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BEGIN:VEVENT
SUMMARY:Hulya Argüz (Université de Versailles)
DTSTART;VALUE=DATE-TIME:20200427T130000Z
DTEND;VALUE=DATE-TIME:20200427T143000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/1
DESCRIPTION:Title: Tropical enumeration of real log curves in toric varieti
es\nby Hulya Argüz (Université de Versailles) as part of Real and co
mplex Geometry\n\n\nAbstract\nWe define real log curves in toric varieties
and set up a well-defined counting problem for them using the degeneratio
n approach of Nishinou--Siebert. We then investigate the tropical analogue
s of such curves to obtain a formula for their counts from the tropical de
scription. Focusing on the two dimensional case\, we also explain how to c
apture Welschinger signs from a local analysis of the degeneration\, to ob
tain log Welschinger invariants. This is joint work with Pierrick Bousseau
.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ethan Cotterill (Universidade Federal Fluminense)
DTSTART;VALUE=DATE-TIME:20200511T130000Z
DTEND;VALUE=DATE-TIME:20200511T143000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/2
DESCRIPTION:Title: Rational curves with hyperelliptic singularities\nby
Ethan Cotterill (Universidade Federal Fluminense) as part of Real and com
plex Geometry\n\n\nAbstract\nWe study singular rational curves in projecti
ve space\, deducing conditions on their parameterizations from the value s
emigroups of their singularities. Here we focus on rational curves with cu
sps whose semigroups are of hyperelliptic type. We prove that a genus-g hy
perelliptic singularity imposes at least (n-1)g conditions on rational cur
ves of sufficiently large fixed degree in P^n\, and we prove that this bou
nd is exact when g is small. We also provide evidence for a conjectural ge
neralization of this bound for rational curves with cusps with arbitrary v
alue semigroup S. Our conjecture\, if true\, produces infinitely many new
examples of reducible Severi-type varieties M^n_{d\,g} of holomorphic maps
P^1 -> P^n with images of degree d and arithmetic genus g.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boulos El Hilany (Johannes Radon Institute for Computational and A
pplied Mathematics\, Linz)
DTSTART;VALUE=DATE-TIME:20200525T130000Z
DTEND;VALUE=DATE-TIME:20200525T143000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/4
DESCRIPTION:Title: Counting isolated points outside the image of a polynomi
al map\nby Boulos El Hilany (Johannes Radon Institute for Computationa
l and Applied Mathematics\, Linz) as part of Real and complex Geometry\n\n
\nAbstract\nA dominant polynomial map from the complex plane to itself giv
es rise to a finite set of curves and isolated points outside its image. Z
. Jelonek provided an upper bound on the number of such isolated points th
at is quadratic in\, and depends only on\, the degrees of the polynomials
involved. I will introduce in this talk a large family of dominant non-pro
per maps above for which this upper bound is linear in the degrees. Moreov
er\, I will illustrate constructions proving asymptotical sharpness up to
multiplication by a constant.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Arnal (Institut de Mathematiques de Jussieu)
DTSTART;VALUE=DATE-TIME:20201022T130000Z
DTEND;VALUE=DATE-TIME:20201022T143000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/5
DESCRIPTION:Title: Families of real projective algebraic hypersurfaces with
large asymptotic Betti numbers\nby Charles Arnal (Institut de Mathema
tiques de Jussieu) as part of Real and complex Geometry\n\n\nAbstract\nWe
describe a recursive method for constructing a family of real projective a
lgebraic hypersurfaces in ambient dimension $n$ from families of such hype
rsurfaces in ambient dimensions $k=1\,\\ldots\,n-1$. The asymptotic Betti
numbers of real parts of the resulting family can then be described in ter
ms of the asymptotic Betti numbers of the real parts of the families used
as ingredients. The algorithm is based on Viro's Patchwork and inspired by
I. Itenberg's and O. Viro's construction of asymptotically maximal famili
es in arbitrary dimension. Using it\, we prove that for any $n$ and $i=0\,
\\ldots\,n-1$\, there is a family of asymptotically maximal real projectiv
e algebraic hypersurfaces $\\{X^n_d\\}_d$ in $\\R \\PP ^n$ such that the $
i$-th Betti numbers $b_i(\\R X^n_d)$ are asymptotically strictly greater t
han the $(i\,n-1-i)$-th Hodge numbers $h^{i\,n-1-i}(\\C X^n _d)$. We also
build families of real projective algebraic hypersurfaces whose real parts
have asymptotic (in the degree $d$) Betti numbers that are asymptotically
(in the ambient dimension $n$) very large.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stepan Orevkov (Steklov Math. Institute and Universite Paul Sabati
er\, Toulouse)
DTSTART;VALUE=DATE-TIME:20201029T140000Z
DTEND;VALUE=DATE-TIME:20201029T153000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/6
DESCRIPTION:Title: On real algebraic and real pseudoholomorphic curves in $
RP^2$\nby Stepan Orevkov (Steklov Math. Institute and Universite Paul
Sabatier\, Toulouse) as part of Real and complex Geometry\n\n\nAbstract\nI
will present an inequality for the isotopy type of a plane non-singular r
eal algebraic curve endowed with a complex orientation (i.e.\, for its com
plex scheme according to Rokhlin's terminology) which implies in particula
r that an infinite series of complex schemes are realizable pseudoholomorp
hically but not algebraically.\nThese are the first known examples of this
kind for complex schemes of non-singular curves in $RP^2$.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Blomme (Universite de Neuchatel)
DTSTART;VALUE=DATE-TIME:20201105T140000Z
DTEND;VALUE=DATE-TIME:20201105T153000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/7
DESCRIPTION:Title: Refined count of rational tropical curves in arbitrary d
imension\nby Thomas Blomme (Universite de Neuchatel) as part of Real a
nd complex Geometry\n\n\nAbstract\nIn this talk we will introduce a refine
d multiplicity for rational tropical curves in any dimension. This multipl
icity generalizes the multiplicity of Block-Göttsche for planar tropical
curves. We also show that the count of solutions to some general tropical
enumerative problem using this new multiplicity leads tropical refined inv
ariants\, hinting toward the existence of classical refined invariants for
classical rational curves.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arielle Leitner (Weizmann Institute of Science)
DTSTART;VALUE=DATE-TIME:20201112T140000Z
DTEND;VALUE=DATE-TIME:20201112T153000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/8
DESCRIPTION:Title: Deformations of Generalized Cusps on Convex Projective M
anifolds\nby Arielle Leitner (Weizmann Institute of Science) as part o
f Real and complex Geometry\n\n\nAbstract\nConvex projective manifolds are
a generalization of hyperbolic manifolds. Koszul showed that the set of h
olonomies of convex projective structures on a compact manifold is open in
the representation variety. We will describe an extension of this result
to convex projective manifolds whose ends are generalized cusps\, due to C
ooper-Long-Tillmann. Generalized cusps are certain ends of convex projecti
ve manifolds. They may contain both hyperbolic and parabolic elements. We
will describe their classification (due to Ballas-Cooper-Leitner)\, and ex
plain how generalized cusps turn out to be deformations of cusps of hyperb
olic manifolds. We will also explore the moduli space of generalized cusps
\, it is a semi-algebraic set of dimension n^2-n\, contractible\, and may
be studied using several different invariants. For the case of three manif
olds\, the moduli space is homeomorphic to R^2 times a cone on a solid tor
us.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Ancona (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20201126T140000Z
DTEND;VALUE=DATE-TIME:20201126T153000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/9
DESCRIPTION:Title: Exponential rarefaction of maximal hypersurfaces\nby
Michele Ancona (Tel Aviv University) as part of Real and complex Geometry
\n\n\nAbstract\nSmith-Thom's inequality tells us that the sum of Betti num
bers of the real locus of a real algebraic variety is always smaller than
or equal to the sum of Betti numbers of its complex locus. In the case of
equality\, the real algebraic variety is called maximal. Given a real holo
morphic line bundle L over a real algebraic variety X\, I will prove that
the probability that a real holomorphic section of L^d defines a maximal h
ypersurface tends to 0 exponentially fast when d tends to infinity.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Benoist (ENS\, Paris)
DTSTART;VALUE=DATE-TIME:20210318T140000Z
DTEND;VALUE=DATE-TIME:20210318T153000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/10
DESCRIPTION:Title: Rational curves on real algebraic varieties\nby Oli
vier Benoist (ENS\, Paris) as part of Real and complex Geometry\n\n\nAbstr
act\nLet X be a smooth projective real algebraic variety. When is it possi
ble to approximate loops in the real locus X(R) by real loci of rational c
urves on X? In this talk\, I will provide a positive answer for a class of
varieties that includes cubic hypersurfaces and compactifications of homo
geneous spaces under connected linear algebraic groups. This is joint work
with Olivier Wittenberg.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier de Gaay Fortman (ENS\, Paris)
DTSTART;VALUE=DATE-TIME:20210311T140000Z
DTEND;VALUE=DATE-TIME:20210311T153000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/11
DESCRIPTION:Title: Real Noether-Lefschetz loci and density of non-simple a
belian varieties over the real numbers\nby Olivier de Gaay Fortman (EN
S\, Paris) as part of Real and complex Geometry\n\n\nAbstract\nSometimes t
he geometry of an algebraic variety poses restrictions on the geometry of
its algebraic subvarieties. A beautiful example is the Noether-Lefschetz T
heorem which states that on a general complex algebraic surface of degree
greater than three in three dimensional projective space\, any curve is ob
tained as a complete intersection of the surface with another hypersurface
. In spite of this\, Green's density criterion enabled Ciliberto\, Harris
and Miranda to prove that the Noether-Lefschetz locus is dense for the Euc
lidean topology in the space of all smooth degree d > 3 complex polynomial
s. Over the real numbers\, things are more complicated. The general real h
ypersurface in P^3 of degree larger than three still has Picard rank one b
ut real surfaces with jumping Picard rank are not dense at all in the spac
e of real smooth degree d > 3 polynomials: the latter is not connected and
the real Noether-Lefschetz locus can miss a connected component entirely.
There is a density criterion but it is much harder to fulfill and can onl
y be applied to one component at a time. Our goal in this talk is to pose
an analogous question in the setting of real abelian varieties and to prov
e that in that situation\, none of these problems occur. Fixing natural nu
mbers g\, k\, and a polarized family of abelian varieties of dimension g d
efined over the real numbers\, when are real (resp. complex) abelian varie
ties that contain a real (resp. complex) abelian subvariety of dimension k
dense in the set of real (resp. complex) points of the base? For each of
these densities there is a natural criterion and surprisingly\, they are t
he same. Various applications are given along these lines\, such as densit
y of such loci in moduli spaces of principally polarized real abelian vari
eties\, real algebraic curves\, and real plane curves.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Tyomkin (Ben-Gurion University)
DTSTART;VALUE=DATE-TIME:20210429T130000Z
DTEND;VALUE=DATE-TIME:20210429T143000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/12
DESCRIPTION:Title: On (ir)reducibility of Severi varieties on toric surfac
es\nby Ilya Tyomkin (Ben-Gurion University) as part of Real and comple
x Geometry\n\n\nAbstract\nIn my talk I will discuss the problem of irreduc
ibility of families of curves of given degree and genus on toric surfaces.
Such families\, called Severi varieties\, have been intensively studied d
ue to a variety of applications of their geometry to the study of moduli s
paces of curves\, and to various enumerative problems. After reviewing bri
efly known irreducibility results\, I'll describe examples of toric surfac
es admitting reducible Severi varieties\, and introduce certain topologica
l and tropical invariants that allow one to distinguish between different
irreducible components. The talk is based on a joint work with Lionel Lang
.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lev Radzivilovsky (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20210617T130000Z
DTEND;VALUE=DATE-TIME:20210617T143000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/13
DESCRIPTION:Title: Enumeration of rational surfaces and moduli spaces of c
onfigurations of points in the projective plane\nby Lev Radzivilovsky
(Tel Aviv University) as part of Real and complex Geometry\n\n\nAbstract\n
We discuss the problem of enumerating rational surfaces in 3-dimensional p
rojective space\, as an analogue of Gromov-Witten invariants. It leads nat
urally to moduli spaces of cofigurations of $n$ marked points in projectiv
e planes. We discuss the "Chow quotients" of Kapranov\, and present a new
version of this construction which gives a smooth moduli space for configu
rations of 6 points. We conjecture that the same construction yields a smo
othing of the moduli space of configurations of any number of points in th
e plane. We also briefly present a formula for enumeration of surfaces wit
h a singular line.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:KhazhgaliKozhasov
DTSTART;VALUE=DATE-TIME:20210715T130000Z
DTEND;VALUE=DATE-TIME:20210715T143000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/14
DESCRIPTION:Title: Nodes on quintic spectrahedra\nby KhazhgaliKozhasov
as part of Real and complex Geometry\n\n\nAbstract\nGiven generic real sy
mmetric matrices A\, B\, C of size n x n\, it is of interest to study the
set S of positive-semidefinite matrices of the form Id + x A + y B + z C\,
where x\, y\, z are some real numbers. The set S is a closed convex set i
n R^3\, called a spectrahedron. The Zariski closure of the Eucllidean boun
dary of S is an algebraic surface {(x\,y\,z): det(Id+ x A+y B+ z C)=0}\, w
hich turns out to be always singular. A natural question in real algebraic
geometry is to understand (for a fixed n) possible restrictions on the nu
mbers P\, Q of real singular points\, respectively\, of those singularitie
s that lie on S. In my talk I will discuss this problem for quintic spectr
ahedra (n=5) and present a complete classification of pairs (P\,Q)\, obtai
ned in a joint work with Taylor Brysiewicz and Mario Kummer.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Kerner (Ben-Gurion University)
DTSTART;VALUE=DATE-TIME:20210812T130000Z
DTEND;VALUE=DATE-TIME:20210812T143000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/15
DESCRIPTION:Title: Germs of maps\, group actions and large modules inside
group orbits\nby Dmitry Kerner (Ben-Gurion University) as part of Real
and complex Geometry\n\n\nAbstract\nA map (k^n\,o)-> (k^p\,o) with no cri
tical point at the origin can be rectified to a linear map. Maps with crit
ical points have rich structure and are studied up to the groups of right/
left-right/contact equivalence. The group orbits are complicated and are t
raditionally studied via their tangent space. This transition is classical
ly done by vector fields integration\, thus binding the theory to the real
/complex case. I will present the new approach to this subject. One studie
s the maps of germs of Noetherian schemes\, in any characteristic. The cor
responding groups of equivalence admit `good' tangent spaces. The submodul
es of the tangent spaces lead to submodules of the group orbits. This allo
ws to bring these maps to `convenient' forms. For example\, we get the (re
lative) finite determinacy\, and accordingly the (relative) algebraization
of maps/ideals/modules.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erwan Brugalle
DTSTART;VALUE=DATE-TIME:20211021T130000Z
DTEND;VALUE=DATE-TIME:20211021T143000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/16
DESCRIPTION:Title: Euler characteristic and signature of real semi-stable
degenerations\nby Erwan Brugalle as part of Real and complex Geometry\
n\n\nAbstract\nIt is interesting to compare the Euler characteristic of th
e real part of a real algebraic variety to the signature of its complex pa
rt. For example\, a theorem by Itenberg and Bertrand states that both quan
tities are equal for "primitive T-hypersurfaces". After defining these lat
ter\, I will give a motivic proof of this theorem via the motivic nearby f
iber of a real semi-stable degeneration. This proof extends in particular
the original statement by Itenberg and Bertrand to non-singular tropical v
arieties.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierrick Bousseau
DTSTART;VALUE=DATE-TIME:20211104T140000Z
DTEND;VALUE=DATE-TIME:20211104T153000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/17
DESCRIPTION:Title: Gromov-Witten theory of complete intersections\nby
Pierrick Bousseau as part of Real and complex Geometry\n\n\nAbstract\nI wi
ll describe an inductive algorithm computing Gromov-Witten invariants in a
ll genera with arbitrary insertions of all smooth complete intersections i
n projective space. The main idea is to show that invariants with insertio
ns of primitive cohomology classes are controlled by their monodromy and b
y invariants defined without primitive insertions but with imposed nodes i
n the domain curve. To compute these nodal Gromov-Witten invariants\, we i
ntroduce the new notion of nodal relative Gromov-Witten invariants. This i
s joint work with Hülya Argüz\, Rahul Pandharipande\, and Dimitri Zvonki
ne (arxiv:2109.13323).\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierrick Bousseau
DTSTART;VALUE=DATE-TIME:20211104T140000Z
DTEND;VALUE=DATE-TIME:20211104T153000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/18
DESCRIPTION:Title: Gromov-Witten theory of complete intersections\nby
Pierrick Bousseau as part of Real and complex Geometry\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Penka Georgieva
DTSTART;VALUE=DATE-TIME:20211118T140000Z
DTEND;VALUE=DATE-TIME:20211118T153000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/19
DESCRIPTION:Title: Higher-genus real/open counts in dimension 2\nby Pe
nka Georgieva as part of Real and complex Geometry\n\n\nAbstract\nAfter di
scussing some of the difficulties and progress in defining real and open c
ounts\, I will describe a generalisation of the higher-genus Welschinger i
nvariants defined by E. Shustin to the symplectic setting. I will then out
line a recursive formula allowing for reduction of the genus and the degre
e for computing these invariants. This is a joint work in progress with E.
Brugallé\, Y. Ding\, and A. Renaudineau.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Stecconi
DTSTART;VALUE=DATE-TIME:20211202T140000Z
DTEND;VALUE=DATE-TIME:20211202T153000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/20
DESCRIPTION:Title: Semicontinuity of Betti numbers and singular sets\n
by Michele Stecconi as part of Real and complex Geometry\n\n\nAbstract\nTh
ere are many objects in geometry that are called "singularities"\, \ndepen
ding on the context. The most basic examples are the zero set (i.e. \nhype
rsurface) or the set of critical points of a function\, the set of \npoint
s where two hypersurfaces are tangent to each other\, etc. In this \ntalk
we will investigate the topology of different types of singular \nloci fro
m a broad perspective.\n\nThe topology of the singular set of a polynomial
imposes a lower bound \non the degree\, due to the Thom-Milnor bound and
similar results. I will \ndiscuss some quantitative version of this concep
t\, for smooth maps. Such \ntopic is relevant in the context of smooth rig
idity and Whitney \nextension problem\, but it also offer an alternative a
pproach to the \npolynomial case.\n\nBy using polynomial approximations in
a quantitative way\, one obtains a \nThom-Milnor bound valid for all smoo
th maps. However\, the standard way \nof controlling the topology in the a
pproximation: maintaining a \ntransversality condition\, produces a non-sh
arp inequality. I will \npresent a general result about the behavior of th
e Betti numbers under \nC^0 approximations that allows to improve the abov
e method.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Abramovich (Brown University)
DTSTART;VALUE=DATE-TIME:20211209T140000Z
DTEND;VALUE=DATE-TIME:20211209T153000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/21
DESCRIPTION:Title: Punctured logarithmic maps\nby Dan Abramovich (Brow
n University) as part of Real and complex Geometry\n\n\nAbstract\nGromov-W
itten theory revolves around the enumerative question of counting algebrai
c curves in a smooth algebraic variety X meeting n given cycles - the utmo
st generalization of the question "how many lines pass through two given p
oints". Enumerative geometry\, degeneration techniques\, and mirror symmet
ry lead us to consider the analogous question where one also imposes conta
ct orders with a suitable divisor. I will introduce our work laying genera
l foundations for such a theory.\nThis is joint work with Q. Chen\, M. Gro
ss\, and B. Siebert.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Abramovich (Brown University)
DTSTART;VALUE=DATE-TIME:20211209T140000Z
DTEND;VALUE=DATE-TIME:20211209T153000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/22
DESCRIPTION:Title: Punctured logarithmic maps\nby Dan Abramovich (Brow
n University) as part of Real and complex Geometry\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Rubio (Universitat de Barcelona)
DTSTART;VALUE=DATE-TIME:20211216T140000Z
DTEND;VALUE=DATE-TIME:20211216T153000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/23
DESCRIPTION:Title: Generalized complex geometry and three-manifolds\nb
y Roberto Rubio (Universitat de Barcelona) as part of Real and complex Geo
metry\n\n\nAbstract\nGeneralized geometry is a unifying approach to geomet
ric structures where\, for example\, complex and symplectic structures bec
ome particular instances of a more general structure: a generalized comple
x structure. After a self-contained introduction to generalized complex ge
ometry (which is only possible for even-dimensional manifolds)\, I will ex
plain how generalized geometry can be upgraded to Bn-generalized geometry\
, in which the generalized-complex approach applies as well to odd dimensi
ons. Finally\, I will comment on some ongoing joint work with J. Porti in
which we look at the case of three-manifolds.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Polyak (Technion)
DTSTART;VALUE=DATE-TIME:20220106T140000Z
DTEND;VALUE=DATE-TIME:20220106T153000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/24
DESCRIPTION:Title: Refined tropical counting\, ribbon structures and the q
uantum torus\nby Michael Polyak (Technion) as part of Real and complex
Geometry\n\n\nAbstract\nTropical geometry is a powerful instrument in alg
ebraic geometry\, allowing for a simple combinatorial treatment of various
enumerative problems. Tropical curves are planar metric graphs with certa
in requirements of balancing\, rationality of slopes and integrality. An a
ddition of a ribbon structure (and a removal of rationality/integrality re
quirements) lead to a particularly simple combinatorial construction of mo
duli of ribbon (pseudo)tropical curves. Refined Block-Goettsche counting o
f rational tropical curves turns into a construction of some simple top-di
mensional cycles on these moduli and maps of spheres. These cycles turn ou
t to be closely related to associative algebras\; curves with "flat" verti
ces necessitate a passage from associative to Lie algebras. In particular\
, counting of (both complex and real) curves in toric varieties is related
to the quantum torus algebra. More complicated counting invariants (the s
o-called Gromov-Witten descendants\, or relative Welschinger invariants) a
re treated similarly and are related to the super-Lie structure on the qua
ntum torus. As a by-product we obtain a new one-parameter family of weight
s for a refined counting of the descendants.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Viatcheslav Kharlamov (Universite de Strasbourg)
DTSTART;VALUE=DATE-TIME:20220113T140000Z
DTEND;VALUE=DATE-TIME:20220113T153000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/25
DESCRIPTION:Title: On surgery invariant counts in real algebraic geometry<
/a>\nby Viatcheslav Kharlamov (Universite de Strasbourg) as part of Real a
nd complex Geometry\n\n\nAbstract\nOriginal Welschinger invariants as well
as their various generalizations are very sensitive to the change of topo
logy of the underlying real structure. However\, as was later noticed\, so
me combinations of Welschinger invariants may have a stronger invariance p
roperty which I call "surgery invariance": the property to be preserved un
der "wall-crossing" and as a result to be independent on a chosen real str
ucture in a given complex deformation class of varieties under considerati
on. The starting example is the signed count of real lines on cubic surfac
es in accordance with B. Segre's division of such lines in 2 kinds\, hyper
bolic and elliptic. This example gave rise to the discovery of similar cou
nts on higher dimensional hypersurfaces and complete intersections\, and s
erved as one of the roots for a development of an integer valued real Schu
bert calculus. In this talk (based on a work in progress\, joint with Serg
ey Finashin) I intend to discuss an extension of the above example with re
al lines on cubic surfaces in a bit different direction: from lines on a c
ubic surface to lines\, and even arbitrary degree rational curves\, on oth
er del Pezzo surfaces. Apart of surgery invariance property\, the invarian
ts we built also have other remarkable properties\, like a "magic" direct
relation to Gromov-Witten invariants and surprisingly elementary closed co
mputational formulae.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Blomme (Universite de Geneve)
DTSTART;VALUE=DATE-TIME:20220127T140000Z
DTEND;VALUE=DATE-TIME:20220127T153000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/26
DESCRIPTION:Title: Enumeration of tropical curves in abelian surfaces\
nby Thomas Blomme (Universite de Geneve) as part of Real and complex Geome
try\n\n\nAbstract\nTropical geometry is a powerful tool that allows one to
compute enumerative algebraic invariants through the use of some correspo
ndence theorem\, transforming an algebraic problem into a combinatorial pr
oblem. Moreover\, the tropical approach also allows one to twist definitio
ns to introduce mysterious refined invariants\, obtained by counting curve
s with polynomial multiplicities. So far\, this correspondence has mainly
been implemented in toric varieties. In this talk we will study enumeratio
n of curves in abelian surfaces and line bundles over an elliptic curve.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marvin Anas Hahn (Institut de Mathematiques Jussieu)
DTSTART;VALUE=DATE-TIME:20220303T141500Z
DTEND;VALUE=DATE-TIME:20220303T154500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/27
DESCRIPTION:Title: : Intersecting psi-classes on tropical Hassett spaces\nby Marvin Anas Hahn (Institut de Mathematiques Jussieu) as part of Rea
l and complex Geometry\n\n\nAbstract\nIn this talk\, we study the tropical
intersection theory of Hassett spaces in genus 0. Hassett spaces are alte
rnative compactifications of the moduli space of curves with n marked poin
ts induced by a vector of rational numbers. These spaces have a natural co
mbinatorial analogue in tropical geometry\, called tropical Hassett spaces
\, provided by the Bergman fan of a matroid which parametrizes certain n m
arked graphs. We introduce a notion of Psi-classes on these tropical Hasse
tt spaces and determine their intersection behavior. In particular\, we sh
ow that for a large family of rational vectors - namely the so-called heav
y/light vectors - the intersection products of Psi-classes of the associat
ed tropical Hassett spaces agree with their algebra-geometric analogue. Th
is talk is based on a joint work with Shiyue Li.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kris Shaw (University of Oslo)
DTSTART;VALUE=DATE-TIME:20220224T141500Z
DTEND;VALUE=DATE-TIME:20220224T154500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/28
DESCRIPTION:Title: A tropical approach to the enriched count of bitangents
to quartic curves\nby Kris Shaw (University of Oslo) as part of Real
and complex Geometry\n\n\nAbstract\nUsing A1 enumerative geometry Larson a
nd Vogt have provided an enriched count of the 28 bitangents to a quartic
curve. In this talk\, I will explain how these enriched counts can be comp
uted combinatorially using tropical geometry. I will also introduce an ari
thmetic analogue of Viro's patchworking for real algebraic curves which\,
in some cases\, retains enough data to recover the enriched counts. This t
alk is based on joint work with Hannah Markwig and Sam Payne.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yelena Mandelshtam (University of California\, Berkeley)
DTSTART;VALUE=DATE-TIME:20220310T141500Z
DTEND;VALUE=DATE-TIME:20220310T154500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/29
DESCRIPTION:Title: Curves\, degenerations\, and Hirota varieties\nby Y
elena Mandelshtam (University of California\, Berkeley) as part of Real an
d complex Geometry\n\n\nAbstract\nThe Kadomtsev-Petviashvili (KP) equation
is a differential equation whose study yields interesting connections bet
ween integrable systems and algebraic geometry. In this talk I will discus
s solutions to the KP equation whose underlying algebraic curves undergo t
ropical degenerations. In these cases\, Riemann's theta function becomes a
finite exponential sum that is supported on a Delaunay polytope. I will i
ntroduce the Hirota variety which parametrizes all KP solutions arising fr
om such a sum. I will then discuss a special case\, studying the Hirota va
riety of a rational nodal curve. Of particular interest is an irreducible
subvariety that is the image of a parameterization map. Proving that this
is a component of the Hirota variety entails solving a weak Schottky probl
em for rational nodal curves.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vivek Shende (University of California\, Berkeley)
DTSTART;VALUE=DATE-TIME:20220331T131500Z
DTEND;VALUE=DATE-TIME:20220331T144500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/30
DESCRIPTION:Title: Skein valued curve counting and quantum mirror symmetry
for the conifold\nby Vivek Shende (University of California\, Berkele
y) as part of Real and complex Geometry\n\n\nAbstract\nI'll explain how to
define counts of all-genus curves with Lagrangian boundary conditions in
Calabi-Yau 3-folds. Then I'll do an example: the conifold with a single Ag
anagic-Vafa brane. Here I'll show a priori (i.e. without first computing t
he invariants)\, that the partition function satisfies an operator equatio
n\, given by a skein-valued quantization of the mirror curve. Said equatio
n gives a recursion which can be solved explicitly. [This talk presents jo
int work with Tobias Ekholm.]\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rahul Pandharipande (ETH)
DTSTART;VALUE=DATE-TIME:20220407T131500Z
DTEND;VALUE=DATE-TIME:20220407T144500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/31
DESCRIPTION:Title: Log intersection theory of the moduli space of curves\nby Rahul Pandharipande (ETH) as part of Real and complex Geometry\n\n\
nAbstract\nThe logarithmic intersection theory of the moduli space of curv
es\nis defined via a limit over all log blow-ups (with respect to the norm
al crossings\nboundary structure). I will explain some new results and dir
ections related\nto the log cohomology theory and the log double ramificat
ion cycle. Joint\nwork with D. Holmes\, S. Mocho\, A. Pixton\, and J. Schm
itt.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shaoyun Bai (Princeton University)
DTSTART;VALUE=DATE-TIME:20220428T131500Z
DTEND;VALUE=DATE-TIME:20220428T144500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/32
DESCRIPTION:Title: Integral counterpart of Gromov-Witten invariants\nb
y Shaoyun Bai (Princeton University) as part of Real and complex Geometry\
n\n\nAbstract\nAs a virtual enumeration of (pseudo-)holomorphic curves\, G
romov-Witten invariants are generally rational-valued due to the presence
of non-trivial symmetries of the curves. Realizing a proposal of Fukaya-On
o back in the 1990s\, I will explain how to define integer-valued Gromov-W
itten type invariants for all closed symplectic manifolds. I will also dis
cuss how this construction fits into a larger program on refining curve-co
unting invariants initiated by Joyce\, Pardon\, and Abouzaid-McLean-Smith.
This is based on joint work with Guangbo Xu.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shaoyun Bai (Princeton University)
DTSTART;VALUE=DATE-TIME:20220428T131500Z
DTEND;VALUE=DATE-TIME:20220428T144500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/33
DESCRIPTION:Title: Integral counterpart of Gromov-Witten invariants\nb
y Shaoyun Bai (Princeton University) as part of Real and complex Geometry\
n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sourav Das (University of Haifa)
DTSTART;VALUE=DATE-TIME:20220512T131500Z
DTEND;VALUE=DATE-TIME:20220512T144500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/34
DESCRIPTION:Title: Higgs bundles on nodal curves\nby Sourav Das (Unive
rsity of Haifa) as part of Real and complex Geometry\n\n\nAbstract\nIn I98
7 Nigel Hitchin proved that the moduli space of Higgs bundles on a smooth
projective curve (of genus greater than equal to 2) has a natural symplect
ic structure. In this talk\, I will briefly recall a few features of the m
oduli space. Then I will discuss the moduli spaces of Higgs bundles on nod
al curves and how they are related to the moduli spaces of Higgs bundles o
n smooth curves via nice degenerations. I will also show that there is a r
elative log-symplectic structure on such a degeneration.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiu-Chu Melissa Liu (Columbia University)
DTSTART;VALUE=DATE-TIME:20220526T131500Z
DTEND;VALUE=DATE-TIME:20220526T144500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/35
DESCRIPTION:Title: Higgs-Coulomb correspondence for abelian gauged linear
sigma models\nby Chiu-Chu Melissa Liu (Columbia University) as part of
Real and complex Geometry\n\n\nAbstract\nThe input data of a gauged linea
r sigma model (GLSM) consists of a GIT quotient of a complex vector space
V by the linear action of a reductive algebraic group G (the gauge group)
and a G-invariant polynomial function on V (the superpotential) which is q
uasi-homogeneous with respect to a C^*-action (R symmetries) on V. The Hig
gs-Coulomb correspondence relates (1) GLSM invariants which are virtual co
unts of Landau-Ginzburg quasimaps (Higgs branch)\, and (2) Mellin-Barnes t
ype integrals on the Lie algebra of G (Coulomb branch). In this talk\, I w
ill describe the correspondence when G is an algebraic torus\, and explain
how to use the correspondence to study the dependence of GLSM invariants
on the stability condition. This is based on joint work with Konstantin Al
eshkin.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amanda Hirschi (Cambridge University)
DTSTART;VALUE=DATE-TIME:20220609T131500Z
DTEND;VALUE=DATE-TIME:20220609T144500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/36
DESCRIPTION:Title: A construction of global Kuranishi charts for Gromov-Wi
tten moduli spaces of arbitrary genus\nby Amanda Hirschi (Cambridge Un
iversity) as part of Real and complex Geometry\n\n\nAbstract\nSymplectic G
romov-Witten invariants have long been complicated by the fact that delica
te local-to-global arguments were required in their construction. In 2021
Abouzaid-McLean-Smith gave the first construction of global charts for gen
eral Gromov-Witten moduli spaces in genus zero. I will describe a generali
zation of their construction for stable maps of higher genera and discuss
potential applications. This is joint work in progress with Mohan Swaminat
han.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grigory Mikhalkin (University of Geneve)
DTSTART;VALUE=DATE-TIME:20221110T141500Z
DTEND;VALUE=DATE-TIME:20221110T154500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/37
DESCRIPTION:Title: Tropical\, real and symplectic geometry\nby Grigory
Mikhalkin (University of Geneve) as part of Real and complex Geometry\n\n
\nAbstract\nThis lecture will focus on the way how tropical curves appear
in symplectic geometry settings. On one hand\, tropical curves can be lift
ed as Lagrangian submanifolds in the ambient toric variety. On the other h
and\, they can be lifted as holomorphic curves. The two lifts use two diff
erent tropical structures on the same space\, related by a certain potenti
al function. We pay special attention to correspondence theorems between t
ropical curves and real curves\, i.e. holomorphic curves invariant with re
spect to an antiholomorphic involution. The resulting real curves produce\
, in their turn\, holomorphic membranes for tropical Lagrangian submanifol
ds.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kai Hugtenburg (University of Edinburgh)
DTSTART;VALUE=DATE-TIME:20221124T141500Z
DTEND;VALUE=DATE-TIME:20221124T154500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/38
DESCRIPTION:Title: Gromov-Witten theory: some computational tools\nby
Kai Hugtenburg (University of Edinburgh) as part of Real and complex Geome
try\n\n\nAbstract\nGromov-Witten invariants of a space X can intuitively b
e defined as counts of maps from a genus-g curve into X with certain const
raints. In this talk I will talk about two tools for computing Gromov-Witt
en invariants. The first of these will be the WDVV equations\, which were
used by Kontsevich to determine the number of degree d rational curves thr
ough 3d-1 points in CP^2. The second one are R-matrices\, which were used
by Givental and Teleman to recover all-genus invariants from the genus 0\,
3 point invariants. This method is not very widely applicable though: it
requires the quantum cohomology ring of X (which is a deformation of the u
sual cohomology ring) to be semi-simple. After overviewing this constructi
on\, I will give an example of a construction of an R-matrix in a more gen
eral setting.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Kerner (Ben-Gurion University)
DTSTART;VALUE=DATE-TIME:20221222T141500Z
DTEND;VALUE=DATE-TIME:20221222T154500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/39
DESCRIPTION:Title: Unfolding theory\, Stable maps and Mather-Yau/Gaffney-H
auser results in arbitrary characteristic\nby Dmitry Kerner (Ben-Gurio
n University) as part of Real and complex Geometry\n\n\nAbstract\nIn 40's
Whitney studied maps of C^\\infty manifolds. When a map is not an immersio
n/submersion\, one tries to deform it locally\, in hope to make it 'generi
c'. This approach has led to the rich theory of stable maps\, developed by
Mather\, Thom and many others. The main 'engine' was vector field integra
tion. This chained the whole theory to the C^\\infty\, or R/C-analytic set
ting. I will present the purely algebraic approach\, studying maps of germ
s of Noetherian schemes\, in any characteristic. The relevant groups of eq
uivalence admit 'good' tangent spaces. Submodules of the tangent spaces le
ad to submodules of the group orbits. Then goes the theory of unfoldings (
triviality and versality). Then I will discuss the new results on stable m
aps and theorems of Mather-Yau/Gaffney-Hauser.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Kreines (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20221229T141500Z
DTEND;VALUE=DATE-TIME:20221229T154500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/40
DESCRIPTION:Title: Embedded graphs on Riemann surfaces and beyond\nby
Elena Kreines (Tel Aviv University) as part of Real and complex Geometry\n
\n\nAbstract\nThis talk is based on the joint works with Natalia Amburg an
d George Shabat. The subject of the talk lies on the intersection of algeb
ra\, algebraic geometry\, and topology\, and produces new interrelations b
etween different branches of mathematics and mathematical physics. The mai
n objects of our discussion are so-called Belyi pairs and Grothendieck des
sins d'enfants. Belyi pair is a smooth connected algebraic curve together
with a non-constant meromorphic function on it with no more than 3 critica
l values. Grothendieck dessins d'enfants are tamely embedded graphs on Rie
mann surfaces. The interrelations between Belyi pairs and dessins d'enfant
s provide a new way to visualize absolute Galois group action\, new compac
tifications of moduli spaces of algebraic curves with marked and numbered
points\, a new way to visualize some classical objects of string theory\,
mathematical physics\, etc. I plan to present a brief introduction to the
theory with an emphasis on the geometrical aspects as well as several rece
nt results and useful examples. Among the examples\, we compute the Belyi
pair for the dessin provided by the natural cell decomposition of the orie
ntation covering of the moduli space of genus zero real stable curves with
5 marked points. In particular\, we prove that the corresponding Belyi fu
nction lies on the Bring curve.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uriel Sinichkin (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20230105T141500Z
DTEND;VALUE=DATE-TIME:20230105T154500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/41
DESCRIPTION:Title: Floor diagrams in tropical geometry\nby Uriel Sinic
hkin (Tel Aviv University) as part of Real and complex Geometry\n\n\nAbstr
act\nThis is the third talk in the introductory series\, following "Introd
uction to tropical geometry" and "Refined tropical enumerative invariants"
. Floor diagrams is a combinatorial tool introduced by Brugalle and Mikhal
kin to solve tropical enumerative questions and thus\, by the corresponden
ce theorem\, classical questions in enumerative algebraic geometry. We wil
l describe Mikhalkin's so-called "lattice path algorithm" and show how flo
or diagrams arise naturally from it. We then will show how floor diagrams
can be used to compute and analyze complex\, real\, and refined invariants
we saw in previous talks of the series. If time permits we will explore c
onnections to relative Gromov-Witten invariants and generalizations to the
enumeration of tropical hypersurfaces in higher dimensions.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Bychkov (Haifa University)
DTSTART;VALUE=DATE-TIME:20230112T141500Z
DTEND;VALUE=DATE-TIME:20230112T154500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/42
DESCRIPTION:Title: Topological recursion for generalized double Hurwitz nu
mbers\nby Boris Bychkov (Haifa University) as part of Real and complex
Geometry\n\n\nAbstract\nTopological recursion is a remarkable universal r
ecursive procedure that has been found in many enumerative geometry proble
ms\, from combinatorics of maps\, to random matrices\, Gromov-Witten invar
iants\, Hurwitz numbers\, Mirzakhani's hyperbolic volumes of moduli spaces
\, knot polynomials. A recursion needs an initial data: a spectral curve\,
and the recursion defines the sequence of invariants of that spectral cur
ve. In the talk I will define the topological recursion\, spectral curves
and their invariants\, and illustrate it with examples\; I will introduce
the Fock space formalism which proved to be very efficient for computing T
R-invariants for the various classes of Hurwitz-type numbers and I will de
scribe our results on explicit closed algebraic formulas for generating fu
nctions of generalized double Hurwitz numbers\, and how this allows to pro
ve topological recursion for a wide class of problems. If time permits I'l
l talk about the implications for the so-called ELSV-type formulas (relati
ng Hurwitz-type numbers to intersection numbers on the moduli spaces of al
gebraic curves)\; in particular\, I'll explain how this almost immediately
gives proofs (of a purely combinatorial-algebraic nature) of the original
ELSV formula and of its r-spin generalization (originally conjectured by
D.Zvonkine). The talk is based on the series of joint works with P. Dunin-
Barkowski\, M. Kazarian and S. Shadrin.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lothar Goettsche (ICTP\, Trieste)
DTSTART;VALUE=DATE-TIME:20230119T141500Z
DTEND;VALUE=DATE-TIME:20230119T154500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/43
DESCRIPTION:Title: (Refined) Verlinde and Segre formulas for Hilbert schem
es of points\nby Lothar Goettsche (ICTP\, Trieste) as part of Real and
complex Geometry\n\n\nAbstract\nSegre and Verlinde numbers of Hilbert sch
emes of points have been studied for a long time. The Segre numbers are ev
aluations of top Chern and Segre classes of so-called tautological bundles
on Hilbert schemes of points. The Verlinde numbers are the holomorphic Eu
ler characteristics of line bundles on these Hilbert schemes. We give the
generating functions for the Segre and Verlinde numbers of Hilbert schemes
of points. The formula is proven for surfaces with K_S^2=0\, and conjectu
red in general. Without restriction on K_S^2 we prove the conjectured Verl
inde-Segre correspondence relating Segre and Verlinde numbers of Hilbert s
chemes. Finally we find a generating function for finer invariants\, which
specialize to both the Segre and Verlinde numbers\, giving some kind of e
xplanation of the Verlinde-Segre correspondence. This is joint work with A
nton Mellit.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeny Feigin (HSE\, Moscow)
DTSTART;VALUE=DATE-TIME:20230202T141500Z
DTEND;VALUE=DATE-TIME:20230202T154500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/44
DESCRIPTION:Title: Cyclic quivers and totally nonnegative Grassmannians\nby Evgeny Feigin (HSE\, Moscow) as part of Real and complex Geometry\n\
n\nAbstract\nTotally nonnegative Grassmannians were introduced and studied
by Postnikov. In short\, these are subsets of the real Grassmann varietie
s consisting of points whose Pluecker coordinates have the same sign. The
tnn Grassmannians enjoy a lot of nice algebraic\, topological and combinat
orial properties. In particular\, they admit cellular decompositions with
explicitly described posets of cells. We construct complex algebraic varie
ties admitting a decomposition into complex cells with the corresponding p
oset being dual to that of the tnn Grassmannians. Our varieties are realiz
ed as quiver Grassmannians for the cyclic quivers. The quiver Grassmannian
s we consider also show up as local models of Shimura varieties. Joint wor
k with Martina Lanini and Alexander Puetz.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Vassiliev (Weizmann Institute)
DTSTART;VALUE=DATE-TIME:20230316T151500Z
DTEND;VALUE=DATE-TIME:20230316T164500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/45
DESCRIPTION:Title: Complements of discriminants of real function singulari
ties\nby Victor Vassiliev (Weizmann Institute) as part of Real and com
plex Geometry\n\n\nAbstract\nLet $f: ( {\\mathbb R}^n\,0) \\to ( {\\mathbb
R}\, 0)$ be a smooth function with a singularity at the origin (i.e. $df(
0)=0$)\, and $F: {\\mathbb R}^n \\times {\\mathbb R}^l \\to {\\mathbb R}$
be its deformation (which can be considered as a family of functions $f_\\
lambda$\, where $\\lambda \\in {\\mathbb R}^l$ is a parameter\, $f_0 \\equ
iv f$). The {\\em discriminant variety} of such a deformation is the set o
f parameters $\\lambda$ such that $f_\\lambda$ has a critical point with z
ero critical value. For a generic deformation\, this set is a hypersurface
in the parameter space\, dividing it into several local connected compone
nts. The enumeration of these components is a variation of the problem of
real algebraic geometry on rigid isotopy classification of non-singular al
gebraic hypersurfaces: it differs from the classical problem by the functi
on space\, equivalence relation\, and "boundary conditions" imposed by the
original singular function.\nIn the case of simple singularities $A_k$\,
$D_k$\, $E_6$\, $E_7$\, $E_8$\, E.Looijenga has proved in 1978 a one-to-on
e correspondence between these components and conjugacy classes of involut
ions with respect to eponymous reflection groups. I will give an explicit
enumeration of these components for simple singularities (which therefore
also gives an enumeration of these conjugacy classes)\, and for the next i
n difficulty class of {\\em parabolic} singularities. Also\, I will descri
be a combinatorial algorithm for searching and enumerating such components
for arbitrary isolated singularities.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sara Tukachinsky (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20230330T141500Z
DTEND;VALUE=DATE-TIME:20230330T154500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/46
DESCRIPTION:Title: Introduction to log geometry\nby Sara Tukachinsky (
Tel Aviv University) as part of Real and complex Geometry\n\n\nAbstract\nL
og geometry gives a neat way of dealing with some degenerations in algebra
ic geometry. For the purposes of our Introduction series\, the main motiva
tion comes from the Gross-Siebert mirror symmetry program\, where logarith
mic stable maps play a central and essential role. In this talk\, we will
start with a refresher on schemes. A definition of some basic notions in l
og geometry will follow\, including log schemes\, log differentials\, and
log smoothness. We will illustrate these ideas in basic cases (to be defin
ed in the talk) such as the trivial log structure\, a toric log scheme\, a
normal crossing divisor\, a logarithmic point\, and a logarithmic line. I
f time permits\, we will proceed to discuss the Kato-Nakayama space -- a t
opological space associated to a log scheme that encodes information about
the log structure.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Zelenko (Texas A&M University)
DTSTART;VALUE=DATE-TIME:20230427T131500Z
DTEND;VALUE=DATE-TIME:20230427T144500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/47
DESCRIPTION:Title: Gromov's h-principle for corank two distribution of odd
rank with maximal first Kronecker index\nby Igor Zelenko (Texas A&M U
niversity) as part of Real and complex Geometry\n\n\nAbstract\nMany natura
l geometric structures on manifolds are given as sections of certain bundl
es satisfying open relations at every point\, depending on the derivatives
of these sections. Such relations are called open differential relations.
Contact\, even-contact\, and (exact) symplectic structures on manifolds c
an be described in this way. The natural question is: do structures satisf
ying given open relations (called the genuine solutions of the differentia
l relation) exist on a given manifold? Replacing all derivatives appearing
in a differential relation by the additional independent variables one ob
tains an open subset of the corresponding jet bundle. A formal solution of
the differential relation is a section of the jet bundle lying in this op
en set. The existence of a formal solution is obviously a necessary condit
ion for the existence of the genuine one. One says that a differential rel
ation satisfies a (nonparametric) h-principle if any formal solution is ho
motopic to the genuine solution in the space of formal solutions.\nVersion
s of the h-principle have been successfully established for corank 1 distr
ibutions satisfying natural open relations. Such results are among the mos
t remarkable advances in differential topology in the last four decades. H
owever\, very little is known about analogous results for other classes of
distributions\, e.g. generic distributions of corank 2 or higher (except
the so-called Engel distributions\, the smallest dimensional case of maxim
ally nonholonomic distributions of corank 2 distributions on 4-dimensional
manifolds).\nIn my talk\, I will show how to use the method of convex int
egration in order to establish all versions of the h-principle for corank
2 distributions of arbitrary odd rank satisfying a natural generic assumpt
ion on the associated pencil of skew-symmetric forms. During the talk\, I
will try to give all the necessary background. This is the joint work with
Milan Jovanovic\, Javier Martinez-Aguinaga\, and Alvaro del Pino.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sheldon Katz (University of Illinois at Urbana-Champaign)
DTSTART;VALUE=DATE-TIME:20230504T141500Z
DTEND;VALUE=DATE-TIME:20230504T154500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/48
DESCRIPTION:Title: Enumerative Invariants of Calabi-Yau Threefolds with To
rsion and Noncommutative Resolutions\nby Sheldon Katz (University of I
llinois at Urbana-Champaign) as part of Real and complex Geometry\n\n\nAbs
tract\nA Calabi-Yau threefold X with torsion in H_2(X\,Z) has a disconnect
ed complexified Kahler moduli space and multiple large volume limits. B-mo
del techniques and mirror symmetry need to be applied at all of these larg
e volume limits in order to extract the Gromov-Witten invariants of X. In
this talk\, I focus on the double cover of degree 8 determinantal surfaces
in P^3\, their non-Kahler small resolutions possessing Z_2 torsion\, and
their noncommutative resolutions. There is a derived equivalence between s
heaves on the noncommutative resolutions and twisted sheaves on the small
resolutions\, suggesting a theory of Donaldson-Thomas invariants for these
noncommutative resolutions.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lev Birbrair (Universidade Federal do Ceará\, Fortaleza & Jagiell
onian University\, Krakow)
DTSTART;VALUE=DATE-TIME:20230521T111000Z
DTEND;VALUE=DATE-TIME:20230521T124000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/49
DESCRIPTION:Title: Lipschitz Geometry of Real Surface Singularities\nb
y Lev Birbrair (Universidade Federal do Ceará\, Fortaleza & Jagiellonian
University\, Krakow) as part of Real and complex Geometry\n\n\nAbstract\nI
will make an introduction to Lipschitz Geometry of Real Surface Singulari
ties. Inner\, Outer and Ambient classification questions will be considere
d.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Kerner (Ben-Gurion University)
DTSTART;VALUE=DATE-TIME:20230601T131500Z
DTEND;VALUE=DATE-TIME:20230601T144500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/50
DESCRIPTION:Title: Which ICIS are IMC's ?\nby Dmitry Kerner (Ben-Gurio
n University) as part of Real and complex Geometry\n\n\nAbstract\nLet (X\,
o) be a complex analytic germ. How to visualize it? The conic structure th
eorem reads: (X\,o) is homeomorphic to the cone over Link[X].\nIn ``most c
ases" this homeomorphism cannot be chosen differentiable (in whichever sen
se). The natural weaker question is: whether (X\,o) is ``inner metrically
conical" (IMC)\, i.e. whether (X\,o) is bi-Lipschitz homeomorphic to the c
one over its link.\nAny curve-germ is inner metrically conical. In higher
dimensions the (non-)IMC verification is more complicated.\nWe study this
question for complex-analytic ICIS\, giving necessary/sufficient criteria
to be IMC. For surface germs this becomes an ``if and only if'' condition.
So we get (explicitly) a lot of ICIS that are IMC's\, and the other lot o
f ICIS that are not IMC's.\nOur criteria are of two types: via the polar l
ocus/discriminant (in the general case) and via weights (for semi-weighted
homogeneous ICIS).\njoint work with L. Birbrair and R. Mendes Pereira\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Givental (University of California Berkeley)
DTSTART;VALUE=DATE-TIME:20230615T141500Z
DTEND;VALUE=DATE-TIME:20230615T154500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/51
DESCRIPTION:Title: Chern-Euler intersection theory and Gromov-Witten invar
iants\nby Alexander Givental (University of California Berkeley) as pa
rt of Real and complex Geometry\n\n\nAbstract\nIn the talk I will outline
our (joint with Irit Huq-Kuruvilla) attempt to develop the theory of Gromo
v-Witten invariants based on Euler characteristics rather than intersectio
n numbers. The purely homotopy-theoretic aspects of the story begin with t
he observation that in the category of stably almost complex manifolds the
usual Euler characteristic is bordism-invariant. This leads to the abstra
ct cohomology theory where the intersection of (stably almost complex) cyc
les is defined as the Euler characteristic of their transverse intersectio
n\, and where the total Chern class occurs in the role of the abstract Tod
d class. Our goal\, however\, is to apply this idea in the context of Grom
ov-Witten (GW) theory. In the talk I will outline the underlying philosoph
y and zoom in on some elementary examples.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takeo Nishinou (Rikkyo University)
DTSTART;VALUE=DATE-TIME:20231116T141500Z
DTEND;VALUE=DATE-TIME:20231116T154500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/54
DESCRIPTION:Title: Deformation of singular curves on surfaces\nby Take
o Nishinou (Rikkyo University) as part of Real and complex Geometry\n\n\nA
bstract\nIn this talk\, we will consider deformations of singular complex
curves on complex surfaces. More precisely\, if $\\varphi\\colon C\\to S$
is a map from a smooth projective curve to a projective surface\, we consi
der the deformation of $\\varphi$. Despite the simplicity of the problem\,
little seems to be known for surfaces of positive Kodaira dimension. The
problem of the existence of deformations can be reduced to two more tracta
ble problems: checking certain cohomological condition\, and solving a cer
tain system of polynomial equations which is independent of geometry. The
latter problem is almost always expected to be solved\, and in this case\,
the map has virtually optimal deformation property. This talk will be bas
ed on arxiv:2310.14039.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Gross (University of Frankfurt)
DTSTART;VALUE=DATE-TIME:20231130T141500Z
DTEND;VALUE=DATE-TIME:20231130T154500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/55
DESCRIPTION:Title: Tropicalizing Psi Classes\nby Andreas Gross (Univer
sity of Frankfurt) as part of Real and complex Geometry\n\n\nAbstract\nTro
pical curves are piecewise linear objects arising as degenerations of alge
braic curves. The close connection between algebraic curves and their trop
ical limits persists when considering moduli. This exhibits certain spaces
of tropical curves as the tropicalizations of the moduli spaces of stable
curves. It is\, however\, still unclear which properties of the algebraic
moduli spaces of curves are reflected in their tropical counterparts. \n\
nIn work with Renzo Cavalieri and Hannah Markwig we defined\, in a purely
tropical way\, tropical psi classes in arbitrary genus. They are operation
al cocycles on a stack of tropical curves\, which enjoy several propertie
s that we know from their algebraic ancestors. We also computed two exampl
es in genus one and gave a tropical explanation for the psi class on the m
oduli space of 1-marked stable genus-1 curves to be 1/24 times a point.\n\
nIn my talk\, I will report on joint work in progress with Renzo Cavalieri
\, where we explore the missing piece in the story: the link to algebraic
geometry. I will explain how to obtain\, if we are lucky\, a family of tro
pical curves from a family of algebraic curves. Naturally\, there also is
a correspondence-type theorem that equates algebraic and tropical intersec
tion products with psi classes\, thus showing that the tropical computatio
ns done with Cavalieri and Markwig faithfully reflect the algebraic world.
\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Molcho (ETH)
DTSTART;VALUE=DATE-TIME:20231207T141500Z
DTEND;VALUE=DATE-TIME:20231207T154500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/56
DESCRIPTION:Title: Intersection Theory on Compactified Jacobians\nby S
am Molcho (ETH) as part of Real and complex Geometry\n\n\nAbstract\nFix a
vector of integers $A = (a_1\,a_2\,...\,a_n)$. The double ramification cyc
le $DR_{g\,A}$ is formally defined via the virtual fundamental class of th
e space of relative stable maps to the projective line\, and informally is
the locus in the moduli space of n-pointed stable curves parametrizing cu
rves on which the line bundle $O(\\sum a_ix_i)$ is trivial. One of the gre
at achievements of the field was a calculation of this cycle in the tautol
ogical ring by Janda\, Pandharipande\, Pixton and Zvonkine. The methods of
JPPZ have however been limited to the DR\, and have not been sufficient t
o understand related cycles -- the Brill-Noether cycles $w_{g\,r\,A}^d$\,
which roughly speaking paramatrize curves on which $O(\\sum a_ix_i)$ has $
r+1$ linearly independent sections\, and the higher ramification cycles\,
which arise from the virtual fundamental class of the space of relative st
able maps to higher dimensional toric varieties. \n\nIn this talk\, I will
discuss how recent intersection-theoretic techniques originating from log
arithmic and tropical geometry\, and a logarithmic study of compactified J
acobians are the common framework underlying all these problems\, and in p
articular\, recover the calculation of the DR\, but also lead to explicit
formulas for the Brill-Noether and higher ramification cycles as well.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amanda Hirschi (Cambridge)
DTSTART;VALUE=DATE-TIME:20231221T141500Z
DTEND;VALUE=DATE-TIME:20231221T154500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/57
DESCRIPTION:Title: Global Kuranishi charts and a localisation formula in s
ymplectic GW theory\nby Amanda Hirschi (Cambridge) as part of Real and
complex Geometry\n\n\nAbstract\nI will briefly describe how the construct
ion of a global Kuranishi chart for moduli spaces of stable pseudoholomorp
hic maps allows for a straightforward definition of sympletic GW invariant
s\, including gravitational descendants. Subsequently\, I will describe ho
w to extend this to the equivariant setting and sketch the proof of a loca
lisation formula for the equivariant GW invariants of a Hamiltonian torus
manifold. This is partially joint work with Mohan Swaminathan.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renzo Cavalieri (Colorado State)
DTSTART;VALUE=DATE-TIME:20240201T141500Z
DTEND;VALUE=DATE-TIME:20240201T154500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/61
DESCRIPTION:Title: A log/tropical take on Hurwitz numbers\nby Renzo Ca
valieri (Colorado State) as part of Real and complex Geometry\n\n\nAbstrac
t\nI will present some joint work with Hannah Markwig and Dhruv Ranganatha
n\, in which we interpret double Hurwitz numbers as intersection numbers o
f the double ramification cycle with a logarithmic boundary class on the m
oduli space of curves. This approach removes the "need" for a branch morph
ism and therefore allows the generalization to related enumerative problem
s on moduli spaces of pluricanonical divisors - which have a natural comb
inatorial structure coming from their tropical interpretation. I will disc
uss some generalizations springing out from this approach that are current
ly being pursued in joint work with Hannah Markwig and Johannes Schmitt.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandr Buryak (HSE)
DTSTART;VALUE=DATE-TIME:20240215T141500Z
DTEND;VALUE=DATE-TIME:20240215T154500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/62
DESCRIPTION:Title: Intersection numbers on the moduli space of curves and
the Gromov--Witten invariants of the projective line with an insertion of
a Hodge class\nby Alexandr Buryak (HSE) as part of Real and complex Ge
ometry\n\n\nAbstract\nI will talk about our recent joint work with Xavier
Blot where we related the intersection numbers of psi-classes on the modul
i space of curves to the stationary relative Gromov--Witten invariants of
the complex projective line with an insertion of the top Chern class of th
e Hodge bundle. The proof is based on the theory of DR hierarchies\, which
gives a direct and explicit relation between the geometry of the moduli s
pace of curves and integrable systems of evolutionary PDEs. I will also tr
y to mention a development of this result\, which involves what we called
quantum intersection numbers on the moduli space of curves.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ran Tessler (Weizmann)
DTSTART;VALUE=DATE-TIME:20240118T141500Z
DTEND;VALUE=DATE-TIME:20240118T154500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/63
DESCRIPTION:Title: Mirror Symmetry for Landau-Ginzburg Models\nby Ran
Tessler (Weizmann) as part of Real and complex Geometry\n\n\nAbstract\nWe
will start with a short overview of mirror symmetry. We will then describe
Saito-Givental's theory and its mirror dual using FJRW theory and open FJ
RW theory.\n\nBased on joint works with Mark Gross and Tyler Kelly.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Kerner (BGU)
DTSTART;VALUE=DATE-TIME:20240229T131500Z
DTEND;VALUE=DATE-TIME:20240229T144500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/64
DESCRIPTION:Title: Artin approximation. The ordinary\, the inverse\, the l
eft-right and on quivers\nby Dmitry Kerner (BGU) as part of Real and c
omplex Geometry\n\n\nAbstract\nConsider a system of equations of implicit
function type\, F(x\,y)=0. Here F(x\,y) is a vector of analytic/algebraic
power series. (Artin) Any formal solution y(x) of this system is approxima
ted (x-adically) by solutions in analytic/algebraic series. Geometrically\
, suppose a morphism of (analytic/Nash) scheme-germs admits a formal secti
on. This formal section is adically approximated by analytic/Nash sections
.\n(The inverse question of Grothendieck) Given a map of (analytic/Nash) s
cheme-germs. Suppose its formal stalk is a section of some formal morphism
. Is the initial map a section of some (analytic/Nash) morphism? The answe
r is yes in the Nash case (Popescu) and no in the analytic case (Gabrielov
).\nThe left-right version of this question is important for the study of
morphisms of scheme-germs\, and was addressed by M.Shiota in the real-anal
ytic/Nash context. These versions appear to be particular cases of the gen
eral "Artin approximation problem on quivers". I will present the characte
ristic-free results.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeniya Akhmedova (Weizmann)
DTSTART;VALUE=DATE-TIME:20240314T141500Z
DTEND;VALUE=DATE-TIME:20240314T154500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/65
DESCRIPTION:Title: The tropical amplituhedron\nby Evgeniya Akhmedova (
Weizmann) as part of Real and complex Geometry\n\n\nAbstract\nThe Amplituh
edron is a geometric object discovered recently by Arkani-Hamed and Trnka\
, that provides a completely new direction for calculating scattering ampl
itudes in quantum field theory (QFT).\n\n We define a tropical analogue of
this object\, the tropicial amplituhedron and study its structure and bou
ndaries. It can be considered as both the tropical limit of the amplituhed
ron and a generalization of the tropical positive Grassmannian.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erwan Brugallé (Nantes)
DTSTART;VALUE=DATE-TIME:20240606T131500Z
DTEND;VALUE=DATE-TIME:20240606T144500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/66
DESCRIPTION:Title: A quadratically enriched Abramovich-Bertram formula
\nby Erwan Brugallé (Nantes) as part of Real and complex Geometry\n\n\nAb
stract\nBy interpreting 1 as the unique complex quadratic form $z\\to z^2$
\, some classical enumerations (i.e. with values in $\\mathbb N$) acquire
meaning when the field of complex numbers is replaced with an arbitrary fi
eld $k$. The result of the enumeration is then a quadratic form over $k$ r
ather than an integer.\nThis talk will focus on such enumeration for ratio
nal curves in del Pezzo surfaces. In particular I will report on a recent
joint work with Kirsten Wickelgren where we generalize a formula originall
y due to Abramovich and Bertram in the complex setting\, that I later exte
nded over the real numbers. This quadratically enriched version of the AB-
formula relates enumerative invariants for different $k$-forms on the same
del Pezzo surfaces.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Fock (Strasbourg)
DTSTART;VALUE=DATE-TIME:20240620T131500Z
DTEND;VALUE=DATE-TIME:20240620T144500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/67
DESCRIPTION:Title: Singularities\, Stokes data and clusters\nby Vladim
ir Fock (Strasbourg) as part of Real and complex Geometry\n\n\nAbstract\nI
n the talk we will suggest an explantation of a correspondence between sin
gularities and quivers stated first by S.Fomin\, P.Pylyavsky\, E.Shustin\,
and D.Thurston. The observation is that a singularity in two variables as
well as its versal deformations can (non-canonically) be transformed into
a differential operators of one complex variable. The Stokes data of thes
e operator amounts to be a flag configuration. The space of such configura
tions admits a cluster coordinates corresponding to FPST quiver. Amazingly
\, different differential operators corresponding to a given singularities
give apparently different but birationally canonically isomorphic varieti
es.\nWe will discuss tropical limit of this construction making it more ca
nonical and its relation to the combinatorics of FPST.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:László Fehér (Eötvös\, Budapest)
DTSTART;VALUE=DATE-TIME:20240704T131500Z
DTEND;VALUE=DATE-TIME:20240704T144500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/68
DESCRIPTION:Title: Thom polynomials of real singularities\nby László
Fehér (Eötvös\, Budapest) as part of Real and complex Geometry\n\n\nAb
stract\nThom polynomials are designed to solve enumerative problems. The t
heory of Thom polynomials of complex singularities is well established. A
theorem of Borel and Haeiger allows us to translate the complex results to
mod 2 results for real singularities\, which leads to solutions for mod 2
enumerative problems. The theory of integer valued Thom polynomials of re
al singularities is not very well understood. I will talk about some impor
tant examples calculated jointly with András Szenes. A sample result is $
tp(A_4(2l-1)) = (p_l)^2 + 3\\sum_{i=1}^l 4^{i-1}p_{l-i}p_{l+i}$ where $p_i
$ denote the Pontryagin classes and $A_4(2l .. 1)$ is the Thom-Boardman cl
ass $\\Sigma^{1\,1\,1\,1}$ in relative codimension $2l-1$. Notice the simi
larity with Ronga's formula for the Thom polynomial of the cusp (or $A_2$
or $\\Sigma^{1\,1}$ singularities in the complex case. These results lead
to non-trivial lower bounds for enumerative problems. Another direction to
find new results is to stay in the mod 2 world but enhance the Thom polyn
omials. In the complex case the Segre-Schwartz-MacPherson Thom polynomials
were introduced by Ohmoto Toru. In a joint work with Ákos Matszangosz we
introduced the real version\, the Segre-Stiefel-Whitney Thom polynomials.
These allow us for example to find obstructionsand geometric meaning for
them for the existence of Morin or fold maps of real projective spaces int
o a Euclidean space. As an example of these geometric interpretations of o
bstructions we can calculate the modulo 2 Euler class of certain degenerac
y loci of generic smooth maps.\nJoint work with András Szenes and Ákos M
atszangosz.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javier Fernandez de Bobadilla (BCAM)
DTSTART;VALUE=DATE-TIME:20240718T131500Z
DTEND;VALUE=DATE-TIME:20240718T144500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/69
DESCRIPTION:Title: Symplectic geometry of degenerations at radius 0\nb
y Javier Fernandez de Bobadilla (BCAM) as part of Real and complex Geometr
y\n\n\nAbstract\nGiven a normal crossings degeneration $f:(X\,w_X)\\to D$
of compact Kahler manifolds\, in recent work with T. Pelka we have shown
how to associate a smooth locally trivial fibration $f_A:X_A\\to D_{log}$
over the real oriented blow up of the disc Δ. It is moreover endowed wit
h a closed 2-form $w_A$ giving it the structure of a symplectic fibration.
The restriction of $w_A$ to every fibre of $f_A$ «at positive radius» (
that is over a point of $D\\setminus \\{0\\}$) is the modification by a po
tential of the restriction of $w_X$ to the same fibre. The construction ca
n be regarded as a symplectic realization of A'Campo model for the monodro
my and has found the following applications:\n\n(1) We can produce symplec
tic representatives of the monodromy with very special dynamics\, and base
d on this and on a spectral sequence due to McLean prove the family versio
n of Zariski’s multiplicity conjecture.\n\n(2) If f is a maximal Calabi-
Yau degeneration we can produce Lagrangian torus fibrations over a the com
plement of a codimension 2 set over the (expanded) essential skeleton of t
he degeneration\, satisfying many of the properties conjectured by Kontsev
ich and Soibelman. \n\nIn the talk I will highlight the main aspects of th
e construction\, and present some of the application (2).\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Misha Verbitsky (IMPA / HSE)
DTSTART;VALUE=DATE-TIME:20240711T131500Z
DTEND;VALUE=DATE-TIME:20240711T144500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/70
DESCRIPTION:Title: Complex geometry and the isometries of the hyperbolic s
pace\nby Misha Verbitsky (IMPA / HSE) as part of Real and complex Geom
etry\n\n\nAbstract\nThe isometries of a hyperbolic space are classified in
to three classes - elliptic\, parabolic\, and loxodromic\; this classifica
tion plays the major role in homogeneous dynamics of hyperbolic manifolds.
Since the work of Serge Cantat in the early 2000-ies it is known that a s
imilar classification exists for complex surfaces\, that is\, compact comp
lex manifolds of dimension 2. These results were recently generalized to h
olomorphically symplectic manifolds of arbitrary dimension. I would explai
n the ergodic properties of the parabolic automorphisms\, and prove the er
godicity of the automorphism group action for an appropriate deformation o
f any compact holomorphically symplectic manifold. This is a joint work w
ith Ekaterina Amerik.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Degtyarev (Bilkent)
DTSTART;VALUE=DATE-TIME:20240815T131500Z
DTEND;VALUE=DATE-TIME:20240815T144500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/71
DESCRIPTION:by Alex Degtyarev (Bilkent) as part of Real and complex Geomet
ry\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Dettweiler (Bayreuth)
DTSTART;VALUE=DATE-TIME:20240801T131500Z
DTEND;VALUE=DATE-TIME:20240801T144500Z
DTSTAMP;VALUE=DATE-TIME:20240715T183856Z
UID:AlgebraicGeometryTopology/72
DESCRIPTION:Title: Galois realizations of special linear groups\nby Mi
chael Dettweiler (Bayreuth) as part of Real and complex Geometry\n\nAbstra
ct: TBA\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/72/
END:VEVENT
END:VCALENDAR