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BEGIN:VEVENT
SUMMARY:Hulya Argüz (Université de Versailles)
DTSTART:20200427T130000Z
DTEND:20200427T143000Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/1
DESCRIPTION:Title: Tropical enumeration of real log curves in toric
varieties\nby Hulya Argüz (Université de Versailles) as part of Real
and complex Geometry\n\n\nAbstract\nWe define real log curves in toric va
rieties and set up a well-defined counting problem for them using the dege
neration approach of Nishinou--Siebert. We then investigate the tropical a
nalogues of such curves to obtain a formula for their counts from the trop
ical description. Focusing on the two dimensional case\, we also explain h
ow to capture Welschinger signs from a local analysis of the degeneration\
, to obtain log Welschinger invariants. This is joint work with Pierrick B
ousseau.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ethan Cotterill (Universidade Federal Fluminense)
DTSTART:20200511T130000Z
DTEND:20200511T143000Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/2
DESCRIPTION:Title: Rational curves with hyperelliptic singularities<
/a>\nby Ethan Cotterill (Universidade Federal Fluminense) as part of Real
and complex Geometry\n\n\nAbstract\nWe study singular rational curves in p
rojective space\, deducing conditions on their parameterizations from the
value semigroups of their singularities. Here we focus on rational curves
with cusps whose semigroups are of hyperelliptic type. We prove that a gen
us-g hyperelliptic singularity imposes at least (n-1)g conditions on ratio
nal curves of sufficiently large fixed degree in P^n\, and we prove that t
his bound is exact when g is small. We also provide evidence for a conject
ural generalization of this bound for rational curves with cusps with arbi
trary value semigroup S. Our conjecture\, if true\, produces infinitely ma
ny new examples of reducible Severi-type varieties M^n_{d\,g} of holomorph
ic maps P^1 -> P^n with images of degree d and arithmetic genus g.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boulos El Hilany (Johannes Radon Institute for Computational and A
pplied Mathematics\, Linz)
DTSTART:20200525T130000Z
DTEND:20200525T143000Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/4
DESCRIPTION:Title: Counting isolated points outside the image of a p
olynomial map\nby Boulos El Hilany (Johannes Radon Institute for Compu
tational and Applied Mathematics\, Linz) as part of Real and complex Geome
try\n\n\nAbstract\nA dominant polynomial map from the complex plane to its
elf gives rise to a finite set of curves and isolated points outside its i
mage. Z. Jelonek provided an upper bound on the number of such isolated po
ints that is quadratic in\, and depends only on\, the degrees of the polyn
omials involved. I will introduce in this talk a large family of dominant
non-proper maps above for which this upper bound is linear in the degrees.
Moreover\, I will illustrate constructions proving asymptotical sharpness
up to multiplication by a constant.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Arnal (Institut de Mathematiques de Jussieu)
DTSTART:20201022T130000Z
DTEND:20201022T143000Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/5
DESCRIPTION:Title: Families of real projective algebraic hypersurfac
es with large asymptotic Betti numbers\nby Charles Arnal (Institut de
Mathematiques de Jussieu) as part of Real and complex Geometry\n\n\nAbstra
ct\nWe describe a recursive method for constructing a family of real proje
ctive algebraic hypersurfaces in ambient dimension $n$ from families of su
ch hypersurfaces in ambient dimensions $k=1\,\\ldots\,n-1$. The asymptotic
Betti numbers of real parts of the resulting family can then be described
in terms of the asymptotic Betti numbers of the real parts of the familie
s used as ingredients. The algorithm is based on Viro's Patchwork and insp
ired by I. Itenberg's and O. Viro's construction of asymptotically maximal
families 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 pr
ojective algebraic hypersurfaces $\\{X^n_d\\}_d$ in $\\R \\PP ^n$ such tha
t the $i$-th Betti numbers $b_i(\\R X^n_d)$ are asymptotically strictly gr
eater than the $(i\,n-1-i)$-th Hodge numbers $h^{i\,n-1-i}(\\C X^n _d)$. W
e also build families of real projective algebraic hypersurfaces whose rea
l parts have asymptotic (in the degree $d$) Betti numbers that are asympto
tically (in the ambient dimension $n$) very large.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stepan Orevkov (Steklov Math. Institute and Universite Paul Sabati
er\, Toulouse)
DTSTART:20201029T140000Z
DTEND:20201029T153000Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/6
DESCRIPTION:Title: On real algebraic and real pseudoholomorphic curv
es in $RP^2$\nby Stepan Orevkov (Steklov Math. Institute and Universit
e Paul Sabatier\, Toulouse) as part of Real and complex Geometry\n\n\nAbst
ract\nI will present an inequality for the isotopy type of a plane non-sin
gular real algebraic curve endowed with a complex orientation (i.e.\, for
its complex scheme according to Rokhlin's terminology) which implies in pa
rticular that an infinite series of complex schemes are realizable pseudoh
olomorphically 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://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Blomme (Universite de Neuchatel)
DTSTART:20201105T140000Z
DTEND:20201105T153000Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/7
DESCRIPTION:Title: Refined count of rational tropical curves in arbi
trary dimension\nby Thomas Blomme (Universite de Neuchatel) as part of
Real and complex Geometry\n\n\nAbstract\nIn this talk we will introduce a
refined multiplicity for rational tropical curves in any dimension. This
multiplicity generalizes the multiplicity of Block-Göttsche for planar tr
opical curves. We also show that the count of solutions to some general tr
opical enumerative problem using this new multiplicity leads tropical refi
ned invariants\, hinting toward the existence of classical refined invaria
nts for classical rational curves.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arielle Leitner (Weizmann Institute of Science)
DTSTART:20201112T140000Z
DTEND:20201112T153000Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/8
DESCRIPTION:Title: Deformations of Generalized Cusps on Convex Proje
ctive Manifolds\nby Arielle Leitner (Weizmann Institute of Science) as
part of Real and complex Geometry\n\n\nAbstract\nConvex projective manifo
lds are a generalization of hyperbolic manifolds. Koszul showed that the s
et of holonomies 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\, d
ue to Cooper-Long-Tillmann. Generalized cusps are certain ends of convex p
rojective manifolds. They may contain both hyperbolic and parabolic elemen
ts. We will describe their classification (due to Ballas-Cooper-Leitner)\,
and explain how generalized cusps turn out to be deformations of cusps of
hyperbolic manifolds. We will also explore the moduli space of generalize
d cusps\, it is a semi-algebraic set of dimension n^2-n\, contractible\, a
nd may be studied using several different invariants. For the case of thre
e manifolds\, the moduli space is homeomorphic to R^2 times a cone on a so
lid torus.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Ancona (Tel Aviv University)
DTSTART:20201126T140000Z
DTEND:20201126T153000Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/9
DESCRIPTION:Title: Exponential rarefaction of maximal hypersurfaces<
/a>\nby Michele Ancona (Tel Aviv University) as part of Real and complex G
eometry\n\n\nAbstract\nSmith-Thom's inequality tells us that the sum of Be
tti numbers of the real locus of a real algebraic variety is always smalle
r than or equal to the sum of Betti numbers of its complex locus. In the c
ase of equality\, the real algebraic variety is called maximal. Given a re
al holomorphic line bundle L over a real algebraic variety X\, I will prov
e that the probability that a real holomorphic section of L^d defines a ma
ximal hypersurface tends to 0 exponentially fast when d tends to infinity.
\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Benoist (ENS\, Paris)
DTSTART:20210318T140000Z
DTEND:20210318T153000Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/10
DESCRIPTION:Title: Rational curves on real algebraic varieties\
nby Olivier Benoist (ENS\, Paris) as part of Real and complex Geometry\n\n
\nAbstract\nLet X be a smooth projective real algebraic variety. When is i
t possible to approximate loops in the real locus X(R) by real loci of rat
ional curves on X? In this talk\, I will provide a positive answer for a c
lass of varieties that includes cubic hypersurfaces and compactifications
of homogeneous spaces under connected linear algebraic groups. This is joi
nt work with Olivier Wittenberg.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier de Gaay Fortman (ENS\, Paris)
DTSTART:20210311T140000Z
DTEND:20210311T153000Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/11
DESCRIPTION:Title: Real Noether-Lefschetz loci and density of non-s
imple abelian varieties over the real numbers\nby Olivier de Gaay Fort
man (ENS\, Paris) as part of Real and complex Geometry\n\n\nAbstract\nSome
times the geometry of an algebraic variety poses restrictions on the geome
try of its algebraic subvarieties. A beautiful example is the Noether-Lefs
chetz Theorem which states that on a general complex algebraic surface of
degree greater than three in three dimensional projective space\, any curv
e is obtained as a complete intersection of the surface with another hyper
surface. In spite of this\, Green's density criterion enabled Ciliberto\,
Harris and Miranda to prove that the Noether-Lefschetz locus is dense for
the Euclidean topology in the space of all smooth degree d > 3 complex pol
ynomials. Over the real numbers\, things are more complicated. The general
real hypersurface in P^3 of degree larger than three still has Picard ran
k one but real surfaces with jumping Picard rank are not dense at all in t
he space of real smooth degree d > 3 polynomials: the latter is not connec
ted and the real Noether-Lefschetz locus can miss a connected component en
tirely. There is a density criterion but it is much harder to fulfill and
can only be applied to one component at a time. Our goal in this talk is t
o pose an analogous question in the setting of real abelian varieties and
to prove that in that situation\, none of these problems occur. Fixing nat
ural numbers g\, k\, and a polarized family of abelian varieties of dimens
ion g defined over the real numbers\, when are real (resp. complex) abelia
n varieties that contain a real (resp. complex) abelian subvariety of dime
nsion k dense in the set of real (resp. complex) points of the base? For e
ach of these densities there is a natural criterion and surprisingly\, the
y are the same. Various applications are given along these lines\, such as
density of such loci in moduli spaces of principally polarized real abeli
an varieties\, real algebraic curves\, and real plane curves.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Tyomkin (Ben-Gurion University)
DTSTART:20210429T130000Z
DTEND:20210429T143000Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/12
DESCRIPTION:Title: On (ir)reducibility of Severi varieties on toric
surfaces\nby Ilya Tyomkin (Ben-Gurion University) as part of Real and
complex Geometry\n\n\nAbstract\nIn my talk I will discuss the problem of
irreducibility of families of curves of given degree and genus on toric su
rfaces. Such families\, called Severi varieties\, have been intensively st
udied due to a variety of applications of their geometry to the study of m
oduli spaces of curves\, and to various enumerative problems. After review
ing briefly known irreducibility results\, I'll describe examples of toric
surfaces admitting reducible Severi varieties\, and introduce certain top
ological and tropical invariants that allow one to distinguish between dif
ferent irreducible components. The talk is based on a joint work with Lion
el Lang.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lev Radzivilovsky (Tel Aviv University)
DTSTART:20210617T130000Z
DTEND:20210617T143000Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/13
DESCRIPTION:Title: Enumeration of rational surfaces and moduli spac
es of configurations of points in the projective plane\nby Lev Radzivi
lovsky (Tel Aviv University) as part of Real and complex Geometry\n\n\nAbs
tract\nWe discuss the problem of enumerating rational surfaces in 3-dimens
ional projective space\, as an analogue of Gromov-Witten invariants. It le
ads naturally to moduli spaces of cofigurations of $n$ marked points in pr
ojective planes. We discuss the "Chow quotients" of Kapranov\, and present
a new version of this construction which gives a smooth moduli space for
configurations of 6 points. We conjecture that the same construction yield
s a smoothing of the moduli space of configurations of any number of point
s in the plane. We also briefly present a formula for enumeration of surfa
ces with a singular line.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:KhazhgaliKozhasov
DTSTART:20210715T130000Z
DTEND:20210715T143000Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/14
DESCRIPTION:Title: Nodes on quintic spectrahedra\nby KhazhgaliK
ozhasov as part of Real and complex Geometry\n\n\nAbstract\nGiven generic
real symmetric matrices A\, B\, C of size n x n\, it is of interest to stu
dy 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 conve
x set in R^3\, called a spectrahedron. The Zariski closure of the Eucllide
an boundary of S is an algebraic surface {(x\,y\,z): det(Id+ x A+y B+ z C)
=0}\, which turns out to be always singular. A natural question in real al
gebraic geometry is to understand (for a fixed n) possible restrictions on
the numbers P\, Q of real singular points\, respectively\, of those singu
larities that lie on S. In my talk I will discuss this problem for quintic
spectrahedra (n=5) and present a complete classification of pairs (P\,Q)\
, obtained in a joint work with Taylor Brysiewicz and Mario Kummer.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Kerner (Ben-Gurion University)
DTSTART:20210812T130000Z
DTEND:20210812T143000Z
DTSTAMP:20260404T094149Z
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 critical point at the origin can be rectified to a linear map. Maps wi
th critical points have rich structure and are studied up to the groups of
right/left-right/contact equivalence. The group orbits are complicated an
d are traditionally studied via their tangent space. This transition is cl
assically done by vector fields integration\, thus binding the theory to t
he real/complex case. I will present the new approach to this subject. One
studies the maps of germs of Noetherian schemes\, in any characteristic.
The corresponding groups of equivalence admit `good' tangent spaces. The s
ubmodules of the tangent spaces lead to submodules of the group orbits. Th
is allows to bring these maps to `convenient' forms. For example\, we get
the (relative) finite determinacy\, and accordingly the (relative) algebra
ization of maps/ideals/modules.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erwan Brugalle
DTSTART:20211021T130000Z
DTEND:20211021T143000Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/16
DESCRIPTION:Title: Euler characteristic and signature of real semi-
stable degenerations\nby Erwan Brugalle as part of Real and complex Ge
ometry\n\n\nAbstract\nIt is interesting to compare the Euler characteristi
c of the real part of a real algebraic variety to the signature of its com
plex part. For example\, a theorem by Itenberg and Bertrand states that bo
th quantities are equal for "primitive T-hypersurfaces". After defining th
ese latter\, I will give a motivic proof of this theorem via the motivic n
earby fiber of a real semi-stable degeneration. This proof extends in part
icular the original statement by Itenberg and Bertrand to non-singular tro
pical varieties.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierrick Bousseau
DTSTART:20211104T140000Z
DTEND:20211104T153000Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/17
DESCRIPTION:Title: Gromov-Witten theory of complete intersections\nby Pierrick Bousseau as part of Real and complex Geometry\n\n\nAbstrac
t\nI will describe an inductive algorithm computing Gromov-Witten invarian
ts in all genera with arbitrary insertions of all smooth complete intersec
tions in projective space. The main idea is to show that invariants with i
nsertions of primitive cohomology classes are controlled by their monodrom
y and by invariants defined without primitive insertions but with imposed
nodes in the domain curve. To compute these nodal Gromov-Witten invariants
\, we introduce the new notion of nodal relative Gromov-Witten invariants.
This is joint work with Hülya Argüz\, Rahul Pandharipande\, and Dimitri
Zvonkine (arxiv:2109.13323).\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierrick Bousseau
DTSTART:20211104T140000Z
DTEND:20211104T153000Z
DTSTAMP:20260404T094149Z
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://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Penka Georgieva
DTSTART:20211118T140000Z
DTEND:20211118T153000Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/19
DESCRIPTION:Title: Higher-genus real/open counts in dimension 2
\nby Penka Georgieva as part of Real and complex Geometry\n\n\nAbstract\nA
fter discussing some of the difficulties and progress in defining real and
open counts\, I will describe a generalisation of the higher-genus Welsch
inger invariants defined by E. Shustin to the symplectic setting. I will t
hen outline a recursive formula allowing for reduction of the genus and th
e degree for computing these invariants. This is a joint work in progress
with E. Brugallé\, Y. Ding\, and A. Renaudineau.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Stecconi
DTSTART:20211202T140000Z
DTEND:20211202T153000Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/20
DESCRIPTION:Title: Semicontinuity of Betti numbers and singular set
s\nby Michele Stecconi as part of Real and complex Geometry\n\n\nAbstr
act\nThere are many objects in geometry that are called "singularities"\,
\ndepending on the context. The most basic examples are the zero set (i.e.
\nhypersurface) or the set of critical points of a function\, the set of
\npoints where two hypersurfaces are tangent to each other\, etc. In this
\ntalk we will investigate the topology of different types of singular \nl
oci from a broad perspective.\n\nThe topology of the singular set of a pol
ynomial imposes a lower bound \non the degree\, due to the Thom-Milnor bou
nd and similar results. I will \ndiscuss some quantitative version of this
concept\, for smooth maps. Such \ntopic is relevant in the context of smo
oth rigidity and Whitney \nextension problem\, but it also offer an altern
ative approach to the \npolynomial case.\n\nBy using polynomial approximat
ions in a quantitative way\, one obtains a \nThom-Milnor bound valid for a
ll smooth maps. However\, the standard way \nof controlling the topology i
n the approximation: maintaining a \ntransversality condition\, produces a
non-sharp inequality. I will \npresent a general result about the behavio
r of the Betti numbers under \nC^0 approximations that allows to improve t
he above method.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Abramovich (Brown University)
DTSTART:20211209T140000Z
DTEND:20211209T153000Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/21
DESCRIPTION:Title: Punctured logarithmic maps\nby Dan Abramovic
h (Brown University) as part of Real and complex Geometry\n\n\nAbstract\nG
romov-Witten theory revolves around the enumerative question of counting a
lgebraic curves in a smooth algebraic variety X meeting n given cycles - t
he utmost generalization of the question "how many lines pass through two
given points". Enumerative geometry\, degeneration techniques\, and mirror
symmetry lead us to consider the analogous question where one also impose
s contact orders with a suitable divisor. I will introduce our work laying
general foundations for such a theory.\nThis is joint work with Q. Chen\,
M. Gross\, and B. Siebert.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Abramovich (Brown University)
DTSTART:20211209T140000Z
DTEND:20211209T153000Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/22
DESCRIPTION:Title: Punctured logarithmic maps\nby Dan Abramovic
h (Brown University) as part of Real and complex Geometry\n\nAbstract: TBA
\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Rubio (Universitat de Barcelona)
DTSTART:20211216T140000Z
DTEND:20211216T153000Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/23
DESCRIPTION:Title: Generalized complex geometry and three-manifolds
\nby Roberto Rubio (Universitat de Barcelona) as part of Real and comp
lex Geometry\n\n\nAbstract\nGeneralized geometry is a unifying approach to
geometric structures where\, for example\, complex and symplectic structu
res become particular instances of a more general structure: a generalized
complex structure. After a self-contained introduction to generalized com
plex geometry (which is only possible for even-dimensional manifolds)\, I
will explain how generalized geometry can be upgraded to Bn-generalized ge
ometry\, in which the generalized-complex approach applies as well to odd
dimensions. Finally\, I will comment on some ongoing joint work with J. Po
rti in which we look at the case of three-manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Polyak (Technion)
DTSTART:20220106T140000Z
DTEND:20220106T153000Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/24
DESCRIPTION:Title: Refined tropical counting\, ribbon structures an
d the quantum torus\nby Michael Polyak (Technion) as part of Real and
complex Geometry\n\n\nAbstract\nTropical geometry is a powerful instrument
in algebraic geometry\, allowing for a simple combinatorial treatment of
various enumerative problems. Tropical curves are planar metric graphs wit
h certain requirements of balancing\, rationality of slopes and integralit
y. An addition of a ribbon structure (and a removal of rationality/integra
lity requirements) lead to a particularly simple combinatorial constructio
n of moduli of ribbon (pseudo)tropical curves. Refined Block-Goettsche cou
nting of rational tropical curves turns into a construction of some simple
top-dimensional cycles on these moduli and maps of spheres. These cycles
turn out to be closely related to associative algebras\; curves with "flat
" vertices necessitate a passage from associative to Lie algebras. In part
icular\, counting of (both complex and real) curves in toric varieties is
related to the quantum torus algebra. More complicated counting invariants
(the so-called Gromov-Witten descendants\, or relative Welschinger invari
ants) are treated similarly and are related to the super-Lie structure on
the quantum torus. As a by-product we obtain a new one-parameter family of
weights for a refined counting of the descendants.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Viatcheslav Kharlamov (Universite de Strasbourg)
DTSTART:20220113T140000Z
DTEND:20220113T153000Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/25
DESCRIPTION:Title: On surgery invariant counts in real algebraic ge
ometry\nby Viatcheslav Kharlamov (Universite de Strasbourg) as part of
Real and complex Geometry\n\n\nAbstract\nOriginal Welschinger invariants
as well as their various generalizations are very sensitive to the change
of topology of the underlying real structure. However\, as was later notic
ed\, some combinations of Welschinger invariants may have a stronger invar
iance property which I call "surgery invariance": the property to be prese
rved under "wall-crossing" and as a result to be independent on a chosen r
eal structure in a given complex deformation class of varieties under cons
ideration. The starting example is the signed count of real lines on cubic
surfaces in accordance with B. Segre's division of such lines in 2 kinds\
, hyperbolic and elliptic. This example gave rise to the discovery of simi
lar counts on higher dimensional hypersurfaces and complete intersections\
, and served as one of the roots for a development of an integer valued re
al Schubert calculus. In this talk (based on a work in progress\, joint wi
th Sergey Finashin) I intend to discuss an extension of the above example
with real lines on cubic surfaces in a bit different direction: from lines
on a cubic surface to lines\, and even arbitrary degree rational curves\,
on other del Pezzo surfaces. Apart of surgery invariance property\, the i
nvariants we built also have other remarkable properties\, like a "magic"
direct relation to Gromov-Witten invariants and surprisingly elementary cl
osed computational formulae.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Blomme (Universite de Geneve)
DTSTART:20220127T140000Z
DTEND:20220127T153000Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/26
DESCRIPTION:Title: Enumeration of tropical curves in abelian surfac
es\nby Thomas Blomme (Universite de Geneve) as part of Real and comple
x Geometry\n\n\nAbstract\nTropical geometry is a powerful tool that allows
one to compute enumerative algebraic invariants through the use of some c
orrespondence theorem\, transforming an algebraic problem into a combinato
rial problem. Moreover\, the tropical approach also allows one to twist de
finitions to introduce mysterious refined invariants\, obtained by countin
g curves with polynomial multiplicities. So far\, this correspondence has
mainly been implemented in toric varieties. In this talk we will study enu
meration of curves in abelian surfaces and line bundles over an elliptic c
urve.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marvin Anas Hahn (Institut de Mathematiques Jussieu)
DTSTART:20220303T141500Z
DTEND:20220303T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/27
DESCRIPTION:Title: : Intersecting psi-classes on tropical Hassett s
paces\nby Marvin Anas Hahn (Institut de Mathematiques Jussieu) as part
of Real and complex Geometry\n\n\nAbstract\nIn this talk\, we study the t
ropical intersection theory of Hassett spaces in genus 0. Hassett spaces a
re alternative compactifications of the moduli space of curves with n mark
ed points induced by a vector of rational numbers. These spaces have a nat
ural combinatorial analogue in tropical geometry\, called tropical Hassett
spaces\, provided by the Bergman fan of a matroid which parametrizes cert
ain n marked graphs. We introduce a notion of Psi-classes on these tropica
l Hassett spaces and determine their intersection behavior. In particular\
, we show that for a large family of rational vectors - namely the so-call
ed heavy/light vectors - the intersection products of Psi-classes of the a
ssociated tropical Hassett spaces agree with their algebra-geometric analo
gue. This talk is based on a joint work with Shiyue Li.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kris Shaw (University of Oslo)
DTSTART:20220224T141500Z
DTEND:20220224T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/28
DESCRIPTION:Title: A tropical approach to the enriched count of bit
angents to quartic curves\nby Kris Shaw (University of Oslo) as part o
f Real and complex Geometry\n\n\nAbstract\nUsing A1 enumerative geometry L
arson and Vogt have provided an enriched count of the 28 bitangents to a q
uartic curve. In this talk\, I will explain how these enriched counts can
be computed combinatorially using tropical geometry. I will also introduce
an arithmetic analogue of Viro's patchworking for real algebraic curves w
hich\, in some cases\, retains enough data to recover the enriched counts.
This talk is based on joint work with Hannah Markwig and Sam Payne.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yelena Mandelshtam (University of California\, Berkeley)
DTSTART:20220310T141500Z
DTEND:20220310T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/29
DESCRIPTION:Title: Curves\, degenerations\, and Hirota varieties\nby Yelena Mandelshtam (University of California\, Berkeley) as part of
Real and complex Geometry\n\n\nAbstract\nThe Kadomtsev-Petviashvili (KP) e
quation is a differential equation whose study yields interesting connecti
ons between integrable systems and algebraic geometry. In this talk I will
discuss solutions to the KP equation whose underlying algebraic curves un
dergo tropical degenerations. In these cases\, Riemann's theta function be
comes a finite exponential sum that is supported on a Delaunay polytope. I
will introduce the Hirota variety which parametrizes all KP solutions ari
sing from such a sum. I will then discuss a special case\, studying the Hi
rota variety of a rational nodal curve. Of particular interest is an irred
ucible subvariety that is the image of a parameterization map. Proving tha
t this is a component of the Hirota variety entails solving a weak Schottk
y problem for rational nodal curves.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vivek Shende (University of California\, Berkeley)
DTSTART:20220331T131500Z
DTEND:20220331T144500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/30
DESCRIPTION:Title: Skein valued curve counting and quantum mirror s
ymmetry for the conifold\nby Vivek Shende (University of California\,
Berkeley) as part of Real and complex Geometry\n\n\nAbstract\nI'll explain
how to define counts of all-genus curves with Lagrangian boundary conditi
ons in Calabi-Yau 3-folds. Then I'll do an example: the conifold with a si
ngle Aganagic-Vafa brane. Here I'll show a priori (i.e. without first comp
uting the invariants)\, that the partition function satisfies an operator
equation\, given by a skein-valued quantization of the mirror curve. Said
equation gives a recursion which can be solved explicitly. [This talk pres
ents joint work with Tobias Ekholm.]\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rahul Pandharipande (ETH)
DTSTART:20220407T131500Z
DTEND:20220407T144500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/31
DESCRIPTION:Title: Log intersection theory of the moduli space of c
urves\nby Rahul Pandharipande (ETH) as part of Real and complex Geomet
ry\n\n\nAbstract\nThe logarithmic intersection theory of the moduli space
of curves\nis defined via a limit over all log blow-ups (with respect to t
he normal crossings\nboundary structure). I will explain some new results
and directions related\nto the log cohomology theory and the log double ra
mification cycle. Joint\nwork with D. Holmes\, S. Mocho\, A. Pixton\, and
J. Schmitt.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shaoyun Bai (Princeton University)
DTSTART:20220428T131500Z
DTEND:20220428T144500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/32
DESCRIPTION:Title: Integral counterpart of Gromov-Witten invariants
\nby Shaoyun Bai (Princeton University) as part of Real and complex Ge
ometry\n\n\nAbstract\nAs a virtual enumeration of (pseudo-)holomorphic cur
ves\, Gromov-Witten invariants are generally rational-valued due to the pr
esence of non-trivial symmetries of the curves. Realizing a proposal of Fu
kaya-Ono back in the 1990s\, I will explain how to define integer-valued G
romov-Witten type invariants for all closed symplectic manifolds. I will a
lso discuss how this construction fits into a larger program on refining c
urve-counting invariants initiated by Joyce\, Pardon\, and Abouzaid-McLean
-Smith. This is based on joint work with Guangbo Xu.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shaoyun Bai (Princeton University)
DTSTART:20220428T131500Z
DTEND:20220428T144500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/33
DESCRIPTION:Title: Integral counterpart of Gromov-Witten invariants
\nby Shaoyun Bai (Princeton University) as part of Real and complex Ge
ometry\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sourav Das (University of Haifa)
DTSTART:20220512T131500Z
DTEND:20220512T144500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/34
DESCRIPTION:Title: Higgs bundles on nodal curves\nby Sourav Das
(University of Haifa) as part of Real and complex Geometry\n\n\nAbstract\
nIn I987 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 s
ymplectic structure. In this talk\, I will briefly recall a few features o
f the moduli space. Then I will discuss the moduli spaces of Higgs bundles
on nodal curves and how they are related to the moduli spaces of Higgs bu
ndles on smooth curves via nice degenerations. I will also show that there
is a relative log-symplectic structure on such a degeneration.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiu-Chu Melissa Liu (Columbia University)
DTSTART:20220526T131500Z
DTEND:20220526T144500Z
DTSTAMP:20260404T094149Z
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 gauge
d linear 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) whi
ch is quasi-homogeneous with respect to a C^*-action (R symmetries) on V.
The Higgs-Coulomb correspondence relates (1) GLSM invariants which are vir
tual counts of Landau-Ginzburg quasimaps (Higgs branch)\, and (2) Mellin-B
arnes type integrals on the Lie algebra of G (Coulomb branch). In this tal
k\, I will describe the correspondence when G is an algebraic torus\, and
explain how to use the correspondence to study the dependence of GLSM inva
riants on the stability condition. This is based on joint work with Konsta
ntin Aleshkin.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amanda Hirschi (Cambridge University)
DTSTART:20220609T131500Z
DTEND:20220609T144500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/36
DESCRIPTION:Title: A construction of global Kuranishi charts for Gr
omov-Witten moduli spaces of arbitrary genus\nby Amanda Hirschi (Cambr
idge University) as part of Real and complex Geometry\n\n\nAbstract\nSympl
ectic Gromov-Witten invariants have long been complicated by the fact that
delicate local-to-global arguments were required in their construction. I
n 2021 Abouzaid-McLean-Smith gave the first construction of global charts
for general Gromov-Witten moduli spaces in genus zero. I will describe a g
eneralization of their construction for stable maps of higher genera and d
iscuss potential applications. This is joint work in progress with Mohan S
waminathan.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grigory Mikhalkin (University of Geneve)
DTSTART:20221110T141500Z
DTEND:20221110T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/37
DESCRIPTION:Title: Tropical\, real and symplectic geometry\nby
Grigory Mikhalkin (University of Geneve) as part of Real and complex Geome
try\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 lifted as Lagrangian submanifolds in the ambient toric variety. On the
other hand\, they can be lifted as holomorphic curves. The two lifts use t
wo different tropical structures on the same space\, related by a certain
potential function. We pay special attention to correspondence theorems be
tween tropical curves and real curves\, i.e. holomorphic curves invariant
with respect to an antiholomorphic involution. The resulting real curves p
roduce\, in their turn\, holomorphic membranes for tropical Lagrangian sub
manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kai Hugtenburg (University of Edinburgh)
DTSTART:20221124T141500Z
DTEND:20221124T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/38
DESCRIPTION:Title: Gromov-Witten theory: some computational tools\nby Kai Hugtenburg (University of Edinburgh) as part of Real and comple
x Geometry\n\n\nAbstract\nGromov-Witten invariants of a space X can intuit
ively be defined as counts of maps from a genus-g curve into X with certai
n constraints. In this talk I will talk about two tools for computing Grom
ov-Witten invariants. The first of these will be the WDVV equations\, whic
h were used by Kontsevich to determine the number of degree d rational cur
ves through 3d-1 points in CP^2. The second one are R-matrices\, which wer
e used by Givental and Teleman to recover all-genus invariants from the ge
nus 0\, 3 point invariants. This method is not very widely applicable thou
gh: it requires the quantum cohomology ring of X (which is a deformation o
f the usual cohomology ring) to be semi-simple. After overviewing this con
struction\, I will give an example of a construction of an R-matrix in a m
ore general setting.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Kerner (Ben-Gurion University)
DTSTART:20221222T141500Z
DTEND:20221222T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/39
DESCRIPTION:Title: Unfolding theory\, Stable maps and Mather-Yau/Ga
ffney-Hauser results in arbitrary characteristic\nby Dmitry Kerner (Be
n-Gurion University) as part of Real and complex Geometry\n\n\nAbstract\nI
n 40's Whitney studied maps of C^\\infty manifolds. When a map is not an i
mmersion/submersion\, one tries to deform it locally\, in hope to make it
'generic'. This approach has led to the rich theory of stable maps\, devel
oped by Mather\, Thom and many others. The main 'engine' was vector field
integration. This chained the whole theory to the C^\\infty\, or R/C-analy
tic setting. I will present the purely algebraic approach\, studying maps
of germs of Noetherian schemes\, in any characteristic. The relevant group
s of equivalence admit 'good' tangent spaces. Submodules of the tangent sp
aces lead to submodules of the group orbits. Then goes the theory of unfol
dings (triviality and versality). Then I will discuss the new results on s
table maps and theorems of Mather-Yau/Gaffney-Hauser.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Kreines (Tel Aviv University)
DTSTART:20221229T141500Z
DTEND:20221229T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/40
DESCRIPTION:Title: Embedded graphs on Riemann surfaces and beyond\nby Elena Kreines (Tel Aviv University) as part of Real and complex Geo
metry\n\n\nAbstract\nThis talk is based on the joint works with Natalia Am
burg and George Shabat. The subject of the talk lies on the intersection o
f algebra\, algebraic geometry\, and topology\, and produces new interrela
tions between different branches of mathematics and mathematical physics.
The main objects of our discussion are so-called Belyi pairs and Grothendi
eck dessins d'enfants. Belyi pair is a smooth connected algebraic curve to
gether with a non-constant meromorphic function on it with no more than 3
critical values. Grothendieck dessins d'enfants are tamely embedded graphs
on Riemann surfaces. The interrelations between Belyi pairs and dessins d
'enfants provide a new way to visualize absolute Galois group action\, new
compactifications of moduli spaces of algebraic curves with marked and nu
mbered points\, a new way to visualize some classical objects of string th
eory\, mathematical physics\, etc. I plan to present a brief introduction
to the theory with an emphasis on the geometrical aspects as well as sever
al recent results and useful examples. Among the examples\, we compute the
Belyi pair for the dessin provided by the natural cell decomposition of t
he orientation covering of the moduli space of genus zero real stable curv
es with 5 marked points. In particular\, we prove that the corresponding B
elyi function lies on the Bring curve.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uriel Sinichkin (Tel Aviv University)
DTSTART:20230105T141500Z
DTEND:20230105T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/41
DESCRIPTION:Title: Floor diagrams in tropical geometry\nby Urie
l Sinichkin (Tel Aviv University) as part of Real and complex Geometry\n\n
\nAbstract\nThis is the third talk in the introductory series\, following
"Introduction to tropical geometry" and "Refined tropical enumerative inva
riants". Floor diagrams is a combinatorial tool introduced by Brugalle and
Mikhalkin to solve tropical enumerative questions and thus\, by the corre
spondence theorem\, classical questions in enumerative algebraic geometry.
We will describe Mikhalkin's so-called "lattice path algorithm" and show
how floor diagrams arise naturally from it. We then will show how floor di
agrams can be used to compute and analyze complex\, real\, and refined inv
ariants we saw in previous talks of the series. If time permits we will ex
plore connections to relative Gromov-Witten invariants and generalizations
to the enumeration of tropical hypersurfaces in higher dimensions.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Bychkov (Haifa University)
DTSTART:20230112T141500Z
DTEND:20230112T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/42
DESCRIPTION:Title: Topological recursion for generalized double Hur
witz numbers\nby Boris Bychkov (Haifa University) as part of Real and
complex Geometry\n\n\nAbstract\nTopological recursion is a remarkable univ
ersal recursive procedure that has been found in many enumerative geometry
problems\, from combinatorics of maps\, to random matrices\, Gromov-Witte
n invariants\, 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 spect
ral curve. In the talk I will define the topological recursion\, spectral
curves and their invariants\, and illustrate it with examples\; I will int
roduce the Fock space formalism which proved to be very efficient for comp
uting TR-invariants for the various classes of Hurwitz-type numbers and I
will describe our results on explicit closed algebraic formulas for genera
ting functions of generalized double Hurwitz numbers\, and how this allows
to prove topological recursion for a wide class of problems. If time perm
its I'll talk about the implications for the so-called ELSV-type formulas
(relating Hurwitz-type numbers to intersection numbers on the moduli space
s of algebraic curves)\; in particular\, I'll explain how this almost imme
diately gives proofs (of a purely combinatorial-algebraic nature) of the o
riginal ELSV formula and of its r-spin generalization (originally conjectu
red 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://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lothar Goettsche (ICTP\, Trieste)
DTSTART:20230119T141500Z
DTEND:20230119T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/43
DESCRIPTION:Title: (Refined) Verlinde and Segre formulas for Hilber
t schemes of points\nby Lothar Goettsche (ICTP\, Trieste) as part of R
eal and complex Geometry\n\n\nAbstract\nSegre and Verlinde numbers of Hilb
ert schemes of points have been studied for a long time. The Segre numbers
are evaluations of top Chern and Segre classes of so-called tautological
bundles on Hilbert schemes of points. The Verlinde numbers are the holomor
phic Euler characteristics of line bundles on these Hilbert schemes. We gi
ve 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 c
onjectured in general. Without restriction on K_S^2 we prove the conjectur
ed Verlinde-Segre correspondence relating Segre and Verlinde numbers of Hi
lbert schemes. Finally we find a generating function for finer invariants\
, which specialize to both the Segre and Verlinde numbers\, giving some ki
nd of explanation of the Verlinde-Segre correspondence. This is joint work
with Anton Mellit.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeny Feigin (HSE\, Moscow)
DTSTART:20230202T141500Z
DTEND:20230202T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/44
DESCRIPTION:Title: Cyclic quivers and totally nonnegative Grassmann
ians\nby Evgeny Feigin (HSE\, Moscow) as part of Real and complex Geom
etry\n\n\nAbstract\nTotally nonnegative Grassmannians were introduced and
studied by Postnikov. In short\, these are subsets of the real Grassmann v
arieties consisting of points whose Pluecker coordinates have the same sig
n. The tnn Grassmannians enjoy a lot of nice algebraic\, topological and c
ombinatorial properties. In particular\, they admit cellular decomposition
s with explicitly described posets of cells. We construct complex algebrai
c varieties admitting a decomposition into complex cells with the correspo
nding poset being dual to that of the tnn Grassmannians. Our varieties are
realized as quiver Grassmannians for the cyclic quivers. The quiver Grass
mannians we consider also show up as local models of Shimura varieties. Jo
int work with Martina Lanini and Alexander Puetz.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Vassiliev (Weizmann Institute)
DTSTART:20230316T151500Z
DTEND:20230316T164500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/45
DESCRIPTION:Title: Complements of discriminants of real function si
ngularities\nby Victor Vassiliev (Weizmann Institute) as part of Real
and complex 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 $F: {\\mathbb R}^n \\times {\\mathbb R}^l \\to {\\math
bb R}$ be its deformation (which can be considered as a family of function
s $f_\\lambda$\, where $\\lambda \\in {\\mathbb R}^l$ is a parameter\, $f_
0 \\equiv f$). The {\\em discriminant variety} of such a deformation is th
e set of parameters $\\lambda$ such that $f_\\lambda$ has a critical point
with zero critical value. For a generic deformation\, this set is a hyper
surface in the parameter space\, dividing it into several local connected
components. The enumeration of these components is a variation of the prob
lem of real algebraic geometry on rigid isotopy classification of non-sing
ular algebraic hypersurfaces: it differs from the classical problem by the
function 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 on
e-to-one correspondence between these components and conjugacy classes of
involutions with respect to eponymous reflection groups. I will give an ex
plicit enumeration of these components for simple singularities (which the
refore also gives an enumeration of these conjugacy classes)\, and for the
next in difficulty class of {\\em parabolic} singularities. Also\, I will
describe a combinatorial algorithm for searching and enumerating such com
ponents for arbitrary isolated singularities.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sara Tukachinsky (Tel Aviv University)
DTSTART:20230330T141500Z
DTEND:20230330T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/46
DESCRIPTION:Title: Introduction to log geometry\nby Sara Tukach
insky (Tel Aviv University) as part of Real and complex Geometry\n\n\nAbst
ract\nLog geometry gives a neat way of dealing with some degenerations in
algebraic geometry. For the purposes of our Introduction series\, the main
motivation comes from the Gross-Siebert mirror symmetry program\, where l
ogarithmic stable maps play a central and essential role. In this talk\, w
e will start with a refresher on schemes. A definition of some basic notio
ns in log geometry will follow\, including log schemes\, log differentials
\, and log smoothness. We will illustrate these ideas in basic cases (to b
e defined in the talk) such as the trivial log structure\, a toric log sch
eme\, a normal crossing divisor\, a logarithmic point\, and a logarithmic
line. If time permits\, we will proceed to discuss the Kato-Nakayama space
-- a topological space associated to a log scheme that encodes informatio
n about the log structure.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Zelenko (Texas A&M University)
DTSTART:20230427T131500Z
DTEND:20230427T144500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/47
DESCRIPTION:Title: Gromov's h-principle for corank two distribution
of odd rank with maximal first Kronecker index\nby Igor Zelenko (Texa
s A&M University) as part of Real and complex Geometry\n\n\nAbstract\nMany
natural geometric structures on manifolds are given as sections of certai
n bundles satisfying open relations at every point\, depending on the deri
vatives of these sections. Such relations are called open differential rel
ations. Contact\, even-contact\, and (exact) symplectic structures on mani
folds can be described in this way. The natural question is: do structures
satisfying given open relations (called the genuine solutions of the diff
erential relation) exist on a given manifold? Replacing all derivatives ap
pearing in a differential relation by the additional independent variables
one obtains an open subset of the corresponding jet bundle. A formal solu
tion of the differential relation is a section of the jet bundle lying in
this open set. The existence of a formal solution is obviously a necessary
condition for the existence of the genuine one. One says that a different
ial relation satisfies a (nonparametric) h-principle if any formal solutio
n is homotopic to the genuine solution in the space of formal solutions.\n
Versions of the h-principle have been successfully established for corank
1 distributions satisfying natural open relations. Such results are among
the most remarkable advances in differential topology in the last four dec
ades. However\, very little is known about analogous results for other cla
sses of distributions\, e.g. generic distributions of corank 2 or higher (
except the so-called Engel distributions\, the smallest dimensional case o
f maximally nonholonomic distributions of corank 2 distributions on 4-dime
nsional manifolds).\nIn my talk\, I will show how to use the method of con
vex integration in order to establish all versions of the h-principle for
corank 2 distributions of arbitrary odd rank satisfying a natural generic
assumption on the associated pencil of skew-symmetric forms. During the ta
lk\, I will try to give all the necessary background. This is the joint wo
rk with Milan Jovanovic\, Javier Martinez-Aguinaga\, and Alvaro del Pino.\
n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sheldon Katz (University of Illinois at Urbana-Champaign)
DTSTART:20230504T141500Z
DTEND:20230504T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/48
DESCRIPTION:Title: Enumerative Invariants of Calabi-Yau Threefolds
with Torsion and Noncommutative Resolutions\nby Sheldon Katz (Universi
ty of Illinois at Urbana-Champaign) as part of Real and complex Geometry\n
\n\nAbstract\nA Calabi-Yau threefold X with torsion in H_2(X\,Z) has a dis
connected complexified Kahler moduli space and multiple large volume limit
s. B-model techniques and mirror symmetry need to be applied at all of the
se large 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 s
urfaces in P^3\, their non-Kahler small resolutions possessing Z_2 torsion
\, and their noncommutative resolutions. There is a derived equivalence be
tween sheaves on the noncommutative resolutions and twisted sheaves on the
small resolutions\, suggesting a theory of Donaldson-Thomas invariants fo
r these noncommutative resolutions.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lev Birbrair (Universidade Federal do Ceará\, Fortaleza & Jagiell
onian University\, Krakow)
DTSTART:20230521T111000Z
DTEND:20230521T124000Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/49
DESCRIPTION:Title: Lipschitz Geometry of Real Surface Singularities
\nby Lev Birbrair (Universidade Federal do Ceará\, Fortaleza & Jagiel
lonian University\, Krakow) as part of Real and complex Geometry\n\n\nAbst
ract\nI will make an introduction to Lipschitz Geometry of Real Surface Si
ngularities. Inner\, Outer and Ambient classification questions will be co
nsidered.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Kerner (Ben-Gurion University)
DTSTART:20230601T131500Z
DTEND:20230601T144500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/50
DESCRIPTION:Title: Which ICIS are IMC's ?\nby Dmitry Kerner (Be
n-Gurion University) as part of Real and complex Geometry\n\n\nAbstract\nL
et (X\,o) be a complex analytic germ. How to visualize it? The conic struc
ture theorem reads: (X\,o) is homeomorphic to the cone over Link[X].\nIn `
`most cases" this homeomorphism cannot be chosen differentiable (in whiche
ver sense). The natural weaker question is: whether (X\,o) is ``inner metr
ically conical" (IMC)\, i.e. whether (X\,o) is bi-Lipschitz homeomorphic t
o the cone over its link.\nAny curve-germ is inner metrically conical. In
higher dimensions the (non-)IMC verification is more complicated.\nWe stud
y this question for complex-analytic ICIS\, giving necessary/sufficient cr
iteria to be IMC. For surface germs this becomes an ``if and only if'' con
dition. So we get (explicitly) a lot of ICIS that are IMC's\, and the othe
r lot of ICIS that are not IMC's.\nOur criteria are of two types: via the
polar locus/discriminant (in the general case) and via weights (for semi-w
eighted homogeneous ICIS).\njoint work with L. Birbrair and R. Mendes Pere
ira\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Givental (University of California Berkeley)
DTSTART:20230615T141500Z
DTEND:20230615T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/51
DESCRIPTION:Title: Chern-Euler intersection theory and Gromov-Witte
n invariants\nby Alexander Givental (University of California Berkeley
) as part of Real and complex Geometry\n\n\nAbstract\nIn the talk I will o
utline our (joint with Irit Huq-Kuruvilla) attempt to develop the theory o
f Gromov-Witten invariants based on Euler characteristics rather than inte
rsection numbers. The purely homotopy-theoretic aspects of the story begin
with the observation that in the category of stably almost complex manifo
lds the usual Euler characteristic is bordism-invariant. This leads to the
abstract cohomology theory where the intersection of (stably almost compl
ex) cycles is defined as the Euler characteristic of their transverse inte
rsection\, and where the total Chern class occurs in the role of the abstr
act Todd class. Our goal\, however\, is to apply this idea in the context
of Gromov-Witten (GW) theory. In the talk I will outline the underlying ph
ilosophy and zoom in on some elementary examples.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takeo Nishinou (Rikkyo University)
DTSTART:20231116T141500Z
DTEND:20231116T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/54
DESCRIPTION:Title: Deformation of singular curves on surfaces\n
by Takeo Nishinou (Rikkyo University) as part of Real and complex Geometry
\n\n\nAbstract\nIn this talk\, we will consider deformations of singular c
omplex curves on complex surfaces. More precisely\, if $\\varphi\\colon C\
\to S$ is a map from a smooth projective curve to a projective surface\, w
e consider the deformation of $\\varphi$. Despite the simplicity of the pr
oblem\, little seems to be known for surfaces of positive Kodaira dimensio
n. The problem of the existence of deformations can be reduced to two more
tractable problems: checking certain cohomological condition\, and solvin
g a certain system of polynomial equations which is independent of geometr
y. 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 based on arxiv:2310.14039.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Gross (University of Frankfurt)
DTSTART:20231130T141500Z
DTEND:20231130T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/55
DESCRIPTION:Title: Tropicalizing Psi Classes\nby Andreas Gross
(University of Frankfurt) as part of Real and complex Geometry\n\n\nAbstra
ct\nTropical curves are piecewise linear objects arising as degenerations
of algebraic curves. The close connection between algebraic curves and the
ir tropical 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 al
gebraic moduli spaces of curves are reflected in their tropical counterpar
ts. \n\nIn work with Renzo Cavalieri and Hannah Markwig we defined\, in a
purely tropical way\, tropical psi classes in arbitrary genus. They are op
erational cocycles on a stack of tropical curves\, which enjoy several pr
operties that we know from their algebraic ancestors. We also computed two
examples in genus one and gave a tropical explanation for the psi class o
n the moduli space of 1-marked stable genus-1 curves to be 1/24 times a po
int.\n\nIn my talk\, I will report on joint work in progress with Renzo Ca
valieri\, where we explore the missing piece in the story: the link to alg
ebraic geometry. I will explain how to obtain\, if we are lucky\, a family
of tropical curves from a family of algebraic curves. Naturally\, there a
lso is a correspondence-type theorem that equates algebraic and tropical i
ntersection products with psi classes\, thus showing that the tropical com
putations done with Cavalieri and Markwig faithfully reflect the algebraic
world.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Molcho (ETH)
DTSTART:20231207T141500Z
DTEND:20231207T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/56
DESCRIPTION:Title: Intersection Theory on Compactified Jacobians\nby Sam 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 ramificat
ion cycle $DR_{g\,A}$ is formally defined via the virtual fundamental clas
s of the space of relative stable maps to the projective line\, and inform
ally is the locus in the moduli space of n-pointed stable curves parametri
zing curves on which the line bundle $O(\\sum a_ix_i)$ is trivial. One of
the great achievements of the field was a calculation of this cycle in the
tautological ring by Janda\, Pandharipande\, Pixton and Zvonkine. The met
hods of JPPZ have however been limited to the DR\, and have not been suffi
cient to 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 cy
cles\, which arise from the virtual fundamental class of the space of rela
tive stable maps to higher dimensional toric varieties. \n\nIn this talk\,
I will discuss how recent intersection-theoretic techniques originating f
rom logarithmic and tropical geometry\, and a logarithmic study of compact
ified Jacobians are the common framework underlying all these problems\, a
nd in particular\, recover the calculation of the DR\, but also lead to ex
plicit formulas for the Brill-Noether and higher ramification cycles as we
ll.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amanda Hirschi (Cambridge)
DTSTART:20231221T141500Z
DTEND:20231221T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/57
DESCRIPTION:Title: Global Kuranishi charts and a localisation formu
la in symplectic GW theory\nby Amanda Hirschi (Cambridge) as part of R
eal and complex Geometry\n\n\nAbstract\nI will briefly describe how the co
nstruction of a global Kuranishi chart for moduli spaces of stable pseudoh
olomorphic maps allows for a straightforward definition of sympletic GW in
variants\, including gravitational descendants. Subsequently\, I will desc
ribe how to extend this to the equivariant setting and sketch the proof of
a localisation formula for the equivariant GW invariants of a Hamiltonian
torus manifold. This is partially joint work with Mohan Swaminathan.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renzo Cavalieri (Colorado State)
DTSTART:20240201T141500Z
DTEND:20240201T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/61
DESCRIPTION:Title: A log/tropical take on Hurwitz numbers\nby R
enzo Cavalieri (Colorado State) as part of Real and complex Geometry\n\n\n
Abstract\nI will present some joint work with Hannah Markwig and Dhruv Ran
ganathan\, in which we interpret double Hurwitz numbers as intersection nu
mbers of the double ramification cycle with a logarithmic boundary class o
n the moduli space of curves. This approach removes the "need" for a branc
h morphism and therefore allows the generalization to related enumerative
problems on moduli spaces of pluricanonical divisors - which have a natura
l combinatorial structure coming from their tropical interpretation. I wi
ll discuss some generalizations springing out from this approach that are
currently being pursued in joint work with Hannah Markwig and Johannes Sch
mitt.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandr Buryak (HSE)
DTSTART:20240215T141500Z
DTEND:20240215T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/62
DESCRIPTION:Title: Intersection numbers on the moduli space of curv
es and the Gromov--Witten invariants of the projective line with an insert
ion of a Hodge class\nby Alexandr Buryak (HSE) as part of Real and com
plex Geometry\n\n\nAbstract\nI will talk about our recent joint work with
Xavier Blot where we related the intersection numbers of psi-classes on th
e moduli space of curves to the stationary relative Gromov--Witten invaria
nts of the complex projective line with an insertion of the top Chern clas
s of the Hodge bundle. The proof is based on the theory of DR hierarchies\
, which gives a direct and explicit relation between the geometry of the m
oduli space of curves and integrable systems of evolutionary PDEs. I will
also try to mention a development of this result\, which involves what we
called quantum intersection numbers on the moduli space of curves.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ran Tessler (Weizmann)
DTSTART:20240118T141500Z
DTEND:20240118T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/63
DESCRIPTION:Title: Mirror Symmetry for Landau-Ginzburg Models\n
by Ran Tessler (Weizmann) as part of Real and complex Geometry\n\n\nAbstra
ct\nWe will start with a short overview of mirror symmetry. We will then d
escribe Saito-Givental's theory and its mirror dual using FJRW theory and
open FJRW theory.\n\nBased on joint works with Mark Gross and Tyler Kelly.
\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Kerner (BGU)
DTSTART:20240229T131500Z
DTEND:20240229T144500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/64
DESCRIPTION:Title: Artin approximation. The ordinary\, the inverse\
, the left-right and on quivers\nby Dmitry Kerner (BGU) as part of Rea
l and complex Geometry\n\n\nAbstract\nConsider a system of equations of im
plicit function type\, F(x\,y)=0. Here F(x\,y) is a vector of analytic/alg
ebraic power series. (Artin) Any formal solution y(x) of this system is ap
proximated (x-adically) by solutions in analytic/algebraic series. Geometr
ically\, suppose a morphism of (analytic/Nash) scheme-germs admits a forma
l section. This formal section is adically approximated by analytic/Nash s
ections.\n(The inverse question of Grothendieck) Given a map of (analytic/
Nash) scheme-germs. Suppose its formal stalk is a section of some formal m
orphism. Is the initial map a section of some (analytic/Nash) morphism? Th
e answer is yes in the Nash case (Popescu) and no in the analytic case (Ga
brielov).\nThe left-right version of this question is important for the st
udy of morphisms of scheme-germs\, and was addressed by M.Shiota in the re
al-analytic/Nash context. These versions appear to be particular cases of
the general "Artin approximation problem on quivers". I will present the c
haracteristic-free results.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeniya Akhmedova (Weizmann)
DTSTART:20240314T141500Z
DTEND:20240314T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/65
DESCRIPTION:Title: The tropical amplituhedron\nby Evgeniya Akhm
edova (Weizmann) as part of Real and complex Geometry\n\n\nAbstract\nThe A
mplituhedron is a geometric object discovered recently by Arkani-Hamed and
Trnka\, that provides a completely new direction for calculating scatteri
ng amplitudes in quantum field theory (QFT).\n\n We define a tropical anal
ogue of this object\, the tropicial amplituhedron and study its structure
and boundaries. It can be considered as both the tropical limit of the amp
lituhedron and a generalization of the tropical positive Grassmannian.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erwan Brugallé (Nantes)
DTSTART:20240606T131500Z
DTEND:20240606T144500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/66
DESCRIPTION:Title: A quadratically enriched Abramovich-Bertram form
ula\nby Erwan Brugallé (Nantes) as part of Real and complex Geometry\
n\n\nAbstract\nBy interpreting 1 as the unique complex quadratic form $z\\
to z^2$\, some classical enumerations (i.e. with values in $\\mathbb N$) a
cquire meaning when the field of complex numbers is replaced with an arbit
rary field $k$. The result of the enumeration is then a quadratic form ove
r $k$ rather than an integer.\nThis talk will focus on such enumeration fo
r rational curves in del Pezzo surfaces. In particular I will report on a
recent joint work with Kirsten Wickelgren where we generalize a formula or
iginally due to Abramovich and Bertram in the complex setting\, that I lat
er extended over the real numbers. This quadratically enriched version of
the AB-formula relates enumerative invariants for different $k$-forms on t
he same del Pezzo surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Fock (Strasbourg)
DTSTART:20240620T131500Z
DTEND:20240620T144500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/67
DESCRIPTION:Title: Singularities\, Stokes data and clusters\nby
Vladimir Fock (Strasbourg) as part of Real and complex Geometry\n\n\nAbst
ract\nIn the talk we will suggest an explantation of a correspondence betw
een singularities and quivers stated first by S.Fomin\, P.Pylyavsky\, E.Sh
ustin\, and D.Thurston. The observation is that a singularity in two varia
bles as well as its versal deformations can (non-canonically) be transform
ed into a differential operators of one complex variable. The Stokes data
of these operator amounts to be a flag configuration. The space of such co
nfigurations admits a cluster coordinates corresponding to FPST quiver. Am
azingly\, different differential operators corresponding to a given singul
arities give apparently different but birationally canonically isomorphic
varieties.\nWe will discuss tropical limit of this construction making it
more canonical and its relation to the combinatorics of FPST.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:László Fehér (Eötvös\, Budapest)
DTSTART:20240704T131500Z
DTEND:20240704T144500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/68
DESCRIPTION:Title: Thom polynomials of real singularities\nby L
ászló Fehér (Eötvös\, Budapest) as part of Real and complex Geometry\
n\n\nAbstract\nThom polynomials are designed to solve enumerative problems
. The theory of Thom polynomials of complex singularities is well establis
hed. A theorem of Borel and Haeiger allows us to translate the complex res
ults to mod 2 results for real singularities\, which leads to solutions fo
r mod 2 enumerative problems. The theory of integer valued Thom polynomial
s of real singularities is not very well understood. I will talk about som
e important examples calculated jointly with András Szenes. A sample resu
lt is $tp(A_4(2l-1)) = (p_l)^2 + 3\\sum_{i=1}^l 4^{i-1}p_{l-i}p_{l+i}$ whe
re $p_i$ denote the Pontryagin classes and $A_4(2l .. 1)$ is the Thom-Boar
dman class $\\Sigma^{1\,1\,1\,1}$ in relative codimension $2l-1$. Notice t
he similarity with Ronga's formula for the Thom polynomial of the cusp (or
$A_2$ or $\\Sigma^{1\,1}$ singularities in the complex case. These result
s lead to non-trivial lower bounds for enumerative problems. Another direc
tion to find new results is to stay in the mod 2 world but enhance the Tho
m polynomials. In the complex case the Segre-Schwartz-MacPherson Thom poly
nomials were introduced by Ohmoto Toru. In a joint work with Ákos Matszan
gosz we introduced the real version\, the Segre-Stiefel-Whitney Thom polyn
omials. These allow us for example to find obstructionsand geometric meani
ng for them for the existence of Morin or fold maps of real projective spa
ces into a Euclidean space. As an example of these geometric interpretatio
ns of obstructions we can calculate the modulo 2 Euler class of certain de
generacy loci of generic smooth maps.\nJoint work with András Szenes and
Ákos Matszangosz.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javier Fernandez de Bobadilla (BCAM)
DTSTART:20240718T131500Z
DTEND:20240718T144500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/69
DESCRIPTION:Title: Symplectic geometry of degenerations at radius 0
\nby Javier Fernandez de Bobadilla (BCAM) as part of Real and complex
Geometry\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 endo
wed with a closed 2-form $w_A$ giving it the structure of a symplectic fib
ration. The restriction of $w_A$ to every fibre of $f_A$ «at positive rad
ius» (that is over a point of $D\\setminus \\{0\\}$) is the modification
by a potential of the restriction of $w_X$ to the same fibre. The construc
tion can be regarded as a symplectic realization of A'Campo model for the
monodromy and has found the following applications:\n\n(1) We can produce
symplectic representatives of the monodromy with very special dynamics\, a
nd based on this and on a spectral sequence due to McLean prove the family
version 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 complement of a codimension 2 set over the (expanded) essential skelet
on of the degeneration\, satisfying many of the properties conjectured by
Kontsevich and Soibelman. \n\nIn the talk I will highlight the main aspect
s of the construction\, and present some of the application (2).\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Misha Verbitsky (IMPA / HSE)
DTSTART:20240711T131500Z
DTEND:20240711T144500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/70
DESCRIPTION:Title: Complex geometry and the isometries of the hyper
bolic space\nby Misha Verbitsky (IMPA / HSE) as part of Real and compl
ex Geometry\n\n\nAbstract\nThe isometries of a hyperbolic space are classi
fied into three classes - elliptic\, parabolic\, and loxodromic\; this cla
ssification plays the major role in homogeneous dynamics of hyperbolic man
ifolds. Since the work of Serge Cantat in the early 2000-ies it is known t
hat a similar classification exists for complex surfaces\, that is\, compa
ct complex manifolds of dimension 2. These results were recently generaliz
ed to holomorphically symplectic manifolds of arbitrary dimension. I would
explain the ergodic properties of the parabolic automorphisms\, and prove
the ergodicity of the automorphism group action for an appropriate deform
ation of any compact holomorphically symplectic manifold. This is a joint
work with Ekaterina Amerik.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Degtyarev (Bilkent)
DTSTART:20240808T131500Z
DTEND:20240808T144500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/71
DESCRIPTION:Title: Real plane sextic curves with smooth real part\nby Alex Degtyarev (Bilkent) as part of Real and complex Geometry\n\n\n
Abstract\n(Joint w/ Ilia Itenberg)\n\nWe have obtained the complete deform
ation classification of\nsingular real plane sextic\ncurves with smooth re
al part\, i.e.\, those without real singular points.\n\nThis was made poss
ible due to the fact that\, under the assumption\,\ncontrary to the genera
l case\, the\nequivariant equisingular deformation type is determined by t
he so-called\n$\\textit{real homological type}$ in its most naïve sense\,
i.e.\, the\nhomological information about the polarization\, singularitie
s\, and real\nstructure\; one does not need to compute the fundamental pol
yhedron of the\ngroup generated by reflections and identify the classes of
ovals therein.\nShould time permit\, I will outline our proof of this the
orem.\n\nAs usual\, this classification leads us to a number of observatio
ns\, some of\nwhich we have already managed to generalize. Thus\, we have
an\nArnol$'$d--Gudkov--Rokhlin type congruence for close to maximal surfac
es (and\, hence\, even\ndegree curves) with certain singularities. Another
observation (which has not\nbeen quite understood yet and may turn out $K
3$-specific) is that the\ncontraction of\nany empty oval of a $\\textit{ty
pe I}$ real scheme results in a\n$\\textit{bijection}$ of the sets of defo
rmation classes.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Dettweiler (Bayreuth)
DTSTART:20240801T131500Z
DTEND:20240801T144500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/72
DESCRIPTION:Title: Galois realizations of special linear groups
\nby Michael Dettweiler (Bayreuth) as part of Real and complex Geometry\n\
n\nAbstract\nThe inverse Galois problem (IGP) asks\, if any given finite g
roup can be realized as Galois group over the rational numbers. We use the
theory of l-adic Fourier transform and convolution to find new Galois rea
lizations of special linear groups\, answering the IGP for these groups po
sitively.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ritwik Mukherjee (NISER)
DTSTART:20241107T141500Z
DTEND:20241107T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/73
DESCRIPTION:Title: Extension of Caporaso-Harris formula to count cu
spidal curves\nby Ritwik Mukherjee (NISER) as part of Real and complex
Geometry\n\n\nAbstract\nIn this talk\, we will study the following questi
on: how many degree $d$ \ncurves are there in $\\mathbb{CP}^2$\, that pass
through $d(d+3)/2-2$ generic points and \nhave one cusp? While this quest
ion has been studied earlier by several different \napproaches\, in this t
alk\, we will give a solution to this problem by extending \nthe degenerat
ion idea of Caporaso and Harris (which so far has been used \nto enumerate
nodal curves). \n\nIf time permits\, we will also talk about another gen
eralization of the Caporaso-Harris \n formula\, namely a family version of
their formula\, which can be used to count curves \nin a moving family of
surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gus Schrader (Northwestern)
DTSTART:20241205T141500Z
DTEND:20241205T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/74
DESCRIPTION:Title: Skeins\, clusters and wavefunctions\nby Gus
Schrader (Northwestern) as part of Real and complex Geometry\n\n\nAbstract
\nEkholm and Shende have proposed a version of open Gromov-Witten theory i
n which holomorphic maps from Riemann surfaces with boundary landing on a
Lagrangian 3-manifold L are counted via the image of the boundary in the H
OMFLYPT skein module of L. I'll describe joint work with Mingyuan Hu and E
ric Zaslow which gives a method to compute the Ekholm-Shende generating fu
nction ('wavefunction') enumerating such maps for a class of Lagrangian br
anes L in C^3. The method uses a skein-theoretic analog of cluster theory\
, in which skein-valued wavefunctions for different Lagrangians are relate
d by skein mutation operators.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davesh Maulik (MIT)
DTSTART:20241219T141500Z
DTEND:20241219T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/75
DESCRIPTION:Title: D-equivalence conjecture for varieties of K3^[n]
-type\nby Davesh Maulik (MIT) as part of Real and complex Geometry\n\n
\nAbstract\nThe D-equivalence conjecture of Bondal and Orlov predicts that
birational Calabi-Yau varieties have equivalent derived categories of coh
erent sheaves. I will explain how to prove this conjecture for hyperkahle
r varieties of K3^[n] type (i.e. those that are deformation equivalent to
Hilbert schemes of K3 surfaces). This is joint work with Junliang Shen\,
Qizheng Yin\, and Ruxuan Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Batyrev (Tübingen)
DTSTART:20241212T141500Z
DTEND:20241212T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/76
DESCRIPTION:Title: On birational minimal models of non-degenerate s
urfaces in 3-dimensional algebraic tori\nby Victor Batyrev (Tübingen)
as part of Real and complex Geometry\n\n\nAbstract\nAccording to the clas
sical birational classification of surfaces\, every algebraic surface \\(
X\\) of non-negative Kodaira dimension is birational to a unique smooth pr
ojective algebraic surface \\(S\\) which is called birational minimal mode
l of \\(X\\). We explicitly show this statement in case of non-degenerate
affine surfaces \\(X\\) given as zero \nloci of Laurent polynomials \\(F
\\) in 3-dimensional affine algebraic \ntori. The purpose of the talk is t
o give an explicit construction of the minimal birational model \\(S\\) of
\\(X\\) and to explain combinatorial formulas for computing its main top
ological invariants using the 3-dimensional Newton polytope \\(P\\) of \\
(F\\).\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qaasim Shafi (Heidelberg)
DTSTART:20250116T141500Z
DTEND:20250116T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/77
DESCRIPTION:Title: Tropical refined curve counting and mirror symme
try\nby Qaasim Shafi (Heidelberg) as part of Real and complex Geometry
\n\n\nAbstract\nAn old theorem\, due to Mikhalkin\, says that the number o
f rational plane curves of degree d through 3d-1 points is equal to a coun
t of tropical curves (combinatorial objects which are more amenable to com
putations). There are two natural directions for generalising this result:
extending to higher genus curves and allowing for more general conditions
than passing through points. I’ll discuss a generalisation which does b
oth\, which on the tropical side relates to the refined invariants of Blec
hman and Shustin. At the end I will mention some recent work connecting th
is story to mirror symmetry for log Calabi-Yau surfaces. This is joint wor
k with Patrick Kennedy-Hunt and Ajith Urundolil Kumaran.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gurvan Mével (LMJL\, Nantes)
DTSTART:20250109T141500Z
DTEND:20250109T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/78
DESCRIPTION:Title: Floor diagrams and refined invariants in positiv
e genus\nby Gurvan Mével (LMJL\, Nantes) as part of Real and complex
Geometry\n\n\nAbstract\nGöttche-Schroeter invariants are a rational tropi
cal refined invariant\, i.e. a polynomial \ncounting genus 0 curves on tor
ic surfaces. In this talk I will use a floor diagrams approach to extend t
hese invariants in any genus. I will then say few words on the link betwee
n this new quantity and the one simultaneously defined by Shustin and Sini
chkin.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bogdan Adrian Dina (Tel Aviv)
DTSTART:20250130T141500Z
DTEND:20250130T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/79
DESCRIPTION:Title: Abelian varieties with complex multiplication: E
xploring Shimura class groups and superspecial abelian varieties\nby B
ogdan Adrian Dina (Tel Aviv) as part of Real and complex Geometry\n\n\nAbs
tract\nThe first part of this talk examines the isomorphism classes $M_{O_
K}(\\Phi)$ of simple principally polarized abelian varieties of dimensions
$g = 2\, 3$ over number fields\, with complex multiplication (CM) of type
$(K\, \\Phi)$. A critical aspect of understanding the structure of $M_{O_
K}(\\Phi)$ lies in analyzing the Shimura class group $C_K$ of $K$ and the
reflex-type-norm map $N_{\\Phi^r}$ within $C_K$. According to Shimura's Ma
in Theorem of CM\, the orbits of $M_{O_K}(\\Phi)$ under the action of the
Galois group $\\Gal(\\bar Q | K^r)$ correspond to the elements of the quot
ient $C_K/N_{\\Phi^r}$. In this part of the talk\, we will define all the
relevant structures involved in the characteristic zero case\, including t
he Shimura class group\, the reflex-type-norm maps\, and their interaction
s with CM abelian varieties.\nThe second part of this talk\, a joint proje
ct with P. Kutas (ELTE)\, G. Lorenzon\, and W. Castryck (KU Leuven)\, focu
ses on oriented principally polarized superspecial abelian surfaces in pos
itive characteristic $p$. This section explores how insights from $M_{O_K}
(\\Phi)$ in characteristic zero can inform our understanding of these stru
ctures in characteristic $p$. We will also introduce some challenges of de
scending the Shimura class group action from characteristic zero to positi
ve characteristic.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dusa McDuff (Columbia)
DTSTART:20250327T141500Z
DTEND:20250327T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/80
DESCRIPTION:Title: The stabilized ellispoidal symplectic embedding
problem and scattering diagrams\nby Dusa McDuff (Columbia) as part of
Real and complex Geometry\n\n\nAbstract\nI will explain joint work with Ky
ler Siegel that solves the stabilized symplectic embedding problem for ell
ipsoids into rigid Fano surfaces. The key is to translate this into a prob
lem of constructing suitable unicuspidal curves\, and then to investigate
this via scattering diagrams and their symmetries. \n
\nThe talk will
be based on the papers arXiv:2404.00561 and ArXiv:2412.14702.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dhruv Ranganathan (Cambridge)
DTSTART:20250508T131500Z
DTEND:20250508T144500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/81
DESCRIPTION:Title: Extraneous components in moduli and extended tro
picalizations\nby Dhruv Ranganathan (Cambridge) as part of Real and co
mplex Geometry\n\n\nAbstract\nIn the last few years\, researchers have obs
erved a phenomenon in several different moduli problems in logarithmic and
tropical geometry. The phenomenon is a form of non-transversality of inte
rsections that arises in many natural geometric problems. The examples rel
ate to degeneration formulas for enumerative invariants\, the geometry of
the double ramification cycle\, and the Gromov-Witten theory of infinite r
oot stacks. Tropical geometry\, and more specifically the combinatorics of
extended (or compactified) tropicalizations\, seems to be very good at de
tecting and controlling these extraneous components. After giving an overv
iew of these ideas\, I will share a formalism that explains what is going
on here\, and how it leads to a conjecture about certain moduli spaces of
higher dimensional varieties. Joint work with Thibault Poiret\, and relate
d to prior work with Battistella\, Molcho\, Nabijou.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Blomme (Geneva)
DTSTART:20250320T141500Z
DTEND:20250320T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/82
DESCRIPTION:Title: A short proof of the multiple cover formula\
nby Thomas Blomme (Geneva) as part of Real and complex Geometry\n\n\nAbstr
act\nEnumerating genus g curves passing through g points in an abelian sur
face is a natural problem\, whose difficulty highly depends on the degree
of the curves. For "primitive" degrees\, we have an easy explicit answer.
For "divisible" classes\, such a resolution is quite demanding and often o
ut of reach. Yet\, the invariants for divisible classes easily express in
terms of the invariants for primitive classes through the multiple cover f
ormula\, conjectured by G. Oberdieck a few years ago. In this talk\, we'll
show how tropical geometry enables to prove the formula without any kind
of concrete enumeration.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Tyomkin (Ben-Gurion)
DTSTART:20250424T131500Z
DTEND:20250424T144500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/83
DESCRIPTION:Title: The irreducibility problem for Severi varieties
on toric surfaces\nby Ilya Tyomkin (Ben-Gurion) as part of Real and co
mplex Geometry\n\n\nAbstract\nI will present the current state of the art
on the irreducibility problem for Severi varieties on polarized toric surf
aces. There exist several approaches to this problem. In my talk\, I will
explore the tropical one\, which applies in arbitrary characteristic. In a
ddition\, I will provide examples and general constructions of reducible S
everi varieties and offer a complete classification of the irreducible com
ponents in the genus-one case.
\nThis talk is based on a series of joi
nt works with Lionel Lang\, Michael Barash\, Karl Christ\, and Xiang He.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Bychkov (Haifa)
DTSTART:20250515T131500Z
DTEND:20250515T144500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/84
DESCRIPTION:Title: Fully simple maps and x-y duality in topological
recursion\nby Boris Bychkov (Haifa) as part of Real and complex Geome
try\n\n\nAbstract\nBy a combinatorial map we mean a graph embedded in the
two dimensional surface. Enumeration of combinatorial maps and fully simpl
e maps (maps with some additional conditions on them) are governed by Chek
hov-Eynard-Orantin topological recursion --- a universal recursive procedu
re which\, by the small amount of the initial data (Riemann surface with t
wo functions x and y on it)\, produces symmetric meromorphic n-differentia
ls possessing all the information about the underlying enumerative problem
.\nThe duality between maps and fully simple maps goes through the monoton
e Hurwitz numbers was obtained by G.Borot\, S.Charbonnier\, N.Do and E.Gar
cia-Failde in 2019. In the talk I will explain this result and\, using the
combinatorics of the symmetric group and Fock space formalism\, will desc
ribe its connection to the general x-y duality in topological recursion.\n
\nThe talk is based on the series of papers joined with A. Alexandrov\, P.
Dunin-Barkowski\, M.Kazarian and S.Shadrin https://arxiv.org/abs/2106.0836
8\, https://arxiv.org/abs/2212.00320.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tim Gräfnitz (Hannover)
DTSTART:20250522T131500Z
DTEND:20250522T144500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/85
DESCRIPTION:Title: Enumerative geometry of quantum periods\nby
Tim Gräfnitz (Hannover) as part of Real and complex Geometry\n\n\nAbstrac
t\nI talk about joint work with Helge Ruddat\, Eric Zaslow and Benjamin Zh
ou interpreting the q-refined theta function of a log Calabi-Yau surface a
s a natural q-refinement of the open mirror map\, defined by quantum perio
ds of mirror curves for outer Aganagic-Vafa branes on the local Calabi-Yau
threefold. The series coefficients are all-genus logarithmic two-point in
variants\, directly extending the relation found by the first three author
s. The main part of the proof is combinatorial in nature\, using a convolu
tion relation for Bell polynomials\, and thus works in any dimension. We f
ind an explicit discrepancy at higher genus in the relation to open Gromov
-Witten invariants of the Aganagic-Vafa brane\, expressible in terms of re
lative invariants of an elliptic curve.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Brini (Sheffield / CNRS)
DTSTART:20250626T131500Z
DTEND:20250626T144500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/87
DESCRIPTION:Title: Refined Gromov-Witten invariants\nby Andrea
Brini (Sheffield / CNRS) as part of Real and complex Geometry\n\n\nAbstrac
t\nI will discuss a conjectural definition of refined curve counting invar
iants of Calabi-Yau threefolds with a C*-action in terms of stable maps on
Calabi-Yau fivefolds. The corresponding disconnected generating function
should conjecturally equate the Nekrasov-Okounkov K-theoretic membrane ind
ex under a refined version of the Gromov-Witten/Pandharipande-Thomas corre
spondence. I'll present several acid tests validating the conjecture\, bot
h in the A and the B-model. This is based on joint work with Yannik Schule
r (ETH Zurich)\, arXiv:2410.00118.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Esterov (LIMS)
DTSTART:20250612T131500Z
DTEND:20250612T144500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/88
DESCRIPTION:Title: Schön complete intersections\nby Alexander
Esterov (LIMS) as part of Real and complex Geometry\n\n\nAbstract\nThere i
s a number of "aesthetically similar" topics in combinatorial algebraic ge
ometry\, such as toric complete intersections\, hyperplane arrangements\,
simplest singularity strata of general polynomial maps\, some discriminant
and incidence varieties in enumerative geometry and polynomial optimizati
on\, polynomial ODEs such as reaction networks\, generalized Calabi--Yau c
omplete intersections.\n\nI will talk about a convenient umbrella generali
ty for all of them\, which still admits a version of the classical theory
of Newton polytopes (but with so-called tropical complete intersections in
stead of polytopes). \n
\nThis generalization includes the BKK formula
\, the patchworking construction\, and other familiar tools\, but applies
to many new interesting objects.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilia Itenberg (Sorbonne University)
DTSTART:20251113T141500Z
DTEND:20251113T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/89
DESCRIPTION:Title: Real plane sextic curves with smooth real part\nby Ilia Itenberg (Sorbonne University) as part of Real and complex Geo
metry\n\n\nAbstract\nThe talk is devoted to the curves of degree 6 in the
real projective plane. We show that\nthe equisingular deformation type of
a simple real plane sextic curve with smooth real\npart is determined by i
ts real homological type\, that is\, the polarization\, exceptional\ndivis
ors\, and real structure recorded in the homology of the covering K3-surfa
ce.\nWe also present an Arnold-Gudkov-Rokhlin type congruence for real alg
ebraic curves/surfaces\nwith certain singularities and a result concerning
contraction of ovals of a singular real plane sextic with smooth real par
t.
\n(This is a joint work with Alex Degtyarev.)\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Rau (Universidad de los Andes)
DTSTART:20251106T141500Z
DTEND:20251106T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/90
DESCRIPTION:Title: Counting rational curves over any field\nby
Johannes Rau (Universidad de los Andes) as part of Real and complex Geomet
ry\n\n\nAbstract\nAn important problem in enumerative geometry is counting
rational curves that interpolate a configuration of points in $\\mathbb{P
}^2$\, leading to Gromov-Witten invariants (over algebraically closed fiel
ds) and Welschinger invariants (over the real numbers). Recently\, Kass\,
Levine\, Solomon\, and Wickelgren constructed "quadratic" invariants that
work over an (almost) arbitrary base field. The “inconvenience” is tha
t these new invariants are no longer numbers\, but quadratic forms whose r
ank and signature recover the previously mentioned invariants. In a curren
t work with Erwan Brugallé and Kirsten Wickelgren\, we study these invari
ants in the framework of so-called Witt-invariants and show that\, convers
ely\, the quadratic invariants can be recovered from Gromov-Witten and Wel
schinger invariants. In my talk\, I want to give an introduction to this t
opic (and its extension to rational del Pezzo surfaces).\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brett Parker (ANU Math Sciences Institute)
DTSTART:20251211T141500Z
DTEND:20251211T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/91
DESCRIPTION:Title: Holomorphic Lagrangians\, GW invariants\, and re
al structures\nby Brett Parker (ANU Math Sciences Institute) as part o
f Real and complex Geometry\n\n\nAbstract\nI will describe a holomorphic v
ersion of Weinstein’s symplectic category\, in which morphisms are encod
ed by holomorphic Lagrangians. I will explain that Gromov—Witten invaria
nts of log Calabi—Yau 3-folds are canonically encoded as morphisms in th
is category\, and explain that conjecturally\, the GW/DT correspondence is
also a morphism in this category. An advantage of this concretely geometr
ic perspective is that it is compatible with real structures.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carl Lian (Washington University in St. Louis)
DTSTART:20260108T141500Z
DTEND:20260108T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/92
DESCRIPTION:Title: Counting curves on $\\mathbb{P}^r$\nby Carl
Lian (Washington University in St. Louis) as part of Real and complex Geom
etry\n\n\nAbstract\nThe geometric Tevelev degrees of projective space enum
erate general\, pointed curves with fixed complex structure interpolating
through the maximal number of points in $\\mathbb{P}^r$. The study of the
corresponding virtual invariants goes back to the beginning of Gromov-Witt
en theory in the 1990s\, whereas the closely related problem of enumeratin
g linear series on general curves goes back even earlier\, to the 19th cen
tury. We explain a complete calculation of the geometric Tevelev degrees o
f projective space in terms of Schubert calculus\, which interpolates betw
een both of these worlds. The final answer involves torus orbit closures o
n Grassmannians\, which are fundamental objects in matroid theory. Recent
work with Saskia Solotko expresses the invariants alternatively in terms o
f combinatorics of words\, via the RSK correspondence. We discuss some ope
n directions.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lev Radzivilovsky (Tel Aviv University)
DTSTART:20251127T141500Z
DTEND:20251127T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/93
DESCRIPTION:Title: Enumeration of rational surfaces and moduli spac
es of configurations of points in the projective plane\nby Lev Radzivi
lovsky (Tel Aviv University) as part of Real and complex Geometry\n\n\nAbs
tract\nThis is presentation of my Ph.D. thesis which is related to enumera
tive geometry and moduli spaces. \nThe inspiration for this project comes
from enumeration of rational curves of given degree in the projective plan
e. \nThe problem of enumeration of rational goes back to 19th century\, an
d was solved by Kontsevich and Manin in 1994. \nThe first solution was bas
ed on the development of the theory of moduli spaces\, in particular $\\ov
erline{M}_{0\,n}$\nthe compact algebraic space of rational nodal stable cu
rves with $n$ marked points. \nThe unachieved goal was to develop a simila
r theory for enumeration of surfaces in 3-dimensional projective space.\nT
he first step would be to find a smooth compactification for a space of ge
neric configurations of $n$ marked points. \nThere is a construction of Ka
pranov which he called "Chow quotients" of Grassmanians which generalizes
\n$\\overline{M}_{0\,n}$ to any dimension\, in particular it creates a sim
ilar space for configurations of $n$ marked points\nIn the projective plan
e\; it has several nice properties\, but it is not smooth even for 6 point
s in the plane\n(so it would be hard to talk about intersection theory). H
ere\, a new version of Kapranov's construction is presented\, \nby a simil
ar technology but with a blow-up idea: we add lines connecting pairs of ma
rked points before applying Chow quotients.\nWe prove that the new space f
or configuration of 6 marked points in the plane is smooth.\nAnother resul
t (joint with S. Carmeli)\, which is obtained by intersection theory\, is
the enumeration of surfaces of given degree\nwith a singular line\, vanish
ing to order $k$ at the line.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uriel Sinichkin (Tel Aviv University)
DTSTART:20251225T141500Z
DTEND:20251225T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/94
DESCRIPTION:Title: Refined invariants in tropical\, complex\, and r
eal enumerative geometries\nby Uriel Sinichkin (Tel Aviv University) a
s part of Real and complex Geometry\n\n\nAbstract\nRefined invariants were
first introduced into tropical geometry by Block and Gottsche in 2016. Si
nce then\, various authors have investigated their properties and consider
ed several generalizations. In this talk\, I will present a version of ref
ined invariants in positive genera\, incorporating contact information\, w
hich was introduced jointly with Evgenii Shustin. I will also discuss some
limitations of this invariant\, particularly related to real enumerative
geometry\, along with our proposed solution: limiting some of the point co
nditions to lie on the toric boundary.
\nThis is a presentation of my
Ph.D. thesis.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andres Franco Valiente (UC Berkeley)
DTSTART:20260122T141500Z
DTEND:20260122T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/95
DESCRIPTION:Title: Introduction to tropical-topological (tropologic
al) sigma models\nby Andres Franco Valiente (UC Berkeley) as part of R
eal and complex Geometry\n\n\nAbstract\nGromov-Witten invariants have been
historically computed by physicists through the formal use of an infinite
dimensional extension of equivariant localization. In this talk\, I will
review how Gromov-Witten invariants are in principle constructed from this
point of view and how Mikhalkin’s theorem which states that Gromov-Witt
en invariants can be recovered from the tropical limit of pseudoholomorphi
c curves can also be reformulated in this language in terms of what is kno
wn as a tropical topological sigma model. We find that the relevant geomet
ries associated to the tropical limit of the sigma models are no longer re
lated to complex structures but instead based on deformation invariance of
nilpotent endomorphisms on singular foliated manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Webb (Cornell University)
DTSTART:20260326T141500Z
DTEND:20260326T154500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/96
DESCRIPTION:Title: Twisted weighted stable maps\nby Rachel Webb
(Cornell University) as part of Real and complex Geometry\n\n\nAbstract\n
I will present a common generalization of the twisted stable maps of Abram
ovich-Vistoli and the weighted stable maps of Alexeev-Guy and Bayer-Manin
(building on work of Hassett). The theory has potential applications to co
mputing Gromov-Witten invariants of Deligne-Mumford stacks with abelian st
abilizer groups.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierrick Bousseau (Oxford)
DTSTART:20260416T131500Z
DTEND:20260416T144500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/97
DESCRIPTION:by Pierrick Bousseau (Oxford) as part of Real and complex Geom
etry\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vivek Shende (SDU / Berkeley)
DTSTART:20260514T131500Z
DTEND:20260514T144500Z
DTSTAMP:20260404T094149Z
UID:AlgebraicGeometryTopology/98
DESCRIPTION:by Vivek Shende (SDU / Berkeley) as part of Real and complex G
eometry\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeometryTopolog
y/98/
END:VEVENT
END:VCALENDAR