\\
mathbb{P}^2$ with plane curves\, we show that there exists a projective go
od moduli space despite the unboundedness. This is joint work with K. Asch
er\, D. Bejleri\, H. Blum\, K. DeVleming\, G. Inchiostro\, and X. Wang.\n
LOCATION:https://researchseminars.org/talk/notts_ag/163/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carl Lian (Tufts)
DTSTART;VALUE=DATE-TIME:20231019T140000Z
DTEND;VALUE=DATE-TIME:20231019T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/164
DESCRIPTION:Title: Counting curves on P^r\nby Carl Lian (Tufts) as part of Online Nott
ingham algebraic geometry seminar\n\n\nAbstract\nWe will explain a complet
e solution to the following problem. If $(C\,p_1\,\\ldots\,p_n)$ is a gene
ral curve of genus $g$ and $x_1\,\\ldots\,x_n$ are general points on $\\ma
thbb{P}^r$\, then how many degree $d$ maps $f:C\\to\\mathbb{P}^r$ are ther
e with $f(p_i)=x_i$? These are the "Tevelev degrees" of projective space\,
which were previously known only when $r=1$\, when $d$ is large compared
to $g$\, or virtually in Gromov-Witten theory. Time-permitting\, we will a
lso discuss some partial results when the conditions $f(p_i)=x_i$ are repl
aced by conditions $f(p_i) \\in X_i$\, where the $X_i$ are linear spaces o
f any dimension.\n
LOCATION:https://researchseminars.org/talk/notts_ag/164/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kathlén Kohn (KTH)
DTSTART;VALUE=DATE-TIME:20231026T090000Z
DTEND;VALUE=DATE-TIME:20231026T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/165
DESCRIPTION:Title: Rolling-shutter cameras & Kummer's classification of order-one line con
gruences\nby Kathlén Kohn (KTH) as part of Online Nottingham algebrai
c geometry seminar\n\n\nAbstract\nIn this talk\, we explain how algebraic
geometry can be used to model and understand rolling-shutter cameras. Most
consumer cameras today (e.g. in smartphones) use rolling shutters that do
not capture an image at the same time but rather scan rapidly across the
scene to be captured. When such a camera moves and rotates\, the resulting
picture can show the same 3D point several times\, and straight lines in
3-space become higher-degree curves on the image. The set of light rays th
rough such a camera form an algebraic surface in the Grassmannian of lines
in projective 3-space. Kummer classified such surfaces (classically calle
d line congruence) of order-one in 1866. We explain how Kummer's classific
ation essentially characterizes all rolling-shutter cameras that see a gen
eric 3D point exactly once. When such a camera takes a picture of a line i
n 3-space\, the image is a high-degree curve. We compute that degree D in
terms of the movement and rotation of the camera\, and show that the image
curve has multiplicity D-1 at one special point on the image plane. This
talk is based on ongoing work with Marvin Hahn\, Orlando Marigliano\, and
Tomas Pajdla.\n
LOCATION:https://researchseminars.org/talk/notts_ag/165/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haidong Liu (Sun Yat-sen)
DTSTART;VALUE=DATE-TIME:20231207T100000Z
DTEND;VALUE=DATE-TIME:20231207T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/166
DESCRIPTION:Title: On Miyaoka type and Kawamata-Miyaoka type inequalities\nby Haidong
Liu (Sun Yat-sen) as part of Online Nottingham algebraic geometry seminar\
n\n\nAbstract\nIn the classification theory of varieties with nef anti-can
onical divisors\, Miyaoka type and Kawamata-Miyaoka type inequalities whic
h concern about the relations between the first and second Chern classes p
lay an important role. In this talk\, I will show some recent progress on
these inequalities and their application on the classification of 3-folds
with nef anti-canonical divisors. Part of these works is jointed with Masa
taka Iwai and Chen Jiang\, and part is jointed with Jie Liu.\n
LOCATION:https://researchseminars.org/talk/notts_ag/166/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chengxi Wang (UCLA)
DTSTART;VALUE=DATE-TIME:20231116T160000Z
DTEND;VALUE=DATE-TIME:20231116T170000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/167
DESCRIPTION:Title: Fano varieties with extreme behavior\nby Chengxi Wang (UCLA) as par
t of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nIt is att
ractive to classify Fano varieties with various types of singularities tha
t originated from the minimal model program. For a Fano variety\, the Fano
index is the largest integer $m$ such that the anti-canonical divisor is
$\\mathbb{Q}$-linearly equivalent to m times some Weil divisor. For Fano v
arieties of various singularities\, I show the Fano indexes can grow doubl
e exponentially with respect to the dimension. Those examples are also con
jecturally optimal and have a close connection with Calabi-Yau varieties o
f extreme behavior.\n
LOCATION:https://researchseminars.org/talk/notts_ag/167/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thibaut Delcroix (Montpellier)
DTSTART;VALUE=DATE-TIME:20231123T150000Z
DTEND;VALUE=DATE-TIME:20231123T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/168
DESCRIPTION:Title: Fano spherical varieties of small dimension and rank\nby Thibaut De
lcroix (Montpellier) as part of Online Nottingham algebraic geometry semin
ar\n\n\nAbstract\nA spherical variety $(X\,G)$ is a normal complex algebra
ic variety $X$ equipped with the action of a connected complex reductive g
roup $G$ such that a Borel subgroup $B$ of $G$ acts with an open dense orb
it. The rank of $(X\,G)$ is the rank of the lattice of $B$-eigenvalues in
the $B$-module of rational functions on $X$. I will present the classifica
tion of the 260 locally factorial Fano spherical varieties $(X\,G)$ of dim
ension four and of rank two or less\, obtained in a joint work with Pierre
-Louis Montagard. Those spherical varieties are described via combinatoria
l data\, from which it is easy to read off geometric properties of the und
erlying variety $X$\, such as the Picard rank\, anticanonical degree\, K-s
tability\, etc.\n
LOCATION:https://researchseminars.org/talk/notts_ag/168/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jennifer Li (Princeton)
DTSTART;VALUE=DATE-TIME:20231130T150000Z
DTEND;VALUE=DATE-TIME:20231130T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/169
DESCRIPTION:Title: On the cone conjecture for log Calabi-Yau mirrors of Fano 3-folds\n
by Jennifer Li (Princeton) as part of Online Nottingham algebraic geometry
seminar\n\n\nAbstract\nLet $Y$ be a smooth projective 3-fold admitting a
K3 fibration $f: Y \\rightarrow \\mathbb{P}^{1}$ with $-K_{Y} = f^{\\ast}
\\mathcal{O}(1)$. We show that the pseudoautomorphism group of $Y$ acts wi
th finitely many orbits on the codimension one faces of the movable cone i
f $H^{3}(Y\, \\mathbb{C}) = 0$\, confirming a special case of the Kawamata
-Morrison-Totaro cone conjecture. In Coates-Corti-Galkin-Kasprzyk 2016\, P
rzyjalkowski 2018\, and Cheltsov-Przyjalkowski 2018\, the authors construc
t log Calabi-Yau 3-folds with K3 fibrations satisfying the hypotheses of o
ur theorem as the mirrors of Fano 3-folds.\n
LOCATION:https://researchseminars.org/talk/notts_ag/169/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kimoi Kemboi (Cornell)
DTSTART;VALUE=DATE-TIME:20231214T160000Z
DTEND;VALUE=DATE-TIME:20231214T170000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/170
DESCRIPTION:Title: Exceptional collections and window categories\nby Kimoi Kemboi (Cor
nell) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstrac
t\nThe derived category of a variety is a crucial algebraic invariant with
several profound implications on the geometry of the underlying variety.
This talk will focus on a particular structure of derived categories calle
d a full exceptional collection. We will discuss the landscape of full exc
eptional collections and its connections to geometry\, then explore how to
produce them for linear GIT quotients using ideas from "window" categorie
s and equivariant geometry. As an example\, we will consider a large class
of linear GIT quotients by a reductive group of rank two\, where this mac
hinery produces full exceptional collections consisting of tautological ve
ctor bundles. This talk is based on joint work with Daniel Halpern-Leistne
r.\n
LOCATION:https://researchseminars.org/talk/notts_ag/170/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Swaraj Sridhar Parde (Michigan)
DTSTART;VALUE=DATE-TIME:20240118T160000Z
DTEND;VALUE=DATE-TIME:20240118T170000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/171
DESCRIPTION:Title: A Frobenius version of Tian's alpha invariant\, and the F-signature of
Fano varieties\nby Swaraj Sridhar Parde (Michigan) as part of Online N
ottingham algebraic geometry seminar\n\n\nAbstract\nThe Alpha invariant of
a complex Fano manifold was introduced by Tian to detect its $K$-stabilit
y\, an algebraic condition that implies the existence of a Kähler–Einst
ein metric. Demailly later reinterpreted the Alpha invariant algebraically
in terms of a singularity invariant called the log canonical threshold. I
n this talk\, we will present an analog of the Alpha invariant for Fano va
rieties in positive characteristics\, called the Frobenius-Alpha invariant
. This analog is obtained by replacing "log canonical threshold" with "$F$
-pure threshold"\, a singularity invariant defined using the Frobenius map
. We will review the definition of these invariants and the relations betw
een them. The main theorem proves some interesting properties of the Frobe
nius-Alpha invariant\; namely\, we will show that its value is always at m
ost $1/2$ and make connections to a version of local volume called the $F$
-signature. Time permitting\, we will also discuss the semicontinuity prop
erties of the Frobenius-Alpha invariant.\n
LOCATION:https://researchseminars.org/talk/notts_ag/171/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Calla Tschanz (Jagiellonian)
DTSTART;VALUE=DATE-TIME:20240125T100000Z
DTEND;VALUE=DATE-TIME:20240125T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/172
DESCRIPTION:Title: Expansions for Hilbert schemes of points on semistable degenerations\nby Calla Tschanz (Jagiellonian) as part of Online Nottingham algebraic
geometry seminar\n\n\nAbstract\nLet $X\\rightarrow C$ be a projective fami
ly of surfaces over a curve with smooth general fibres and simple normal c
rossing singularity in the special fibre $X_0$. We construct a good compac
tification of the moduli space of relative length $n$ zero-dimensional sub
schemes on $X\\setminus X_0$ over $C\\setminus\\{0\\}$. In order to produc
e this compactification we study expansions of the special fibre $X_0$ tog
ether with various GIT stability conditions\, generalising the work of Gul
brandsen-Halle-Hulek who use GIT to offer an alternative approach to the w
ork of Li-Wu for Hilbert schemes of points on simple degenerations. We con
struct stacks which we prove to be equivalent to the underlying stack of s
ome choices of logarithmic Hilbert schemes produced by Maulik-Ranganathan.
\n
LOCATION:https://researchseminars.org/talk/notts_ag/172/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Annamaria Ortu (Gothenburg)
DTSTART;VALUE=DATE-TIME:20240201T100000Z
DTEND;VALUE=DATE-TIME:20240201T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/173
DESCRIPTION:Title: Moduli of stable fibrations\nby Annamaria Ortu (Gothenburg) as part
of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nSmooth fib
rations between projective varieties can be thought of as both a generalis
ation of vector bundles and as a way of studying the behaviour of projecti
ve varieties in families. On holomorphic vector bundles\, the Hitchin-Koba
yashi correspondence establishes an equivalence between slope-stability an
d the existence of canonical connections\, called Hermite-Einstein connect
ions. A foundational result in the theory of vector bundles is the constru
ction of a moduli space of stable vector bundles\; such a moduli space can
also be constructed analytically through the Hitchin-Kobayashi correspond
ence. On smooth fibrations we will define an analytic stability condition
which we use to construct a moduli space of analytically stable smooth fib
rations.\n
LOCATION:https://researchseminars.org/talk/notts_ag/173/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisa Marquand (Courant Institute)
DTSTART;VALUE=DATE-TIME:20240229T150000Z
DTEND;VALUE=DATE-TIME:20240229T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/174
DESCRIPTION:Title: The defect of a cubic threefold\nby Lisa Marquand (Courant Institut
e) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\n
The defect of a cubic threefold with isolated singularities is a measure o
f the failure of Poincare duality\, and also the failure to be $\\mathbb{Q
}$-factorial. From the work of Cheltsov\, a cubic threefold with only noda
l singularities is $\\mathbb{Q}$-factorial if and only if there are at mos
t 5 nodes. We investigate the defect of cubic threefolds with worse than n
odal isolated singularities\, and provide a geometric method to compute th
is global invariant. One can then compute the Mixed Hodge structure on the
middle cohomology of the cubic threefold\, in terms of the defect (a glob
al invariant) and local invariants (Du Bois and Link invariants) determine
d by the singularity types. We then relate the defect to geometric propert
ies of the cubic threefold\, showing it is positive if and only if the cub
ic contains a plane or a rational normal cubic scroll. The focus of this w
ork is to provide more insight into the existence of reducible fibers for
compactified intermediate jacobian fibrations associated to a smooth (not
necessarily general) cubic fourfold. This is joint work with Sasha Viktoro
va.\n
LOCATION:https://researchseminars.org/talk/notts_ag/174/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduardo da Silva (Universite Paris Saclay)
DTSTART;VALUE=DATE-TIME:20240328T100000Z
DTEND;VALUE=DATE-TIME:20240328T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/175
DESCRIPTION:Title: Log Calabi-Yau geometry and Cremona maps\nby Eduardo da Silva (Univ
ersite Paris Saclay) as part of Online Nottingham algebraic geometry semin
ar\n\n\nAbstract\nIn the context of algebraic geometry\, decomposition and
inertia groups are special subgroups of the Cremona group which preserve
a certain subvariety of $\\mathbb{P}^n$ as a set and pointwise\, respectiv
ely. These groups were and still are classic objects of study in the area\
, with explicit descriptions in several instances. In the particular case
where this fixed subvariety is a hypersurface of degree $n+1$\, we have th
e notion of Calabi-Yau pair which allows us to use new tools to deal with
the study of these groups and one of them is the so-called volume preservi
ng Sarkisov Program. Using this approach we prove that an appropriate algo
rithm of the Sarkisov Program in dimension 2 applied to an element of the
decomposition group of a nonsingular plane cubic is automatically volume p
reserving. From this\, we deduce some properties of the (volume preserving
) Sarkisov factorization of its elements. Regarding now a 3-dimensional co
ntext\, we give a description of which toric weighted blowups of a point a
re volume preserving and among them\, which ones will initiate a volume pr
eserving Sarkisov link from a Calabi-Yau pair $(\\mathbb{P}^3\,D)$ of core
gularity 2. In this case\, $D$ is necessarily an irreducible normal quarti
c surface having canonical singularities. This last result enhances and ex
tends the recent works of Guerreiro and Araujo\, Corti and Massarenti in a
log Calabi-Yau geometrical perspective\, and it is a possible starting po
int to study the decomposition group of such quartics.\n
LOCATION:https://researchseminars.org/talk/notts_ag/175/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Denisova (Edinburgh)
DTSTART;VALUE=DATE-TIME:20240404T090000Z
DTEND;VALUE=DATE-TIME:20240404T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/176
DESCRIPTION:Title: Family 3-5 and $\\delta$-invariant of polarized del Pezzo surfaces\
nby Elena Denisova (Edinburgh) as part of Online Nottingham algebraic geom
etry seminar\n\n\nAbstract\nIt is known that a smooth Fano variety admits
a Kahler Einstein metric if and only if it is K-polystable. For two-dimens
ional Fano varieties (del Pezzo surfaces) Tian and Yau proved that a smoot
h del Pezzo surface is K-polystable if and only if it is not a blow up of
$\\mathbb{P}^2$ in one or two points. A lot of research was done for three
folds however\, not everything is known and often the problem can be reduc
ed to computing $\\delta$-invariant of (possibly singular) del Pezzo surfa
ces. In my talk\, I will present an explicit example of such computation.\
n
LOCATION:https://researchseminars.org/talk/notts_ag/176/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrés Jaramillo Puentes (Duisburg-Essen)
DTSTART;VALUE=DATE-TIME:20240418T090000Z
DTEND;VALUE=DATE-TIME:20240418T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/177
DESCRIPTION:Title: Examples of Enumerative Problems for Arbitrary Fields\nby Andrés J
aramillo Puentes (Duisburg-Essen) as part of Online Nottingham algebraic g
eometry seminar\n\n\nAbstract\nOver the complex numbers the solutions to e
numerative problems are invariant: the number of solutions of a polynomial
equation or polynomial system\, the number of lines or curves in a surfac
e\, etc. Over the real numbers such invariance fails. However\, the signed
count of solutions may lead to numerical invariants: Descartes' rule of s
igns\, Poincaré-Hopf theorem\, real curve-counting invariants.\n\nSince m
any of these problems have a geometric nature\, one may ask the same probl
ems for arbitrary fields. Motivic homotopy theory allows to do enumerative
geometry over an arbitrary base\, leading to additional arithmetic and ge
ometric information.\n\nThe goal of this talk is to illustrate a generaliz
ed notion of sign that allows us to state a motivic version of classical p
roblems: the number of lines on cubic surfaces\, the Bézout theorem\, and
the curve-counting invariants.\n
LOCATION:https://researchseminars.org/talk/notts_ag/177/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mingchen Xia (IMJ-PRG)
DTSTART;VALUE=DATE-TIME:20240509T090000Z
DTEND;VALUE=DATE-TIME:20240509T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/178
DESCRIPTION:Title: Partial Okounkov bodies and toric geometry\nby Mingchen Xia (IMJ-PR
G) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\n
Given a big line bundle $L$ on a projective manifold\, Lazarsfeld–Mustat
ă and Kaveh–Khovanskii introduced method of constructing convex bodies
associated with $L$. These convex bodies are known as Okounkov bodies. Whe
n $L$ is endowed with a singular positive Hermitian metric $h$\, I will ex
plain how to construct smaller convex bodies from the data $(L\,h)$. These
convex bodies play important roles in the study of the singularities of $
h$. As an application\, I will explain a non-trivial application in toric
geometry due to Yi Yao.\n
LOCATION:https://researchseminars.org/talk/notts_ag/178/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Inder Kaur (Glasgow)
DTSTART;VALUE=DATE-TIME:20240523T090000Z
DTEND;VALUE=DATE-TIME:20240523T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T135815Z
UID:notts_ag/179
DESCRIPTION:Title: Examples of varieties satisfying multiplicative Chow-Kunneth decomposit
ion\nby Inder Kaur (Glasgow) as part of Online Nottingham algebraic ge
ometry seminar\n\n\nAbstract\nThe Chow ring of a variety encodes a lot of
information about its geometry and is the subject of many interesting conj
ectures. A conjecture of Shen-Vial predicts that the Chow ring of any hype
rkaehler variety admits a multiplicative Chow-Kunneth decomposition. I wil
l begin by recalling some of the basic properties of the Chow ring\, the o
rigins of the conjecture and then discuss some of the known cases. I will
discuss in detail the case of Hilbert schemes of points on a K3 surface. T
his is joint work in progress with R. Laterveer.\n
LOCATION:https://researchseminars.org/talk/notts_ag/179/
END:VEVENT
END:VCALENDAR