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BEGIN:VEVENT
SUMMARY:Tim Logvinenko (Cardiff)
DTSTART;VALUE=DATE-TIME:20200423T120000Z
DTEND;VALUE=DATE-TIME:20200423T130000Z
DTSTAMP;VALUE=DATE-TIME:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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\nInteractive livestream: https://teams.microsoft.com/l/meetup-join/1
9%3abc0bccd250d74459ac05c0b3e0ff9b76%40thread.tacv2/1627325743532?context=
%7b%22Tid%22%3a%2267bda7ee-fd80-41ef-ac91-358418290a1e%22%2c%22Oid%22%3a%2
22dbd114f-1c6d-4e8b-aab9-fadd00bd8602%22%7d\n\nAbstract\nMatching fields w
ere introduced by Sturmfels and Zelevinsky to study certain Newton polytop
es and more recently have been shown to give rise to toric degenerations o
f various families of varieties. Whenever a matching field gives rise to a
toric degeneration of the Grassmannian\, the polytope of the associated t
oric variety coincides with the matching field polytope. In this talk I wi
ll describe combinatorial mutations of matching field polytopes. We will e
xplore properties of polytopes which are preserved by mutation\, and we wi
ll see that property of giving rise to a toric degeneration is preserved b
y mutations. This gives us an easy way to generate new families of toric d
egenerations of the Grassmannian from old. This talk is based on joint wor
k with Akihiro Higashitani and Fatemeh Mohammadi.\n
LOCATION:https://researchseminars.org/talk/notts_ag/66/
URL:https://teams.microsoft.com/l/meetup-join/19%3abc0bccd250d74459ac05c0b
3e0ff9b76%40thread.tacv2/1627325743532?context=%7b%22Tid%22%3a%2267bda7ee-
fd80-41ef-ac91-358418290a1e%22%2c%22Oid%22%3a%222dbd114f-1c6d-4e8b-aab9-fa
dd00bd8602%22%7d
END:VEVENT
BEGIN:VEVENT
SUMMARY:DongSeon Hwang (Ajou)
DTSTART;VALUE=DATE-TIME:20210826T090000Z
DTEND;VALUE=DATE-TIME:20210826T100000Z
DTSTAMP;VALUE=DATE-TIME:20210804T225605Z
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\nInteractive livestream: https://teams.microsoft.com/l/meetup-join/19%3a
bc0bccd250d74459ac05c0b3e0ff9b76%40thread.tacv2/1627845829084?context=%7b%
22Tid%22%3a%2267bda7ee-fd80-41ef-ac91-358418290a1e%22%2c%22Oid%22%3a%222db
d114f-1c6d-4e8b-aab9-fadd00bd8602%22%7d\n\nAbstract\nI will introduce the
notion of cascades of singular rational surfaces of Picard number one\, wh
ich consists of a sequence of special birational morphisms\, and then disc
uss some applications in the toric case\, Fano case\, and (log) general ty
pe case. The latter application is closely related to algebraic Montgomery
-Yang problem\, conjectured by Kollár.\n
LOCATION:https://researchseminars.org/talk/notts_ag/67/
URL:https://teams.microsoft.com/l/meetup-join/19%3abc0bccd250d74459ac05c0b
3e0ff9b76%40thread.tacv2/1627845829084?context=%7b%22Tid%22%3a%2267bda7ee-
fd80-41ef-ac91-358418290a1e%22%2c%22Oid%22%3a%222dbd114f-1c6d-4e8b-aab9-fa
dd00bd8602%22%7d
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chengxi Wang (UCLA)
DTSTART;VALUE=DATE-TIME:20210708T140000Z
DTEND;VALUE=DATE-TIME:20210708T150000Z
DTSTAMP;VALUE=DATE-TIME:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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:20210804T225605Z
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
\nInteractive livestream: https://teams.microsoft.com/l/meetup-join/19%3ab
c0bccd250d74459ac05c0b3e0ff9b76%40thread.tacv2/1626262368854?context=%7b%2
2Tid%22%3a%2267bda7ee-fd80-41ef-ac91-358418290a1e%22%2c%22Oid%22%3a%222dbd
114f-1c6d-4e8b-aab9-fadd00bd8602%22%7d\n\nAbstract\nThe toric contact cycl
es are loci in the moduli space of curves that parameterize those curves t
hat admit a morphism to a fixed toric variety\, with prescribed tangency d
ata with the toric boundary. The cycles are the fundamental building block
s in higher genus logarithmic Gromov-Witten theory and are higher dimensio
nal analogues of the double ramification cycles\, which have been studied
intensely in the last decade. In recent work\, Sam Molcho (ETH) and I prov
ed that these cycles lie in the tautological part of the Chow ring of the
moduli space of curves. A lesson I learned from this project\, and earlier
work with Navid Nabijou (Cambridge)\, is that it can be quite profitable
to blend Fulton’s analysis of blowups and strict transforms with logarit
hmic Gromov-Witten theory and its virtual class. I’ll try to give a sens
e of the basic geometric phenomena\, and point to some other places where
they come up.\n
LOCATION:https://researchseminars.org/talk/notts_ag/71/
URL:https://teams.microsoft.com/l/meetup-join/19%3abc0bccd250d74459ac05c0b
3e0ff9b76%40thread.tacv2/1626262368854?context=%7b%22Tid%22%3a%2267bda7ee-
fd80-41ef-ac91-358418290a1e%22%2c%22Oid%22%3a%222dbd114f-1c6d-4e8b-aab9-fa
dd00bd8602%22%7d
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Addington (Oregon)
DTSTART;VALUE=DATE-TIME:20210923T150000Z
DTEND;VALUE=DATE-TIME:20210923T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T225605Z
UID:notts_ag/73
DESCRIPTION:by Nicolas Addington (Oregon) as part of Online Nottingham alg
ebraic geometry seminar\n\nAbstract: TBA\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:20210804T225605Z
UID:notts_ag/74
DESCRIPTION:by Julius Giesler (Tübingen) as part of Online Nottingham alg
ebraic geometry seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/notts_ag/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alastair Craw (Bath)
DTSTART;VALUE=DATE-TIME:20211014T090000Z
DTEND;VALUE=DATE-TIME:20211014T100000Z
DTSTAMP;VALUE=DATE-TIME:20210804T225605Z
UID:notts_ag/75
DESCRIPTION:by Alastair Craw (Bath) as part of Online Nottingham algebraic
geometry seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/notts_ag/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Sophie Kaloghiros (Brunel)
DTSTART;VALUE=DATE-TIME:20211021T090000Z
DTEND;VALUE=DATE-TIME:20211021T100000Z
DTSTAMP;VALUE=DATE-TIME:20210804T225605Z
UID:notts_ag/76
DESCRIPTION:by Anne-Sophie Kaloghiros (Brunel) as part of Online Nottingha
m algebraic geometry seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/notts_ag/76/
END:VEVENT
END:VCALENDAR