BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Yuuji Tanaka (Oxford)
DTSTART:20200423T120000Z
DTEND:20200423T140000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/1
DESCRIPTION:Title: Vafa-Witten invariants on projective surfaces\nby Yuuji Tanaka
(Oxford) as part of Algebraic Geometry and Number Theory seminar - ISTA\n
\n\nAbstract\nThe first half of this talk will be a gentle introduction to
the theory of Vafa-Witten invariants\, especially on projective surfaces.
In the second half part - after a break- we focus more on computational r
esults. This talk is based on joint work with Richard Thomas.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Fiorilli (Université Paris-Sud)
DTSTART:20200430T120000Z
DTEND:20200430T140000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/2
DESCRIPTION:Title: On the distribution of the error term in Chebotarev's density theo
rem and applications\nby Daniel Fiorilli (Université Paris-Sud) as pa
rt of Algebraic Geometry and Number Theory seminar - ISTA\n\n\nAbstract\nW
e will discuss both extreme and generic values of the error term in Chebot
arev's density theorem. This will allow us to deduce applications on a con
jecture of K. Murty on the least unramified prime ideal in a given Frobeni
us set as well as on asymptotic properties of Chebyshev's bias.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov (Caltech / MPI Bonn)
DTSTART:20200521T160000Z
DTEND:20200521T180000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/5
DESCRIPTION:Title: From the Generalized Volume Conjecture to Turaev and Ramanujan
\nby Sergei Gukov (Caltech / MPI Bonn) as part of Algebraic Geometry and N
umber Theory seminar - ISTA\n\n\nAbstract\nIn this talk\, intended for a b
road audience\, we will survey the development of a new 3-manifold invaria
nt that provides an answer to questions like this: What do Dedekind eta an
d Alexander polynomial have in common? In fact\, illustrated by this quest
ion is perhaps the most attractive feature of this new invariant: it provi
des new and often unexpected connections between different areas of mathem
atics. Originating from complex Chern-Simons theory and quantization of $\
\operatorname{SL}(2\,\\mathbb{C})$ character varieties\, it evaluates to $
q$-series expressions that are more commonly seen in the theory of mock mo
dular forms and in logarithmic Vertex Operator Algebras (VOAs). The goal o
f the talk will be to survey these relations using least amount of technic
al details.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Humphries (University College London)
DTSTART:20200528T120000Z
DTEND:20200528T130000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/6
DESCRIPTION:Title: Small scale equidistribution of lattice points on the sphere\n
by Peter Humphries (University College London) as part of Algebraic Geomet
ry and Number Theory seminar - ISTA\n\n\nAbstract\nConsider the projection
onto the unit sphere in $\\mathbb{R}^3$ of the set of lattice points $(x_
1\, x_2\, x_3) \\in \\mathbb{Z}^3$ lying on the sphere of radius $\\sqrt{n
}$. Duke and Schulze-Pillot showed in 1990 that these points equidistribut
e on the sphere as $n \\to \\infty$. We study a small scale refinement of
this theorem\, where one asks whether these points equidistribute in subse
ts of the sphere whose surface area shrinks as $n$ grows. A particular cas
e of this is a conjecture of Linnik\, which states that for all $\\delta >
0$\, the equation $x_1^2 + x_2^2 + x_3^2 = n$ has a solution with $|x_3|
< n^{\\delta}$ for all sufficiently large $n$. We make nontrivial progress
towards this\, as well as proving an averaged form of this conjecture. Th
is is joint work with Maksym Radziwiłł.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junliang Shen (MIT)
DTSTART:20200618T120000Z
DTEND:20200618T140000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/8
DESCRIPTION:Title: On the topology of Hitchin fibrations\nby Junliang Shen (MIT)
as part of Algebraic Geometry and Number Theory seminar - ISTA\n\n\nAbstra
ct\nThe topology of the Hitchin fibrations plays crucial role in geometry\
, math physics\, and representation theory. In this talk\, we will discuss
two questions arised naturally in the study of Hitchin fibrations in view
of the P=W conjecture: (a) How to locate the tautological classes in the
perverse filtration? (b) Is the perverse filtration multiplicative for Hit
chin fibrations? \nI will explain how connnections to the geometry of some
special algebraic varieties (Hilbert schemes\, abelian surfaces\, hyper-K
ahler manifolds) lead to progress to answering these questions.\nBased on
joint work with Mark de Cataldo\, Davesh Maulik\, Qizheng Yin\, Zili Zhan
g.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitri Wyss (L'Ecole polytechnique fédérale de Lausanne (EPFL))
DTSTART:20200611T120000Z
DTEND:20200611T140000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/9
DESCRIPTION:Title: P-adic integration\, geometry and Higgs bundles\nby Dimitri Wy
ss (L'Ecole polytechnique fédérale de Lausanne (EPFL)) as part of Algebr
aic Geometry and Number Theory seminar - ISTA\n\n\nAbstract\nIntegration w
ith respect to the Haar measure over a non-archimedean local field F share
s many formal properties with integration over the reals while at the same
time being closely related to the arithmetic and geometry over the residu
e field of F. In the first part I will give an overview of the theory and
explain two classical applications\, namely rationality of Igusa's local z
eta functions and Batyrev's proof of the equality of Hodge numbers for smo
oth projective birational Calabi-Yau varieties.\n\nIn the second part I ex
plain joint work with Michael Groechenig and Paul Ziegler\, where we apply
these ideas to the moduli space of G-Higgs bundles. In quite general situ
ations we can relate p-adic volumes of Higgs spaces for Langlands-dual gro
ups\, from which we derive two results: the topological mirror symmetry co
njecture of Hausel-Thaddeus\, which relates Hodge numbers for SL_n and PGL
_n Higgs spaces\, and the geometric stabilization theorem for anisotropic
Hitchin fibers of Ngô. If time permits I will also discuss recent ideas o
n how to effectively compute the p-adic volumes appearing in our argument.
\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Baird (Memorial University of Newfoundland)
DTSTART:20201001T120000Z
DTEND:20201001T140000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/11
DESCRIPTION:Title: E-polynomials of character varieties for real curves\nby Tom
Baird (Memorial University of Newfoundland) as part of Algebraic Geometry
and Number Theory seminar - ISTA\n\n\nAbstract\nGiven a Riemann surface $\
\Sigma$ denote by $$M_n(\\mathbb{F}) := Hom_{\\xi}( \\pi_1(\\Sigma)\, GL_n
(\\mathbb{F}))/GL_n(\\mathbb{F})$$ the $\\xi$-twisted character variety fo
r $\\xi \\in \\mathbb{F}$ a $n$-th root of unity. An anti-holomorphic inv
olution $\\tau$ on $\\Sigma$ induces an involution on $M_n(\\mathbb{F})$ s
uch that the fixed point variety $M_n^{\\tau}(\\mathbb{F})$ can be identif
ied with the character variety of ``real representations" for the orbifold
fundamental group $\\pi_1(\\Sigma\, \\tau)$. When $\\mathbb{F} = \\mathbb
{C}$\, $M_n(\\mathbb{C})$ is a complex symplectic manifold and $M_n^{\\tau
}(\\mathbb{C})$ embeds as a complex Lagrangian submanifold (or ABA-brane).
\nBy counting points of $M_n(\\mathbb{F}_q)$ for finite fields $\\mathbb{F
}_q$\, Hausel and Rodriguez-Villegas determined the E-polynomial of $M_n(\
\mathbb{C})$ (a specialization of the mixed Hodge polynomial). I will show
how similar methods can be used to calculate the E-polynomial of $M_n^\\t
au(\\mathbb{F}_q)$ using the representation theory of $GL_n(\\mathbb{F}_q)
$. We express our formula as a generating function identity involving the
plethystic logarithm of a product of sums over Young diagrams. The Pieri'
s formula for multiplying Schur polynomials arises in an interesting way.\
n\nThis is joint work with Michael Lennox Wong.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mirko Mauri (Max Planck Institute\, Bonn)
DTSTART:20201008T120000Z
DTEND:20201008T133000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/12
DESCRIPTION:Title: P=W conjectures for character varieties with symplectic resolutio
n\nby Mirko Mauri (Max Planck Institute\, Bonn) as part of Algebraic G
eometry and Number Theory seminar - ISTA\n\n\nAbstract\nCharacter varietie
s parametrise representations of the fundamental group of a curve. They ar
e in general singular moduli spaces\, and for this reason it is customary
to shift attention to smooth analogues\, called twisted character varietie
s. The P=W conjecture formulated by de Cataldo\, Hausel and Migliorini pos
its a relation between the Hodge theory of twisted character varieties and
the geometry of some holomorphic Lagrangian fibrations. In a joint work w
ith Camilla Felisetti\, we explore P=W phenomena in the untwisted case. We
show that the P=W conjecture holds for character varieties which admit a
symplectic resolution\, namely in genus 1 and arbitrary rank and in genus
2 and rank 2. This involves a careful study of alterations of these charac
ter varieties. If time permits\, I will discuss new numerical evidence of
P=W phenomena in higher genus\, when no symplectic resolution exists.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davesh Maulik (MIT Mathematics)
DTSTART:20201029T130000Z
DTEND:20201029T143000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/13
DESCRIPTION:Title: Cohomology of the moduli of Higgs bundles and the Hausel-Thaddeus
conjecture\nby Davesh Maulik (MIT Mathematics) as part of Algebraic G
eometry and Number Theory seminar - ISTA\n\n\nAbstract\nIn this talk\, I w
ill discuss some results on the structure of the cohomology of the moduli
space of stable SL_n Higgs bundles on a curve. One consequence is a new p
roof of he Hausel-Thaddeus conjecture proven previously by Groechenig-Wyss
-Ziegler via p-adic integration. \nWe will also discuss connections to the
P=W conjecture if time permits. Based on joint work with Junliang Shen.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eloise Hamilton (IMJ-PRG\, University of Paris)
DTSTART:20201112T130000Z
DTEND:20201112T143000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/14
DESCRIPTION:Title: Moduli spaces for unstable Higgs bundles of rank 2 and their geom
etry\nby Eloise Hamilton (IMJ-PRG\, University of Paris) as part of Al
gebraic Geometry and Number Theory seminar - ISTA\n\n\nAbstract\nThe modul
i space of semistable Higgs bundles of arbitrary rank and degree on a nons
ingular projective curve was first constructed by Nitsure in 1990\, using
Geometric Invariant Theory (GIT). Thanks to its rich geometric structure\,
this moduli space continues to represent an active area of research. The
aim of this talk is to describe how recent results in Non-Reductive GIT ca
n be used to construct moduli spaces for Higgs bundles which are not semis
table\, and to describe initial steps towards the study of their geometry
in the rank 2 case. In the first part of the talk we will start by giving
a summary of Nitsure's GIT construction of the moduli space and describin
g the main geometric features of the moduli space. We will then consider t
he special case of (twisted) Higgs bundles over the projective line\, in o
rder to introduce unstable Higgs bundles and their moduli spaces in an ele
mentary way. In the second part of the talk we will sketch the Non-Reducti
ve GIT construction of moduli spaces for unstable Higgs bundles over a smo
oth projective curve of arbitrary genus. We will then describe how the geo
metry of these moduli spaces can be studied in the rank 2 case\, using the
Higgs field scaling C-star action on the one hand\, and their constructio
n as Non-Reductive GIT quotients on the other.\nQr image\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ariyan Javanpeykar (Johannes Gutenberg-Universität Mainz)
DTSTART:20201126T130000Z
DTEND:20201126T140000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/15
DESCRIPTION:Title: Hilbert's irreducibility theorem for abelian varieties\nby Ar
iyan Javanpeykar (Johannes Gutenberg-Universität Mainz) as part of Algebr
aic Geometry and Number Theory seminar - ISTA\n\n\nAbstract\nWe will discu
ss joint work with Corvaja\, Demeio\, Lombardo\, and Zannier in which we e
xtend Hilbert's irreducibility theorem (for rational varieties) to the set
ting of abelian varieties. Roughly speaking\, given an abelian variety A o
ver a number field k and a ramified covering X of A\, we show that X has "
less" k-rational points than A.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Feng (MIT Mathematics)
DTSTART:20201203T130000Z
DTEND:20201203T140000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/16
DESCRIPTION:Title: The geometric distribution of Selmer groups over function fields<
/a>\nby Tony Feng (MIT Mathematics) as part of Algebraic Geometry and Numb
er Theory seminar - ISTA\n\n\nAbstract\nMany interesting aspects of the ar
ithmetic of elliptic curves over global fields are governed by Selmer grou
ps\, which are cohomological approximations to the group of rational point
s. The statistical behavior of Selmer groups has been the focus of much re
cent study\, and there is a wide gap between what we can prove and what we
believe is true. On the one hand\, work of Bhargava and Shankar computes
the average size of 2\,3\,4\, and 5-Selmer groups. On the other hand\, Bha
rgava-Kane-Lenstra-Poonen-Rains conjecture a precise distribution for n-Se
lmer groups\, for any n. I will talk about a limiting situation\, in the f
unction field context\, where the BKLPR distribution can actually be prove
d to model the distribution of Selmer groups. This is joint work with Aaro
n Landesman and Eric Rains.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sachi Hashimoto (Boston University)
DTSTART:20201119T130000Z
DTEND:20201119T140000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/17
DESCRIPTION:Title: Transcendental Brauer-Manin obstructions on some Calabi-Yau three
folds\nby Sachi Hashimoto (Boston University) as part of Algebraic Geo
metry and Number Theory seminar - ISTA\n\n\nAbstract\nWe study the arithme
tic properties of a family of Calabi-Yau threefolds originally studied by
Hosono and Takagi in the context of mirror symmetry. The geometry of these
varieties endows them with a 2-torsion Brauer class. Under mild condition
s\, we show this Brauer class prevents the rational points from being dens
e in the adelic points. This is joint work with Katrina Honigs\, Alicia La
marche\, and Isabel Vogt.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arielle Leitner (Weizmann Institute of Science)
DTSTART:20201210T130000Z
DTEND:20201210T140000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/18
DESCRIPTION:Title: Limits of the diagonal Cartan subgroup in SL(n\,R) and SL(n\, Q_p
)\nby Arielle Leitner (Weizmann Institute of Science) as part of Algeb
raic Geometry and Number Theory seminar - ISTA\n\n\nAbstract\nA conjugacy
limit group is the limit of a sequence of conjugates of the positive diago
nal Cartan subgroup\, C \\leq SL(n) in the Chabauty topology. Over R\, t
he group C is naturally associated to a projective n-1 simplex. We can co
mpute the conjugacy limits of C by collapsing the n-1 simplex in different
ways. In low dimensions\, we enumerate all possible ways of doing this.
In higher dimensions we show there are infinitely many non-conjugate limi
ts of C. \nIn the Q_p case\, SL(n\,Q_p) has an associated p+1 regular affi
ne building. (We'll give a gentle introduction to buildings in the talk).
The group C stabilizes an apartment in this building\, and limits are co
ntained in the parabolic subgroups stabilizing the facets in the spherical
building at infinity. There is a strong interplay between the conjugacy l
imit groups and the geometry of the building\, which we exploit to extend
some of the results above. The Q_p part is joint work with Corina Ciobota
ru and Alain Valette.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Márton Hablicsek (Universiteit Leiden\, NL)
DTSTART:20201015T120000Z
DTEND:20201015T140000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/19
DESCRIPTION:Title: Virtual Classes of Representation Varieties of Upper Triangular M
atrices via Topological Quantum Field Theories\nby Márton Hablicsek (
Universiteit Leiden\, NL) as part of Algebraic Geometry and Number Theory
seminar - ISTA\n\n\nAbstract\nLet $X$ be an oriented closed connected surf
ace. The set of group representations from the fundamental group of $X$ to
an algebraic group $G$ has a structure of an algebraic variety. This vari
ety is called the $G$-representation variety of $X$. In this talk\, I will
use a geometric method developed by González-Prieto\, Logares\, Muñoz\,
and Newstead to compute the virtual classes of $G$-representation varieti
es where $G$ is the group of complex upper-triangular matrices of rank 2\,
3\, or 4. This is joint work with Jesse Vogel.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando R. Villegas (ICTP\, Italy)
DTSTART:20201022T120000Z
DTEND:20201022T130000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/20
DESCRIPTION:Title: Character varieties of non-orientable surfaces\nby Fernando R
. Villegas (ICTP\, Italy) as part of Algebraic Geometry and Number Theory
seminar - ISTA\n\n\nAbstract\nWe will discuss various types of character v
arieties parametrizing representations of the fundamental group of a punct
ured non-orientable surface. We compute the number of points of these spa
ces over finite fields from which we get a formula for their E-series (a c
ertain specialization of the mixed Poincare series). For one type of chara
cter variety we extend this calculation to a conjectural formula for the f
ull mixed Poincare series in terms of Macdonald symmetric functions and we
provide some evidence. Unexpectedly\, the formulas we obtain turn out to
be closely related to those arising from the character varieties of punctu
red compact orientable Riemann surfaces. This is joint work with E. Letell
ier.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lior Bary-Soroker (School of Mathematical Sciences of Tel Aviv Uni
versity)
DTSTART:20201217T130000Z
DTEND:20201217T140000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/21
DESCRIPTION:Title: Random Polynomials\, Probabilistic Galois Theory\, and Finite Fie
ld Arithmetic\nby Lior Bary-Soroker (School of Mathematical Sciences o
f Tel Aviv University) as part of Algebraic Geometry and Number Theory sem
inar - ISTA\n\n\nAbstract\nWe will discuss recent advances on the followin
g two question: Let A(X) =Σ ±Xi be a random polynomial of degree n with
coefficients taking the values -1\, 1 independently each with probability
1/2.\nQ1: What is the probability that A is irreducible as the degree goes
to infinity\nQ2: What is the typical Galois of A?\nOne believes that the
answers are YES and THE FULL SYMMETRIC GROUP\, respectively. These questio
ns were studied extensively in recent years\, and we will survey the tools
developed to attack these problems and partial results.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emmanuel Kowalski (ETH Zürich)
DTSTART:20210107T130000Z
DTEND:20210107T140000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/22
DESCRIPTION:Title: Exponential sums and twisted multiplicativity\nby Emmanuel Ko
walski (ETH Zürich) as part of Algebraic Geometry and Number Theory semin
ar - ISTA\n\n\nAbstract\nThe additive exponential sums associated to an in
tegral polynomial\nsatisfy a property of twisted-multiplicativity. Using t
his\, it is\npossible to exploit properties of these sums over finite fiel
ds to gain\nsome understanding of the sums modulo all integers. This invol
ves a\nfine interplay of algebraic methods and analytic techniques. The\ne
xplain will describe some of these\, and explain in particular how to\nded
uce that the mean value of these exponential sums vanishes for\nsuitably g
eneric polynomials.\n\n(Joint work with K. Soundararajan)\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Wang (MIT Mathematics)
DTSTART:20201105T143000Z
DTEND:20201105T160000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/23
DESCRIPTION:Title: Spherical varieties and L-functions via geometric Langlands\n
by Jonathan Wang (MIT Mathematics) as part of Algebraic Geometry and Numbe
r Theory seminar - ISTA\n\n\nAbstract\nThe relative Langlands program\, as
developed by Sakellaridis and Venkatesh\, conjectures relationships betwe
en spherical varieties and automorphic L-functions. In the local setting\,
this is conjecturally related to the computation of asymptotics\, or more
precisely nearby cycles\, of an IC complex on the formal arc space of a s
pherical variety. I explain my joint work with Yiannis Sakellaridis where
we establish this connection and compute this nearby cycles for a nice cla
ss of spherical varieties using perverse sheaves and the geometry of semi-
infinite orbits and affine Grassmannians.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kirsten Wickelgren (Duke University\, North Carolina)
DTSTART:20210114T140000Z
DTEND:20210114T150000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/24
DESCRIPTION:Title: An arithmetic count of rational plane curves\nby Kirsten Wick
elgren (Duke University\, North Carolina) as part of Algebraic Geometry an
d Number Theory seminar - ISTA\n\n\nAbstract\nThere are finitely many degr
ee d rational plane curves passing through 3d-1 points\, and over the comp
lex numbers\, this number is independent of (generically) chosen points. F
or example\, there are 12 degree 3 rational curves through 8 points\, one
conic passing through 5\, and one line passing through 2. Over the real nu
mbers\, one can obtain a fixed number by weighting real rational curves by
their Welschinger invariant\, and work of Solomon identifies this invaria
nt with a local degree. It is a feature of A1-homotopy theory that analogo
us real and complex results can indicate the presence of a common generali
zation\, valid over a general field. We develop and compute an A1-degree\,
following Morel\, of the evaluation map on Kontsevich moduli space to obt
ain an arithmetic count of rational plane curves\, which is valid for any
field k of characteristic not 2 or 3. This shows independence of the count
on the choice of generically chosen points with fixed residue fields\, st
rengthening a count of Marc Levine. This is joint work with Jesse Kass\, M
arc Levine\, and Jake Solomon.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jörg Jahnel (University of Siegen)
DTSTART:20210128T130000Z
DTEND:20210128T140000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/25
DESCRIPTION:Title: On integral points on open degree four del Pezzo surfaces\nby
Jörg Jahnel (University of Siegen) as part of Algebraic Geometry and Num
ber Theory seminar - ISTA\n\n\nAbstract\nI will report on investigations\,
joint with Damaris Schindler \n(Göttingen)\, concerning the algebraic an
d transcendental Brauer-Manin \nobstructions to integral points on complem
ents of a hyperplane section in \ndegree four del Pezzo surfaces. We discu
ss moreover two concepts of an \nobstruction at an archimedean place. Conc
rete examples are given of pairs \nof non-homogeneous quadratic polynomial
s in four variables representing\n$(0\,0)$ over $\\bbQ$ and over $\\bbZ_p$
for all primes $p$\, but not\nover $\\bbZ$. By blow-up\, these yield cubi
c polynomials in three variables \nall integral solutions of which satisfy
a gcd condition.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Otto Overkamp (Leibniz Universität Hannover)
DTSTART:20210121T130000Z
DTEND:20210121T140000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/26
DESCRIPTION:Title: Néron models of pseudo-Abelian varieties\nby Otto Overkamp (
Leibniz Universität Hannover) as part of Algebraic Geometry and Number Th
eory seminar - ISTA\n\n\nAbstract\nWe explain Totaro's notion of pseudo-Ab
elian varieties and show that they admit Néron models over excellent disc
rete valuation rings. As a next step\, we study those Néron models and ge
neralize the notions of good reduction and semiabelian reduction to such a
lgebraic groups. \nWe prove that the well-known representation-theoretic
criteria for good and semiabelian reduction due to Néron-Ogg-Shafarevich
and Grothendieck carry over to the pseudo-Abelian case\, and give examples
to show that our results are the best possible in most cases.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raf Cluckers (University of Lille\, FR\, KU Leuven\, BE)
DTSTART:20210311T130000Z
DTEND:20210311T140000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/27
DESCRIPTION:Title: A number theoretic characterization of (FRS) morphisms\nby Ra
f Cluckers (University of Lille\, FR\, KU Leuven\, BE) as part of Algebrai
c Geometry and Number Theory seminar - ISTA\n\n\nAbstract\nI will present
joint work with Glazer and Hendel\, which extends the Lang-Weil estimates
to estimates working with rings of integers modulo powers of primes rather
than with finite fields (see arxiv). These bounds were found by Serre in
the smooth case\, and by Avni and Aizenbud in the case of rational singula
rities (which is close to the smooth case). We render the situation unifor
m in the fibers of an algebraic morphism each of whose fibers has rational
singularities. Surprizingly\, this relative case with uniform bounds need
s rather different methods\, related to motivic integration\, or more prec
isely uniform p-adic integration. Subtle new results about formally positi
ve uniform p-adic functions needed to be developed for this to work.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uri Onn (Australian National University)
DTSTART:20210408T120000Z
DTEND:20210408T130000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/29
DESCRIPTION:Title: Analytic properties of representation zeta functions of arithmeti
c groups\nby Uri Onn (Australian National University) as part of Algeb
raic Geometry and Number Theory seminar - ISTA\n\n\nAbstract\nA group is s
aid to have polynomial representation growth if the sequence enumerating t
he isomorphism classes of finite dimensional irreducible representations a
ccording to their dimension is polynomially bounded. The representation ze
ta function of such group is the associated Dirichlet generating series. I
n this talk I will focus on representation zeta functions of arithmetic gr
oups and their analytic properties. I will explain the ideas behind a proo
f of a variant of the Larsen-Lubotzky conjecture on the representation gro
wth of arithmetic lattices in high rank semisimple Lie groups (joint with
Nir Avni\, Benjamin Klopsch and Christopher Voll). Time permitting\, I wil
l talk about results on arithmetic groups of type A_2 in positive characte
ristic (joint with Amritanshu Prasad and Pooja Singla) and results towards
meromorphic continuation (joint with Shai Shechter).\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincent Lafforgue (Institute Fournier\, Grenoble)
DTSTART:20210318T130000Z
DTEND:20210318T150000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/30
DESCRIPTION:Title: Classical limits for geometrizations of functoriality kernels and
values of L-functions\nby Vincent Lafforgue (Institute Fournier\, Gre
noble) as part of Algebraic Geometry and Number Theory seminar - ISTA\n\n\
nAbstract\nIn the setting of the geometric Langlands program\, it is conje
ctured that kernels which should give rise to Langlands functoriality\, an
d relations between values of L-functions and some periods\, exist. Some c
ases are known (e.g. the geometric theta correspondence and the geometriza
tion of Rankin-Selberg integrals\, due to Lysenko)\, the rest is mainly co
njectural. However the (partly conjectural) classical limits may be descri
bed and their properties studied. In the first hour I will recall some ele
mentary facts of symplectic geometry and the classical limit of the Langl
ands correspondence via the Hitchin fibration.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oscar Garcia-Prada (ICMAT\, Spain)
DTSTART:20210325T130000Z
DTEND:20210325T150000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/31
DESCRIPTION:Title: Arakelov–Milnor inequalities and maximal variations of Hodge st
ructure\nby Oscar Garcia-Prada (ICMAT\, Spain) as part of Algebraic Ge
ometry and Number Theory seminar - ISTA\n\n\nAbstract\nIn this talk we stu
dy the fixed points under the action of the multiplicative group of non-va
nishing complex numbers on moduli spaces of Higgs bundles over a compact R
iemann surface for complex semisimple Lie groups and their real forms. The
se fixed points are called Hodge bundles and correspond to complex variati
ons of Hodge structure. We introduce a topological invariant for Hodge bun
dles that generalizes the Toledo invariant appearing for Hermitian Lie gro
ups. A main result to discuss is a bound on this invariant which generaliz
es both the Milnor–Wood inequality of the Hermitian case\, and the Arake
lov inequalities of classical variations of Hodge structure. When the gene
ralized Toledo invariant is maximal\, we establish rigidity results for th
e associated variations of Hodge structure which generalize known rigidity
results for maximal Higgs bundles and their associated maximal representa
tions in the Hermitian case (based on joint work with Olivier Biquard\, Br
ian Collier and Domingo Toledo).\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Kamnitzer (University of Toronto)
DTSTART:20210429T120000Z
DTEND:20210429T140000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/32
DESCRIPTION:Title: Affine Grassmannian slices and their quantizations\nby Joel K
amnitzer (University of Toronto) as part of Algebraic Geometry and Number
Theory seminar - ISTA\n\n\nAbstract\nSlices in the affine Grassmannian are
geometric incarnations of weight spaces of representations of semisimple
complex groups. These spaces can also be constructed as Coulomb branches
of quiver gauge theories or in type A\, as bow varieties. They are relate
d to Nakajima quiver varieties using 3d mirror symmetry\, also known as sy
mplectic duality. These spaces are conical symplectic singularities and
have natural quantizations using algebras called truncated shifted Yangian
s. I will survey 10 years of research on these wonderful spaces and descr
ibe some remaining open questions.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mercedes Haiech (University of Rennes)
DTSTART:20210422T120000Z
DTEND:20210422T130000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/33
DESCRIPTION:Title: The Fundamental Theorem of Tropical Partial Differential Algebrai
c Geometry\nby Mercedes Haiech (University of Rennes) as part of Algeb
raic Geometry and Number Theory seminar - ISTA\n\n\nAbstract\nGiven a part
ial differential equation (PDE)\, its solutions can be difficult\, if not
impossible\, to describe.\nThe purpose of the Fundamental theorem of tropi
cal (partial) differential algebraic geometry is to extract from the equat
ions certain properties of the solutions. \nMore precisely\, this theorem
proves that the support of the solutions in $k[[t_1\, \\cdots\, t_m]]$ (wi
th $k$ a field of characteristic zero) can be obtained by solving a so-cal
led tropicalized differential system.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richárd Rimányi (UNC Chapel Hill)
DTSTART:20210415T120000Z
DTEND:20210415T140000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/34
DESCRIPTION:Title: Stable envelopes\, 3d mirror symmetry\, bow varieties\nby Ric
hárd Rimányi (UNC Chapel Hill) as part of Algebraic Geometry and Number
Theory seminar - ISTA\n\n\nAbstract\nThe role played by Schubert classes i
n the geometry of Grassmannians is played by the so-called stable envelope
s in the geometry of Nakajima quiver varieties. Stable envelopes come in t
hree flavors: cohomological\, K theoretic\, and elliptic stable envelopes.
We will show examples\, and explore their appearances in enumerative geom
etry and representation theory. In the second part of the talk we will dis
cuss ``3d mirror symmetry for characteristic classes’’\, namely\, the
fact that for certain pairs of seemingly unrelated spaces the elliptic sta
ble envelopes `match’ in some concrete (but non-obvious) sense. We will
meet Cherkis bow varieties\, a pool of spaces (conjecturally) closed under
``3d mirror symmetry for characteristic classes’’. The combinatorics
necessary to play Schubert calculus on bow varieties includes binary conti
ngency tables\, tie diagrams\, and the Hanany-Witten transition.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philipp Habegger (University of Basel)
DTSTART:20210401T120000Z
DTEND:20210401T130000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/35
DESCRIPTION:Title: Uniformity for the Number of Rational Points on a Curve\nby P
hilipp Habegger (University of Basel) as part of Algebraic Geometry and Nu
mber Theory seminar - ISTA\n\n\nAbstract\nBy Faltings's Theorem\, formerly
known as the Mordell Conjecture\, a smooth projective curve of genus at l
east 2 that is defined over a number field K has at most finitely many K-r
ational points. Votja later gave a second proof. Many authors\, including
Bombieri\, de Diego\, Parshin\, Rémond\, Vojta\, proved upper bounds for
the number of K-rational points. I will discuss joint work with Vesselin D
imitrov and Ziyang Gao where we prove that the number of points on the cur
ve is bounded from above as a function of K\, the genus\, and the rank of
the Mordell-Weil group of the curve's Jacobian. We follow Vojta's approach
to the Mordell Conjecture. I will explain the new feature: an inequality
for the Néron-Tate height in a family of abelian varieties. It allows us
to bound from above the number of points whose height is in the intermedia
te range.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:NOTE unusual time: Geordie Williamson (University of Sidney)
DTSTART:20210610T070000Z
DTEND:20210610T090000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/36
DESCRIPTION:Title: Spectra in representation theory\nby NOTE unusual time: Geord
ie Williamson (University of Sidney) as part of Algebraic Geometry and Num
ber Theory seminar - ISTA\n\n\nAbstract\nIn geometric representation theor
y cohomology\, intersection cohomology and constructible sheaves show up e
verywhere. This might seem strange to an algebraic topologist\, who might
ask: why this emphasis on cohomology\, when there are so many other intere
sting cohomology theories(like K-theory\, elliptic cohomology\, complex co
bordism\, ...) out there? They might also ask: is there something like "in
tersection K-theory"\, or "intersection complex cobordism"? This is someth
ing I've often wondered about. I will describe work in progress with Ben E
lias\, where we use Soergel bimodules to investigate what KU-modules look
like on the affine Grassmannian. We have checked by hand that in types A1\
, A2 and B2\, one gets something roughly resembling the quantum group. Spe
aking very roughly\, the intersection K-theory of Schubert varieties in th
e affine Grassmannian should recover the irreducible representations of th
e quantum group. Inspirations for this work include a strange Cartan matri
x discovered by Ben Elias\, and work of Cautis-Kamnitzer.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhiwei Yun (MIT Mathematics)
DTSTART:20210520T120000Z
DTEND:20210520T140000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/37
DESCRIPTION:Title: Universal global nilpotent cone\nby Zhiwei Yun (MIT Mathemati
cs) as part of Algebraic Geometry and Number Theory seminar - ISTA\n\nAbst
ract: TBA\n\nThe global nilpotent cone is the zero fiber of the Hitchin ma
p in the moduli space of Higgs bundles over an algebraic curve. It is a co
nic Lagrangian in the ambient symplectic moduli space\, and it plays an im
portant role in the geometric Langlands program. In this talk we define a
version of the global nilpotent cone for a family of curves. It will be a
closed conic Lagrangian in the cotangent bundle of the total space of the
family of Bun_G's for the family of curves.\nImplicitly it encodes a "conn
ection" among the category of sheaves on Bun_G as the curve varies. I will
mention the motivation of the construction from Betti geometric Langlands
. This is joint work with David Nadler.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arul Shankar (University of Toronto)
DTSTART:20210527T120000Z
DTEND:20210527T130000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/38
DESCRIPTION:Title: Nonvanishing at the critical point of the Dedekind zeta functions
of cubic $S_3$-fields\nby Arul Shankar (University of Toronto) as par
t of Algebraic Geometry and Number Theory seminar - ISTA\n\n\nAbstract\nLe
t $K$ be a number field\, and denote the Dedekind zeta function of $K$ by
$\\zeta_K(s)$. A classical question in number theory is: Can this zeta fun
ction vanish at the critical point $s=1/2$? In successive works\, Armitag
e\, and then Frohlich\, gave examples of number fields which satisfy $\\z
eta_K(s)=0$. Conversely\, it is believed that certain conditions on $K$ ca
n guarantee the nonvanishing of $\\zeta_K(s)$ at the critical point. For e
xample\, it is believed that $\\zeta_K(s)$ is never $0$ when $K$ is an $S_
n$-number field for any $n\\geq 1$.\nWhen $n=1$\, $\\zeta_K(s)$ is simply
the Riemann zeta function\, and Riemann himself established the non vanish
ing of $\\zeta(1/2)$.\nWhen $n=2$\, there has been amazing progress toward
s understanding the statistics of $\\zeta_K(1/2)$. Jutila first proved tha
t infinitely many quadratic fields $K$ satisfy $\\zeta_K(1/2)\\neq 0$\, an
d Soundararajan establishes that this is in fact true for at least $87.5\\
%$ of fields $K$ in families of quadratic fields. \nIn this talk\, I will
discuss joint work with Anders Södergren and Nicolas Templier\, in which
we study the statistics of $\\zeta_K(1/2)$ in families of $S_3$-cubic fiel
ds. In particular\, we will prove that the Dedekind zeta functions of infi
nitely many such fields have nonvanishing critical value.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diego Izquierdo (École polytechnique)
DTSTART:20220113T120000Z
DTEND:20220113T130000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/41
DESCRIPTION:Title: Milnor K-theory and zero-cycles over p-adic function fields\n
by Diego Izquierdo (École polytechnique) as part of Algebraic Geometry an
d Number Theory seminar - ISTA\n\n\nAbstract\nIn 1986\, Kato and Kuzumaki
introduced a set of conjectures in order to characterize the cohomological
dimension of fields in diophantine terms. The conjectures are known to be
wrong in full generality\, but they provide interesting arithmetical prob
lems over various usual fields in arithmetic geometry. The goal of this ta
lk is to discuss the case of function fields of p-adic curves. This is an
ongoing work with G. Lucchini Arteche\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Groechenig (University of Toronto)
DTSTART:20211007T120000Z
DTEND:20211007T140000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/42
DESCRIPTION:Title: Complex K-theory of dual Hitchin systems\nby Michael Groechen
ig (University of Toronto) as part of Algebraic Geometry and Number Theory
seminar - ISTA\n\n\nAbstract\nLet G and G’ be Langlands dual reductive
groups (e.g. SL(n) and PGL(n)). According to a theorem by Donagi-Pantev\,
the generic fibres of the moduli spaces of G-Higgs bundles and G’-Higgs
bundles are dual abelian varieties and are therefore derived equivalent. I
t is an interesting open problem to prove existence of a derived equivalen
ce over the full Hitchin base. I will report on joint work in progress wit
h Shiyu Shen\, in which we construct a K-theoretic shadow thereof: natural
equivalences between complex K-theory spectra for certain moduli spaces o
f Higgs bundles (in type A).\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Etingof (MIT Mathematics)
DTSTART:20211111T130000Z
DTEND:20211111T150000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/43
DESCRIPTION:Title: Hecke operators over local fields and an analytic approach to the
geometric Langlands correspondence\nby Pavel Etingof (MIT Mathematics
) as part of Algebraic Geometry and Number Theory seminar - ISTA\n\n\nAbst
ract\nI will review an analytic approach to the geometric Langlands corres
pondence\, following my work with E. Frenkel and D. Kazhdan\,\narXiv:1908.
09677\, arXiv:2103.01509\, arXiv:2106.05243. This approach was developed b
y us in the last couple of years and involves ideas from previous and ongo
ing works of a number of mathematicians and mathematical physicists\, Kont
sevich\, Langlands\, Teschner\, and Gaiotto-Witten. One of the goals of th
is approach is to understand single-valued real analytic eigenfunctions of
the quantum Hitchin integrable system. The main method of studying these
functions is realizing them as the eigenbasis for certain compact normal c
ommuting integral operators the Hilbert space of L2 half-densities on the
(complex points of) the moduli space Bun_G of principal G-bundles on a smo
oth projective curve X\, possibly with parabolic points. These operators a
ctually make sense over any local field\, and over non-archimedian fields
are a replacement for the quantum Hitchin system. We conjecture them to be
compact and prove this conjecture in the genus zero case (with parabolic
points) for G=PGL(2). \nI will first discuss the simplest non-trivial exam
ple of Hecke operators over local fields\, namely G=PGL(2) and genus 0 cur
ve with 4 parabolic points. In this case the moduli space of semistable bu
ndles Bun_G^{ss} is P^1\, and the situation is relatively well understood\
; over C it is the theory of single-valued eigenfunctions of the Lame oper
ator with coupling parameter -1/2 (previously studied by Beukers and later
in a more functional-analytic sense in our work with Frenkel and Kazhdan)
. I will consider the corresponding spectral theory and then explain its g
eneralization to N>4 points and conjecturally to higher genus curves.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Green (University of Oxford)
DTSTART:20211104T130000Z
DTEND:20211104T140000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/44
DESCRIPTION:Title: Quadratic forms in 8 prime variables\nby Ben Green (Universit
y of Oxford) as part of Algebraic Geometry and Number Theory seminar - IST
A\n\n\nAbstract\nI will discuss a recent paper of mine\, the aim of which
is to count the number of prime solutions to Q(p_1\,..\,p_8) = N\, for a f
ixed quadratic form Q and varying N. The traditional approach to problems
of this type\, the Hardy-Littlewood circle method\, does not quite suffice
. The main new idea is to involve the Weil representation of the symplecti
c groups Sp_8(Z/qZ). I will explain what this is\, and what it has to do w
ith the original problem. I hope to make the talk accessible to a fairly g
eneral audience.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joachim Jelisiejew (University of Warsaw)
DTSTART:20211021T120000Z
DTEND:20211021T140000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/45
DESCRIPTION:Title: Bialynicki-Birula decompositions old and new\nby Joachim Jeli
siejew (University of Warsaw) as part of Algebraic Geometry and Number The
ory seminar - ISTA\n\n\nAbstract\nBialynicki-Birula decomposition is a pow
erful tool for analysing a smooth variety with a torus action. In the talk
\, I will discuss it and recent developments: the generalization to singul
ar varieties and its applications\, as well as an analogue of BB decomposi
tion for additive group actions. This last generalization\, which is conne
cted to Carrell's rationality conjecture and formal algebraic PDEs\, offer
s several open questions.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrzej Weber (University of Warsaw)
DTSTART:20211209T130000Z
DTEND:20211209T150000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/46
DESCRIPTION:Title: Elliptic characteristic classes of Schubert varieties and duality
\nby Andrzej Weber (University of Warsaw) as part of Algebraic Geometr
y and Number Theory seminar - ISTA\n\n\nAbstract\nWe modify the theory of
Borisov and Libgober to define equivariant characteristic classes of Schub
ert varieties in the generalized flag varieties G/B. The resulting classes
can be considered as functions depending on two sets of parameters: equiv
ariant variables and Kaehler variables. There are two recursions which all
ow to compute inductively these classes: right recursion corresponding to
geometric Demazure-Lusztig operation and left recursion induced by the R-m
atrix appearing in Yang-Baxter equation. When one passes from a group G to
its Langlands' dual the recursions switch they roles. This allows to show
that equivariant elliptic classes for Langlands dual groups coincide afte
r a swap of equivariant variables with Kaehler variables. This duality is
only on the numerical level. The geometric cause remains mysterious.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joni Teräväinen (University of Turku)
DTSTART:20211202T130000Z
DTEND:20211202T140000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/47
DESCRIPTION:Title: On a hybrid of the Hardy-Littlewood and Chowla conjectures\nb
y Joni Teräväinen (University of Turku) as part of Algebraic Geometry an
d Number Theory seminar - ISTA\n\n\nAbstract\nI will discuss a hybrid of t
he Hardy-Littlewood prime tuples conjecture and Chowla's conjecture on the
correlations of the Möbius function. In particular\, it is shown that th
is hybrid conjecture holds "on average" unconditionally\, and without aver
aging if Siegel zeros exist. This is based on joint works with Jared Licht
man and Terence Tao.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alina Carmen Cojocaru (University of Illinois at Chicago)
DTSTART:20211216T150000Z
DTEND:20211216T160000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/48
DESCRIPTION:Title: A geometric generalization of the square sieve with an applicatio
n to cyclic covers over global function fields\nby Alina Carmen Cojoca
ru (University of Illinois at Chicago) as part of Algebraic Geometry and N
umber Theory seminar - ISTA\n\n\nAbstract\nWe formulate a geometric genera
lization of the square sieve and use it to study the number of points of b
ounded height on a prime degree cyclic cover of the n-th projective space
over $\\mathbb{F}_q(T)$. This is joint work with Alina Bucur\, Matilde N.
Lalin\, and Lillian B. Pierce\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David D Ben-Zvi (University of Texas)
DTSTART:20220120T190000Z
DTEND:20220120T210000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/49
DESCRIPTION:Title: Quantization and Duality for Hyperspherical Varieties\nby Dav
id D Ben-Zvi (University of Texas) as part of Algebraic Geometry and Numbe
r Theory seminar - ISTA\n\n\nAbstract\nI will present joint work with Yian
nis Sakellaridis and Akshay Venkatesh\, in which we apply a perspective fr
om topological field theory to the relative Langlands program. The main ge
ometric objects are hyperspherical varieties for a reductive group\, a non
abelian counterpart of hypertoric varieties which include the cotangent bu
ndles of spherical varieties. To a hyperspherical variety one can assign t
wo quantization problems\, automorphic and spectral\, both resulting in st
ructures borrowed from QFT. The automorphic quantization (or A-side) organ
izes objects such as periods\, Plancherel measure\, theta series and relat
ive trace formula\, while the spectral quantization (or B-side) organizes
L-functions and Langlands parameters. Our conjectures organize the relativ
e Langlands program as a duality operation on hyperspherical varieties\, w
hich exchanges automorphic and spectral quantizations (and may be seen as
Langlands duality for boundary conditions in 4d TFT\, a refined form of sy
mplectic duality / 3d mirror symmetry).\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mirko Mauri (University of Michigan)
DTSTART:20211028T110000Z
DTEND:20211028T130000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/50
DESCRIPTION:Title: On the geometric P = W conjecture\nby Mirko Mauri (University
of Michigan) as part of Algebraic Geometry and Number Theory seminar - IS
TA\n\n\nAbstract\nThe geometric P = W conjecture is a conjectural descript
ion of the asymptotic behavior of a celebrated correspondence in non-abeli
an Hodge theory. In a joint work with Enrica Mazzon and Matthew Stevenson\
, we establish the full geometric conjecture for compact Riemann surfaces
of genus one\, and obtain partial results in arbitrary genus: this is the
first non-trivial evidence of the conjecture for compact Riemann surfaces.
To this end\, we employ non-Archimedean\, birational and degeneration tec
hniques to study the topology of the dual boundary complex of certain char
acter varieties.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gufang Zhao (University of Melbourne)
DTSTART:20211118T090000Z
DTEND:20211118T110000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/51
DESCRIPTION:Title: Frobenii on Morava E-theoretical quantum groups\nby Gufang Zh
ao (University of Melbourne) as part of Algebraic Geometry and Number Theo
ry seminar - ISTA\n\n\nAbstract\nThis talk is based on joint work with Yap
ing Yang. We study a family of quantum groups constructed using Morava E-t
heory of Nakajima quiver varieties. We define the quantum Frobenius homomo
rphisms among these quantum groups. This is a geometric generalization of
Lusztig's quantum Frobenius from the quantum groups at a root of unity to
the enveloping algebras. The main ingredient in constructing these Frobeni
i is the transchromatic character map of Hopkins\, Kuhn\, Ravenal\, and St
apleton. In the talk we explain the construction of the Frobenius homomorp
hism\, as well as an application - a Steinberg type tensor product formula
for representations of the quantum groups.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierrick Bousseau
DTSTART:20211125T130000Z
DTEND:20211125T150000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/52
DESCRIPTION:Title: The skein algebra of the 4-punctured sphere from curve counting\nby Pierrick Bousseau as part of Algebraic Geometry and Number Theory s
eminar - ISTA\n\n\nAbstract\nThe Kauffman bracket skein algebra is a quant
ization of the algebra of regular functions on the SL_2 character of a top
ological surface. I will explain how to realize the skein algebra of the 4
-punctured sphere as the output of a mirror symmetry construction based on
higher genus Gromov-Witten invariants of a log Calabi-Yau cubic surface.
This leads to the proof of a previously conjectured positivity property of
the bracelets bases of the skein algebras of the 4-punctured sphere and o
f the 1-punctured torus.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javier Fresán (École polytechnique\, Palaiseau)
DTSTART:20220127T120000Z
DTEND:20220127T130000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/53
DESCRIPTION:Title: Equidistribution of exponential sums over algebraic groups\nb
y Javier Fresán (École polytechnique\, Palaiseau) as part of Algebraic G
eometry and Number Theory seminar - ISTA\n\n\nAbstract\nI will discuss a j
oint work with Arthur Forey and Emmanuel Kowalski in which we obtain an eq
uidistribution theorem for discrete Fourier transforms of trace functions
of perverse sheaves on a commutative algebraic group over a finite field.
The proof relies on a generic vanishing theorem for twists of perverse she
aves\, which allows for the construction of a tannakian category with conv
olution as tensor operation. If time permits\, I will also explain how to
compute the groups governing the equidistribution in a few interesting exa
mples.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kien Nguyen Huu (Katholieke Universiteit Leuven)
DTSTART:20220421T110000Z
DTEND:20220421T120000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/54
DESCRIPTION:by Kien Nguyen Huu (Katholieke Universiteit Leuven) as part of
Algebraic Geometry and Number Theory seminar - ISTA\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quoc P. Ho (Hong Kong University of Science and Technology)
DTSTART:20220317T120000Z
DTEND:20220317T140000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/55
DESCRIPTION:Title: Revisiting mixed geometry\nby Quoc P. Ho (Hong Kong Universit
y of Science and Technology) as part of Algebraic Geometry and Number Theo
ry seminar - ISTA\n\n\nAbstract\nI will present joint work with Penghui Li
on our theory of graded sheaves on Artin stacks. Our sheaf theory comes w
ith a six-functor formalism\, a perverse t-structure in the sense of Beili
nson--Bernstein--Deligne--Gabber\, and a weight (or co-t-)structure in the
sense of Bondarko and Pauksztello\, all compatible\, in a precise sense\,
with the six-functor formalism\, perverse t-structures\, and Frobenius we
ights on ell-adic sheaves. The theory of graded sheaves has a natural inte
rpretation in terms of mixed geometry à la Beilinson--Ginzburg--Soergel a
nd provides a uniform construction thereof. In particular\, it provides a
general construction of graded lifts of many categories arising in geometr
ic representation theory and categorified knot invariants. Historically\,
constructions of graded lifts were done on a case-by-case basis and were t
echnically subtle\, due to Frobenius' non-semisimplicity. Our construction
sidesteps this issue by semi-simplifying the Frobenius action itself. As
an application\, I will conclude the talk by showing that the category of
constructible B-equivariant graded sheaves on the flag variety G/B is a ge
ometrization of the DG-category of bounded chain complexes of Soergel bimo
dules.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Hilburn (Perimeter Institute for Theoretical Physics)
DTSTART:20220310T130000Z
DTEND:20220310T150000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/56
DESCRIPTION:Title: A survey of (abelian) 3d mirror symmetry\nby Justin Hilburn (
Perimeter Institute for Theoretical Physics) as part of Algebraic Geometry
and Number Theory seminar - ISTA\n\n\nAbstract\nBy now it is well known t
hat dualities of 2d and 4d TQFTs\, namely mirror symmetry and electric-mag
netic duality\, organize great swaths of geometry\, representation theory
\, and number theory. In this lecture I will provide an introduction to 3d
mirror symmetry\, which is a lesser known but equally important duality o
f 3d TQFTs associated to hyper-Kahler quotients. To keep things simple I w
ill focus on the simplest such quotients\, known variously as toric hyper-
Kahler manifolds or hypertoric varieties.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Landesman (Harvard University)
DTSTART:20220609T140000Z
DTEND:20220609T150000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/58
DESCRIPTION:Title: Low degree Hurwitz stacks in the Grothendieck ring\nby Aaron
Landesman (Harvard University) as part of Algebraic Geometry and Number Th
eory seminar - ISTA\n\n\nAbstract\nFor $2 \\leq d \\leq 5$\, we show that
the class of the Hurwitz space of smooth degree $d$\, genus $g$ covers of
$\\mathbb P^1$ stabilizes in the Grothendieck ring of stacks as $g \\to \\
infty$. We will survey the connections between this result and related sta
bilizations occuring in algebraic geometry\, number theory\, and topology.
This is based on joint work with Ravi Vakil and Melanie Matchett Wood.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daxin Xu (Morningside Center of Mathematics)
DTSTART:20220428T110000Z
DTEND:20220428T130000Z
DTSTAMP:20260404T111326Z
UID:AGNTISTA/59
DESCRIPTION:Title: Bessel equations\, hypergeometric sums and geometric Langlands co
rrespondence\nby Daxin Xu (Morningside Center of Mathematics) as part
of Algebraic Geometry and Number Theory seminar - ISTA\n\n\nAbstract\nI wi
ll first review the relationship between the Kloosterman sums and the clas
sical Bessel differential equation. Recently\, there are two generalizatio
ns of this story (corresponding to GL_2-case) for arbitrary reductive grou
ps using ideas from the geometric Langlands program\, due to Frenkel-Gross
and Heinloth-Ngô-Yun. I will discuss my joint work with Xinwen Zhu where
we unify previous two constructions from the p-adic aspect and identify t
he exponential sums associated to different groups as conjectured by Heinl
oth-Ngô-Yun. I will also talk about my recent joint work with Masoud Kamg
arpour and Lingfei Yi on the generalization of the above story to hypergeo
metric sheaves.\n
LOCATION:https://stable.researchseminars.org/talk/AGNTISTA/59/
END:VEVENT
END:VCALENDAR