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BEGIN:VEVENT
SUMMARY:Hulya Argüz (Université de Versailles)
DTSTART;VALUE=DATE-TIME:20200427T130000Z
DTEND;VALUE=DATE-TIME:20200427T143000Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/1
DESCRIPTION:Title: Tropical enumeration of real log curves in toric varieti
es\nby Hulya Argüz (Université de Versailles) as part of Real and co
mplex Geometry\n\n\nAbstract\nWe define real log curves in toric varieties
and set up a well-defined counting problem for them using the degeneratio
n approach of Nishinou--Siebert. We then investigate the tropical analogue
s of such curves to obtain a formula for their counts from the tropical de
scription. Focusing on the two dimensional case\, we also explain how to c
apture Welschinger signs from a local analysis of the degeneration\, to ob
tain log Welschinger invariants. This is joint work with Pierrick Bousseau
.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ethan Cotterill (Universidade Federal Fluminense)
DTSTART;VALUE=DATE-TIME:20200511T130000Z
DTEND;VALUE=DATE-TIME:20200511T143000Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/2
DESCRIPTION:Title: Rational curves with hyperelliptic singularities\nby
Ethan Cotterill (Universidade Federal Fluminense) as part of Real and com
plex Geometry\n\n\nAbstract\nWe study singular rational curves in projecti
ve space\, deducing conditions on their parameterizations from the value s
emigroups of their singularities. Here we focus on rational curves with cu
sps whose semigroups are of hyperelliptic type. We prove that a genus-g hy
perelliptic singularity imposes at least (n-1)g conditions on rational cur
ves of sufficiently large fixed degree in P^n\, and we prove that this bou
nd is exact when g is small. We also provide evidence for a conjectural ge
neralization of this bound for rational curves with cusps with arbitrary v
alue semigroup S. Our conjecture\, if true\, produces infinitely many new
examples of reducible Severi-type varieties M^n_{d\,g} of holomorphic maps
P^1 -> P^n with images of degree d and arithmetic genus g.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boulos El Hilany (Johannes Radon Institute for Computational and A
pplied Mathematics\, Linz)
DTSTART;VALUE=DATE-TIME:20200525T130000Z
DTEND;VALUE=DATE-TIME:20200525T143000Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/4
DESCRIPTION:Title: Counting isolated points outside the image of a polynomi
al map\nby Boulos El Hilany (Johannes Radon Institute for Computationa
l and Applied Mathematics\, Linz) as part of Real and complex Geometry\n\n
\nAbstract\nA dominant polynomial map from the complex plane to itself giv
es rise to a finite set of curves and isolated points outside its image. Z
. Jelonek provided an upper bound on the number of such isolated points th
at is quadratic in\, and depends only on\, the degrees of the polynomials
involved. I will introduce in this talk a large family of dominant non-pro
per maps above for which this upper bound is linear in the degrees. Moreov
er\, I will illustrate constructions proving asymptotical sharpness up to
multiplication by a constant.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Arnal (Institut de Mathematiques de Jussieu)
DTSTART;VALUE=DATE-TIME:20201022T130000Z
DTEND;VALUE=DATE-TIME:20201022T143000Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/5
DESCRIPTION:Title: Families of real projective algebraic hypersurfaces with
large asymptotic Betti numbers\nby Charles Arnal (Institut de Mathema
tiques de Jussieu) as part of Real and complex Geometry\n\n\nAbstract\nWe
describe a recursive method for constructing a family of real projective a
lgebraic hypersurfaces in ambient dimension $n$ from families of such hype
rsurfaces in ambient dimensions $k=1\,\\ldots\,n-1$. The asymptotic Betti
numbers of real parts of the resulting family can then be described in ter
ms of the asymptotic Betti numbers of the real parts of the families used
as ingredients. The algorithm is based on Viro's Patchwork and inspired by
I. Itenberg's and O. Viro's construction of asymptotically maximal famili
es in arbitrary dimension. Using it\, we prove that for any $n$ and $i=0\,
\\ldots\,n-1$\, there is a family of asymptotically maximal real projectiv
e algebraic hypersurfaces $\\{X^n_d\\}_d$ in $\\R \\PP ^n$ such that the $
i$-th Betti numbers $b_i(\\R X^n_d)$ are asymptotically strictly greater t
han the $(i\,n-1-i)$-th Hodge numbers $h^{i\,n-1-i}(\\C X^n _d)$. We also
build families of real projective algebraic hypersurfaces whose real parts
have asymptotic (in the degree $d$) Betti numbers that are asymptotically
(in the ambient dimension $n$) very large.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stepan Orevkov (Steklov Math. Institute and Universite Paul Sabati
er\, Toulouse)
DTSTART;VALUE=DATE-TIME:20201029T140000Z
DTEND;VALUE=DATE-TIME:20201029T153000Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/6
DESCRIPTION:Title: On real algebraic and real pseudoholomorphic curves in $
RP^2$\nby Stepan Orevkov (Steklov Math. Institute and Universite Paul
Sabatier\, Toulouse) as part of Real and complex Geometry\n\n\nAbstract\nI
will present an inequality for the isotopy type of a plane non-singular r
eal algebraic curve endowed with a complex orientation (i.e.\, for its com
plex scheme according to Rokhlin's terminology) which implies in particula
r that an infinite series of complex schemes are realizable pseudoholomorp
hically but not algebraically.\nThese are the first known examples of this
kind for complex schemes of non-singular curves in $RP^2$.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Blomme (Universite de Neuchatel)
DTSTART;VALUE=DATE-TIME:20201105T140000Z
DTEND;VALUE=DATE-TIME:20201105T153000Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/7
DESCRIPTION:Title: Refined count of rational tropical curves in arbitrary d
imension\nby Thomas Blomme (Universite de Neuchatel) as part of Real a
nd complex Geometry\n\n\nAbstract\nIn this talk we will introduce a refine
d multiplicity for rational tropical curves in any dimension. This multipl
icity generalizes the multiplicity of Block-Göttsche for planar tropical
curves. We also show that the count of solutions to some general tropical
enumerative problem using this new multiplicity leads tropical refined inv
ariants\, hinting toward the existence of classical refined invariants for
classical rational curves.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arielle Leitner (Weizmann Institute of Science)
DTSTART;VALUE=DATE-TIME:20201112T140000Z
DTEND;VALUE=DATE-TIME:20201112T153000Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/8
DESCRIPTION:Title: Deformations of Generalized Cusps on Convex Projective M
anifolds\nby Arielle Leitner (Weizmann Institute of Science) as part o
f Real and complex Geometry\n\n\nAbstract\nConvex projective manifolds are
a generalization of hyperbolic manifolds. Koszul showed that the set of h
olonomies of convex projective structures on a compact manifold is open in
the representation variety. We will describe an extension of this result
to convex projective manifolds whose ends are generalized cusps\, due to C
ooper-Long-Tillmann. Generalized cusps are certain ends of convex projecti
ve manifolds. They may contain both hyperbolic and parabolic elements. We
will describe their classification (due to Ballas-Cooper-Leitner)\, and ex
plain how generalized cusps turn out to be deformations of cusps of hyperb
olic manifolds. We will also explore the moduli space of generalized cusps
\, it is a semi-algebraic set of dimension n^2-n\, contractible\, and may
be studied using several different invariants. For the case of three manif
olds\, the moduli space is homeomorphic to R^2 times a cone on a solid tor
us.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Ancona (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20201126T140000Z
DTEND;VALUE=DATE-TIME:20201126T153000Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/9
DESCRIPTION:Title: Exponential rarefaction of maximal hypersurfaces\nby
Michele Ancona (Tel Aviv University) as part of Real and complex Geometry
\n\n\nAbstract\nSmith-Thom's inequality tells us that the sum of Betti num
bers of the real locus of a real algebraic variety is always smaller than
or equal to the sum of Betti numbers of its complex locus. In the case of
equality\, the real algebraic variety is called maximal. Given a real holo
morphic line bundle L over a real algebraic variety X\, I will prove that
the probability that a real holomorphic section of L^d defines a maximal h
ypersurface tends to 0 exponentially fast when d tends to infinity.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Benoist (ENS\, Paris)
DTSTART;VALUE=DATE-TIME:20210318T140000Z
DTEND;VALUE=DATE-TIME:20210318T153000Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/10
DESCRIPTION:Title: Rational curves on real algebraic varieties\nby Oli
vier Benoist (ENS\, Paris) as part of Real and complex Geometry\n\n\nAbstr
act\nLet X be a smooth projective real algebraic variety. When is it possi
ble to approximate loops in the real locus X(R) by real loci of rational c
urves on X? In this talk\, I will provide a positive answer for a class of
varieties that includes cubic hypersurfaces and compactifications of homo
geneous spaces under connected linear algebraic groups. This is joint work
with Olivier Wittenberg.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier de Gaay Fortman (ENS\, Paris)
DTSTART;VALUE=DATE-TIME:20210311T140000Z
DTEND;VALUE=DATE-TIME:20210311T153000Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/11
DESCRIPTION:Title: Real Noether-Lefschetz loci and density of non-simple a
belian varieties over the real numbers\nby Olivier de Gaay Fortman (EN
S\, Paris) as part of Real and complex Geometry\n\n\nAbstract\nSometimes t
he geometry of an algebraic variety poses restrictions on the geometry of
its algebraic subvarieties. A beautiful example is the Noether-Lefschetz T
heorem which states that on a general complex algebraic surface of degree
greater than three in three dimensional projective space\, any curve is ob
tained as a complete intersection of the surface with another hypersurface
. In spite of this\, Green's density criterion enabled Ciliberto\, Harris
and Miranda to prove that the Noether-Lefschetz locus is dense for the Euc
lidean topology in the space of all smooth degree d > 3 complex polynomial
s. Over the real numbers\, things are more complicated. The general real h
ypersurface in P^3 of degree larger than three still has Picard rank one b
ut real surfaces with jumping Picard rank are not dense at all in the spac
e of real smooth degree d > 3 polynomials: the latter is not connected and
the real Noether-Lefschetz locus can miss a connected component entirely.
There is a density criterion but it is much harder to fulfill and can onl
y be applied to one component at a time. Our goal in this talk is to pose
an analogous question in the setting of real abelian varieties and to prov
e that in that situation\, none of these problems occur. Fixing natural nu
mbers g\, k\, and a polarized family of abelian varieties of dimension g d
efined over the real numbers\, when are real (resp. complex) abelian varie
ties that contain a real (resp. complex) abelian subvariety of dimension k
dense in the set of real (resp. complex) points of the base? For each of
these densities there is a natural criterion and surprisingly\, they are t
he same. Various applications are given along these lines\, such as densit
y of such loci in moduli spaces of principally polarized real abelian vari
eties\, real algebraic curves\, and real plane curves.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Tyomkin (Ben-Gurion University)
DTSTART;VALUE=DATE-TIME:20210429T130000Z
DTEND;VALUE=DATE-TIME:20210429T143000Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/12
DESCRIPTION:Title: On (ir)reducibility of Severi varieties on toric surfac
es\nby Ilya Tyomkin (Ben-Gurion University) as part of Real and comple
x Geometry\n\n\nAbstract\nIn my talk I will discuss the problem of irreduc
ibility of families of curves of given degree and genus on toric surfaces.
Such families\, called Severi varieties\, have been intensively studied d
ue to a variety of applications of their geometry to the study of moduli s
paces of curves\, and to various enumerative problems. After reviewing bri
efly known irreducibility results\, I'll describe examples of toric surfac
es admitting reducible Severi varieties\, and introduce certain topologica
l and tropical invariants that allow one to distinguish between different
irreducible components. The talk is based on a joint work with Lionel Lang
.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lev Radzivilovsky (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20210617T130000Z
DTEND;VALUE=DATE-TIME:20210617T143000Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/13
DESCRIPTION:Title: Enumeration of rational surfaces and moduli spaces of c
onfigurations of points in the projective plane\nby Lev Radzivilovsky
(Tel Aviv University) as part of Real and complex Geometry\n\n\nAbstract\n
We discuss the problem of enumerating rational surfaces in 3-dimensional p
rojective space\, as an analogue of Gromov-Witten invariants. It leads nat
urally to moduli spaces of cofigurations of $n$ marked points in projectiv
e planes. We discuss the "Chow quotients" of Kapranov\, and present a new
version of this construction which gives a smooth moduli space for configu
rations of 6 points. We conjecture that the same construction yields a smo
othing of the moduli space of configurations of any number of points in th
e plane. We also briefly present a formula for enumeration of surfaces wit
h a singular line.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:KhazhgaliKozhasov
DTSTART;VALUE=DATE-TIME:20210715T130000Z
DTEND;VALUE=DATE-TIME:20210715T143000Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/14
DESCRIPTION:Title: Nodes on quintic spectrahedra\nby KhazhgaliKozhasov
as part of Real and complex Geometry\n\n\nAbstract\nGiven generic real sy
mmetric matrices A\, B\, C of size n x n\, it is of interest to study the
set S of positive-semidefinite matrices of the form Id + x A + y B + z C\,
where x\, y\, z are some real numbers. The set S is a closed convex set i
n R^3\, called a spectrahedron. The Zariski closure of the Eucllidean boun
dary of S is an algebraic surface {(x\,y\,z): det(Id+ x A+y B+ z C)=0}\, w
hich turns out to be always singular. A natural question in real algebraic
geometry is to understand (for a fixed n) possible restrictions on the nu
mbers P\, Q of real singular points\, respectively\, of those singularitie
s that lie on S. In my talk I will discuss this problem for quintic spectr
ahedra (n=5) and present a complete classification of pairs (P\,Q)\, obtai
ned in a joint work with Taylor Brysiewicz and Mario Kummer.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Kerner (Ben-Gurion University)
DTSTART;VALUE=DATE-TIME:20210812T130000Z
DTEND;VALUE=DATE-TIME:20210812T143000Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/15
DESCRIPTION:Title: Germs of maps\, group actions and large modules inside
group orbits\nby Dmitry Kerner (Ben-Gurion University) as part of Real
and complex Geometry\n\n\nAbstract\nA map (k^n\,o)-> (k^p\,o) with no cri
tical point at the origin can be rectified to a linear map. Maps with crit
ical points have rich structure and are studied up to the groups of right/
left-right/contact equivalence. The group orbits are complicated and are t
raditionally studied via their tangent space. This transition is classical
ly done by vector fields integration\, thus binding the theory to the real
/complex case. I will present the new approach to this subject. One studie
s the maps of germs of Noetherian schemes\, in any characteristic. The cor
responding groups of equivalence admit `good' tangent spaces. The submodul
es of the tangent spaces lead to submodules of the group orbits. This allo
ws to bring these maps to `convenient' forms. For example\, we get the (re
lative) finite determinacy\, and accordingly the (relative) algebraization
of maps/ideals/modules.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erwan Brugalle
DTSTART;VALUE=DATE-TIME:20211021T130000Z
DTEND;VALUE=DATE-TIME:20211021T143000Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/16
DESCRIPTION:Title: Euler characteristic and signature of real semi-stable
degenerations\nby Erwan Brugalle as part of Real and complex Geometry\
n\n\nAbstract\nIt is interesting to compare the Euler characteristic of th
e real part of a real algebraic variety to the signature of its complex pa
rt. For example\, a theorem by Itenberg and Bertrand states that both quan
tities are equal for "primitive T-hypersurfaces". After defining these lat
ter\, I will give a motivic proof of this theorem via the motivic nearby f
iber of a real semi-stable degeneration. This proof extends in particular
the original statement by Itenberg and Bertrand to non-singular tropical v
arieties.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierrick Bousseau
DTSTART;VALUE=DATE-TIME:20211104T140000Z
DTEND;VALUE=DATE-TIME:20211104T153000Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/17
DESCRIPTION:Title: Gromov-Witten theory of complete intersections\nby
Pierrick Bousseau as part of Real and complex Geometry\n\n\nAbstract\nI wi
ll describe an inductive algorithm computing Gromov-Witten invariants in a
ll genera with arbitrary insertions of all smooth complete intersections i
n projective space. The main idea is to show that invariants with insertio
ns of primitive cohomology classes are controlled by their monodromy and b
y invariants defined without primitive insertions but with imposed nodes i
n the domain curve. To compute these nodal Gromov-Witten invariants\, we i
ntroduce the new notion of nodal relative Gromov-Witten invariants. This i
s joint work with Hülya Argüz\, Rahul Pandharipande\, and Dimitri Zvonki
ne (arxiv:2109.13323).\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierrick Bousseau
DTSTART;VALUE=DATE-TIME:20211104T140000Z
DTEND;VALUE=DATE-TIME:20211104T153000Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/18
DESCRIPTION:Title: Gromov-Witten theory of complete intersections\nby
Pierrick Bousseau as part of Real and complex Geometry\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Penka Georgieva
DTSTART;VALUE=DATE-TIME:20211118T140000Z
DTEND;VALUE=DATE-TIME:20211118T153000Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/19
DESCRIPTION:Title: Higher-genus real/open counts in dimension 2\nby Pe
nka Georgieva as part of Real and complex Geometry\n\n\nAbstract\nAfter di
scussing some of the difficulties and progress in defining real and open c
ounts\, I will describe a generalisation of the higher-genus Welschinger i
nvariants defined by E. Shustin to the symplectic setting. I will then out
line a recursive formula allowing for reduction of the genus and the degre
e for computing these invariants. This is a joint work in progress with E.
Brugallé\, Y. Ding\, and A. Renaudineau.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Stecconi
DTSTART;VALUE=DATE-TIME:20211202T140000Z
DTEND;VALUE=DATE-TIME:20211202T153000Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/20
DESCRIPTION:Title: Semicontinuity of Betti numbers and singular sets\n
by Michele Stecconi as part of Real and complex Geometry\n\n\nAbstract\nTh
ere are many objects in geometry that are called "singularities"\, \ndepen
ding on the context. The most basic examples are the zero set (i.e. \nhype
rsurface) or the set of critical points of a function\, the set of \npoint
s where two hypersurfaces are tangent to each other\, etc. In this \ntalk
we will investigate the topology of different types of singular \nloci fro
m a broad perspective.\n\nThe topology of the singular set of a polynomial
imposes a lower bound \non the degree\, due to the Thom-Milnor bound and
similar results. I will \ndiscuss some quantitative version of this concep
t\, for smooth maps. Such \ntopic is relevant in the context of smooth rig
idity and Whitney \nextension problem\, but it also offer an alternative a
pproach to the \npolynomial case.\n\nBy using polynomial approximations in
a quantitative way\, one obtains a \nThom-Milnor bound valid for all smoo
th maps. However\, the standard way \nof controlling the topology in the a
pproximation: maintaining a \ntransversality condition\, produces a non-sh
arp inequality. I will \npresent a general result about the behavior of th
e Betti numbers under \nC^0 approximations that allows to improve the abov
e method.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Abramovich (Brown University)
DTSTART;VALUE=DATE-TIME:20211209T140000Z
DTEND;VALUE=DATE-TIME:20211209T153000Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/21
DESCRIPTION:Title: Punctured logarithmic maps\nby Dan Abramovich (Brow
n University) as part of Real and complex Geometry\n\n\nAbstract\nGromov-W
itten theory revolves around the enumerative question of counting algebrai
c curves in a smooth algebraic variety X meeting n given cycles - the utmo
st generalization of the question "how many lines pass through two given p
oints". Enumerative geometry\, degeneration techniques\, and mirror symmet
ry lead us to consider the analogous question where one also imposes conta
ct orders with a suitable divisor. I will introduce our work laying genera
l foundations for such a theory.\nThis is joint work with Q. Chen\, M. Gro
ss\, and B. Siebert.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Abramovich (Brown University)
DTSTART;VALUE=DATE-TIME:20211209T140000Z
DTEND;VALUE=DATE-TIME:20211209T153000Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/22
DESCRIPTION:Title: Punctured logarithmic maps\nby Dan Abramovich (Brow
n University) as part of Real and complex Geometry\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Rubio (Universitat de Barcelona)
DTSTART;VALUE=DATE-TIME:20211216T140000Z
DTEND;VALUE=DATE-TIME:20211216T153000Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/23
DESCRIPTION:Title: Generalized complex geometry and three-manifolds\nb
y Roberto Rubio (Universitat de Barcelona) as part of Real and complex Geo
metry\n\n\nAbstract\nGeneralized geometry is a unifying approach to geomet
ric structures where\, for example\, complex and symplectic structures bec
ome particular instances of a more general structure: a generalized comple
x structure. After a self-contained introduction to generalized complex ge
ometry (which is only possible for even-dimensional manifolds)\, I will ex
plain how generalized geometry can be upgraded to Bn-generalized geometry\
, in which the generalized-complex approach applies as well to odd dimensi
ons. Finally\, I will comment on some ongoing joint work with J. Porti in
which we look at the case of three-manifolds.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Polyak (Technion)
DTSTART;VALUE=DATE-TIME:20220106T140000Z
DTEND;VALUE=DATE-TIME:20220106T153000Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/24
DESCRIPTION:Title: Refined tropical counting\, ribbon structures and the q
uantum torus\nby Michael Polyak (Technion) as part of Real and complex
Geometry\n\n\nAbstract\nTropical geometry is a powerful instrument in alg
ebraic geometry\, allowing for a simple combinatorial treatment of various
enumerative problems. Tropical curves are planar metric graphs with certa
in requirements of balancing\, rationality of slopes and integrality. An a
ddition of a ribbon structure (and a removal of rationality/integrality re
quirements) lead to a particularly simple combinatorial construction of mo
duli of ribbon (pseudo)tropical curves. Refined Block-Goettsche counting o
f rational tropical curves turns into a construction of some simple top-di
mensional cycles on these moduli and maps of spheres. These cycles turn ou
t to be closely related to associative algebras\; curves with "flat" verti
ces necessitate a passage from associative to Lie algebras. In particular\
, counting of (both complex and real) curves in toric varieties is related
to the quantum torus algebra. More complicated counting invariants (the s
o-called Gromov-Witten descendants\, or relative Welschinger invariants) a
re treated similarly and are related to the super-Lie structure on the qua
ntum torus. As a by-product we obtain a new one-parameter family of weight
s for a refined counting of the descendants.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Viatcheslav Kharlamov (Universite de Strasbourg)
DTSTART;VALUE=DATE-TIME:20220113T140000Z
DTEND;VALUE=DATE-TIME:20220113T153000Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/25
DESCRIPTION:Title: On surgery invariant counts in real algebraic geometry<
/a>\nby Viatcheslav Kharlamov (Universite de Strasbourg) as part of Real a
nd complex Geometry\n\n\nAbstract\nOriginal Welschinger invariants as well
as their various generalizations are very sensitive to the change of topo
logy of the underlying real structure. However\, as was later noticed\, so
me combinations of Welschinger invariants may have a stronger invariance p
roperty which I call "surgery invariance": the property to be preserved un
der "wall-crossing" and as a result to be independent on a chosen real str
ucture in a given complex deformation class of varieties under considerati
on. The starting example is the signed count of real lines on cubic surfac
es in accordance with B. Segre's division of such lines in 2 kinds\, hyper
bolic and elliptic. This example gave rise to the discovery of similar cou
nts on higher dimensional hypersurfaces and complete intersections\, and s
erved as one of the roots for a development of an integer valued real Schu
bert calculus. In this talk (based on a work in progress\, joint with Serg
ey Finashin) I intend to discuss an extension of the above example with re
al lines on cubic surfaces in a bit different direction: from lines on a c
ubic surface to lines\, and even arbitrary degree rational curves\, on oth
er del Pezzo surfaces. Apart of surgery invariance property\, the invarian
ts we built also have other remarkable properties\, like a "magic" direct
relation to Gromov-Witten invariants and surprisingly elementary closed co
mputational formulae.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Blomme (Universite de Geneve)
DTSTART;VALUE=DATE-TIME:20220127T140000Z
DTEND;VALUE=DATE-TIME:20220127T153000Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/26
DESCRIPTION:Title: Enumeration of tropical curves in abelian surfaces\
nby Thomas Blomme (Universite de Geneve) as part of Real and complex Geome
try\n\n\nAbstract\nTropical geometry is a powerful tool that allows one to
compute enumerative algebraic invariants through the use of some correspo
ndence theorem\, transforming an algebraic problem into a combinatorial pr
oblem. Moreover\, the tropical approach also allows one to twist definitio
ns to introduce mysterious refined invariants\, obtained by counting curve
s with polynomial multiplicities. So far\, this correspondence has mainly
been implemented in toric varieties. In this talk we will study enumeratio
n of curves in abelian surfaces and line bundles over an elliptic curve.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marvin Anas Hahn (Institut de Mathematiques Jussieu)
DTSTART;VALUE=DATE-TIME:20220303T141500Z
DTEND;VALUE=DATE-TIME:20220303T154500Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/27
DESCRIPTION:Title: : Intersecting psi-classes on tropical Hassett spaces\nby Marvin Anas Hahn (Institut de Mathematiques Jussieu) as part of Rea
l and complex Geometry\n\n\nAbstract\nIn this talk\, we study the tropical
intersection theory of Hassett spaces in genus 0. Hassett spaces are alte
rnative compactifications of the moduli space of curves with n marked poin
ts induced by a vector of rational numbers. These spaces have a natural co
mbinatorial analogue in tropical geometry\, called tropical Hassett spaces
\, provided by the Bergman fan of a matroid which parametrizes certain n m
arked graphs. We introduce a notion of Psi-classes on these tropical Hasse
tt spaces and determine their intersection behavior. In particular\, we sh
ow that for a large family of rational vectors - namely the so-called heav
y/light vectors - the intersection products of Psi-classes of the associat
ed tropical Hassett spaces agree with their algebra-geometric analogue. Th
is talk is based on a joint work with Shiyue Li.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kris Shaw (University of Oslo)
DTSTART;VALUE=DATE-TIME:20220224T141500Z
DTEND;VALUE=DATE-TIME:20220224T154500Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/28
DESCRIPTION:Title: A tropical approach to the enriched count of bitangents
to quartic curves\nby Kris Shaw (University of Oslo) as part of Real
and complex Geometry\n\n\nAbstract\nUsing A1 enumerative geometry Larson a
nd Vogt have provided an enriched count of the 28 bitangents to a quartic
curve. In this talk\, I will explain how these enriched counts can be comp
uted combinatorially using tropical geometry. I will also introduce an ari
thmetic analogue of Viro's patchworking for real algebraic curves which\,
in some cases\, retains enough data to recover the enriched counts. This t
alk is based on joint work with Hannah Markwig and Sam Payne.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yelena Mandelshtam (University of California\, Berkeley)
DTSTART;VALUE=DATE-TIME:20220310T141500Z
DTEND;VALUE=DATE-TIME:20220310T154500Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/29
DESCRIPTION:Title: Curves\, degenerations\, and Hirota varieties\nby Y
elena Mandelshtam (University of California\, Berkeley) as part of Real an
d complex Geometry\n\n\nAbstract\nThe Kadomtsev-Petviashvili (KP) equation
is a differential equation whose study yields interesting connections bet
ween integrable systems and algebraic geometry. In this talk I will discus
s solutions to the KP equation whose underlying algebraic curves undergo t
ropical degenerations. In these cases\, Riemann's theta function becomes a
finite exponential sum that is supported on a Delaunay polytope. I will i
ntroduce the Hirota variety which parametrizes all KP solutions arising fr
om such a sum. I will then discuss a special case\, studying the Hirota va
riety of a rational nodal curve. Of particular interest is an irreducible
subvariety that is the image of a parameterization map. Proving that this
is a component of the Hirota variety entails solving a weak Schottky probl
em for rational nodal curves.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vivek Shende (University of California\, Berkeley)
DTSTART;VALUE=DATE-TIME:20220331T131500Z
DTEND;VALUE=DATE-TIME:20220331T144500Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/30
DESCRIPTION:Title: Skein valued curve counting and quantum mirror symmetry
for the conifold\nby Vivek Shende (University of California\, Berkele
y) as part of Real and complex Geometry\n\n\nAbstract\nI'll explain how to
define counts of all-genus curves with Lagrangian boundary conditions in
Calabi-Yau 3-folds. Then I'll do an example: the conifold with a single Ag
anagic-Vafa brane. Here I'll show a priori (i.e. without first computing t
he invariants)\, that the partition function satisfies an operator equatio
n\, given by a skein-valued quantization of the mirror curve. Said equatio
n gives a recursion which can be solved explicitly. [This talk presents jo
int work with Tobias Ekholm.]\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rahul Pandharipande (ETH)
DTSTART;VALUE=DATE-TIME:20220407T131500Z
DTEND;VALUE=DATE-TIME:20220407T144500Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/31
DESCRIPTION:Title: Log intersection theory of the moduli space of curves\nby Rahul Pandharipande (ETH) as part of Real and complex Geometry\n\n\
nAbstract\nThe logarithmic intersection theory of the moduli space of curv
es\nis defined via a limit over all log blow-ups (with respect to the norm
al crossings\nboundary structure). I will explain some new results and dir
ections related\nto the log cohomology theory and the log double ramificat
ion cycle. Joint\nwork with D. Holmes\, S. Mocho\, A. Pixton\, and J. Schm
itt.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shaoyun Bai (Princeton University)
DTSTART;VALUE=DATE-TIME:20220428T131500Z
DTEND;VALUE=DATE-TIME:20220428T144500Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/32
DESCRIPTION:Title: Integral counterpart of Gromov-Witten invariants\nb
y Shaoyun Bai (Princeton University) as part of Real and complex Geometry\
n\n\nAbstract\nAs a virtual enumeration of (pseudo-)holomorphic curves\, G
romov-Witten invariants are generally rational-valued due to the presence
of non-trivial symmetries of the curves. Realizing a proposal of Fukaya-On
o back in the 1990s\, I will explain how to define integer-valued Gromov-W
itten type invariants for all closed symplectic manifolds. I will also dis
cuss how this construction fits into a larger program on refining curve-co
unting invariants initiated by Joyce\, Pardon\, and Abouzaid-McLean-Smith.
This is based on joint work with Guangbo Xu.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shaoyun Bai (Princeton University)
DTSTART;VALUE=DATE-TIME:20220428T131500Z
DTEND;VALUE=DATE-TIME:20220428T144500Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/33
DESCRIPTION:Title: Integral counterpart of Gromov-Witten invariants\nb
y Shaoyun Bai (Princeton University) as part of Real and complex Geometry\
n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sourav Das (University of Haifa)
DTSTART;VALUE=DATE-TIME:20220512T131500Z
DTEND;VALUE=DATE-TIME:20220512T144500Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/34
DESCRIPTION:Title: Higgs bundles on nodal curves\nby Sourav Das (Unive
rsity of Haifa) as part of Real and complex Geometry\n\n\nAbstract\nIn I98
7 Nigel Hitchin proved that the moduli space of Higgs bundles on a smooth
projective curve (of genus greater than equal to 2) has a natural symplect
ic structure. In this talk\, I will briefly recall a few features of the m
oduli space. Then I will discuss the moduli spaces of Higgs bundles on nod
al curves and how they are related to the moduli spaces of Higgs bundles o
n smooth curves via nice degenerations. I will also show that there is a r
elative log-symplectic structure on such a degeneration.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiu-Chu Melissa Liu (Columbia University)
DTSTART;VALUE=DATE-TIME:20220526T131500Z
DTEND;VALUE=DATE-TIME:20220526T144500Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/35
DESCRIPTION:Title: Higgs-Coulomb correspondence for abelian gauged linear
sigma models\nby Chiu-Chu Melissa Liu (Columbia University) as part of
Real and complex Geometry\n\n\nAbstract\nThe input data of a gauged linea
r sigma model (GLSM) consists of a GIT quotient of a complex vector space
V by the linear action of a reductive algebraic group G (the gauge group)
and a G-invariant polynomial function on V (the superpotential) which is q
uasi-homogeneous with respect to a C^*-action (R symmetries) on V. The Hig
gs-Coulomb correspondence relates (1) GLSM invariants which are virtual co
unts of Landau-Ginzburg quasimaps (Higgs branch)\, and (2) Mellin-Barnes t
ype integrals on the Lie algebra of G (Coulomb branch). In this talk\, I w
ill describe the correspondence when G is an algebraic torus\, and explain
how to use the correspondence to study the dependence of GLSM invariants
on the stability condition. This is based on joint work with Konstantin Al
eshkin.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amanda Hirschi (Cambridge University)
DTSTART;VALUE=DATE-TIME:20220609T131500Z
DTEND;VALUE=DATE-TIME:20220609T144500Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/36
DESCRIPTION:Title: A construction of global Kuranishi charts for Gromov-Wi
tten moduli spaces of arbitrary genus\nby Amanda Hirschi (Cambridge Un
iversity) as part of Real and complex Geometry\n\n\nAbstract\nSymplectic G
romov-Witten invariants have long been complicated by the fact that delica
te local-to-global arguments were required in their construction. In 2021
Abouzaid-McLean-Smith gave the first construction of global charts for gen
eral Gromov-Witten moduli spaces in genus zero. I will describe a generali
zation of their construction for stable maps of higher genera and discuss
potential applications. This is joint work in progress with Mohan Swaminat
han.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grigory Mikhalkin (University of Geneve)
DTSTART;VALUE=DATE-TIME:20221110T141500Z
DTEND;VALUE=DATE-TIME:20221110T154500Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/37
DESCRIPTION:Title: Tropical\, real and symplectic geometry\nby Grigory
Mikhalkin (University of Geneve) as part of Real and complex Geometry\n\n
\nAbstract\nThis lecture will focus on the way how tropical curves appear
in symplectic geometry settings. On one hand\, tropical curves can be lift
ed as Lagrangian submanifolds in the ambient toric variety. On the other h
and\, they can be lifted as holomorphic curves. The two lifts use two diff
erent tropical structures on the same space\, related by a certain potenti
al function. We pay special attention to correspondence theorems between t
ropical curves and real curves\, i.e. holomorphic curves invariant with re
spect to an antiholomorphic involution. The resulting real curves produce\
, in their turn\, holomorphic membranes for tropical Lagrangian submanifol
ds.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kai Hugtenburg (University of Edinburgh)
DTSTART;VALUE=DATE-TIME:20221124T141500Z
DTEND;VALUE=DATE-TIME:20221124T154500Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/38
DESCRIPTION:Title: Gromov-Witten theory: some computational tools\nby
Kai Hugtenburg (University of Edinburgh) as part of Real and complex Geome
try\n\n\nAbstract\nGromov-Witten invariants of a space X can intuitively b
e defined as counts of maps from a genus-g curve into X with certain const
raints. In this talk I will talk about two tools for computing Gromov-Witt
en invariants. The first of these will be the WDVV equations\, which were
used by Kontsevich to determine the number of degree d rational curves thr
ough 3d-1 points in CP^2. The second one are R-matrices\, which were used
by Givental and Teleman to recover all-genus invariants from the genus 0\,
3 point invariants. This method is not very widely applicable though: it
requires the quantum cohomology ring of X (which is a deformation of the u
sual cohomology ring) to be semi-simple. After overviewing this constructi
on\, I will give an example of a construction of an R-matrix in a more gen
eral setting.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Kerner (Ben-Gurion University)
DTSTART;VALUE=DATE-TIME:20221222T141500Z
DTEND;VALUE=DATE-TIME:20221222T154500Z
DTSTAMP;VALUE=DATE-TIME:20221209T134316Z
UID:AlgebraicGeometryTopology/39
DESCRIPTION:Title: Unfolding theory\, Stable maps and Mather-Yau/Gaffney-H
auser results in arbitrary characteristic\nby Dmitry Kerner (Ben-Gurio
n University) as part of Real and complex Geometry\n\n\nAbstract\nIn 40's
Whitney studied maps of C^\\infty manifolds. When a map is not an immersio
n/submersion\, one tries to deform it locally\, in hope to make it 'generi
c'. This approach has led to the rich theory of stable maps\, developed by
Mather\, Thom and many others. The main 'engine' was vector field integra
tion. This chained the whole theory to the C^\\infty\, or R/C-analytic set
ting. I will present the purely algebraic approach\, studying maps of germ
s of Noetherian schemes\, in any characteristic. The relevant groups of eq
uivalence admit 'good' tangent spaces. Submodules of the tangent spaces le
ad to submodules of the group orbits. Then goes the theory of unfoldings (
triviality and versality). Then I will discuss the new results on stable m
aps and theorems of Mather-Yau/Gaffney-Hauser.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeometryTopology/39/
END:VEVENT
END:VCALENDAR