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BEGIN:VEVENT
SUMMARY:Yuuji Tanaka (Oxford)
DTSTART;VALUE=DATE-TIME:20200423T120000Z
DTEND;VALUE=DATE-TIME:20200423T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/1
DESCRIPTION:Title: Vafa-Witten invariants on projective surfaces\nby Yuuji Tanaka (Oxfor
d) as part of Algebraic Geometry and Number Theory seminar - ISTA\n\n\nAbs
tract\nThe first half of this talk will be a gentle introduction to the th
eory of Vafa-Witten invariants\, especially on projective surfaces. In the
second half part - after a break- we focus more on computational results.
This talk is based on joint work with Richard Thomas.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Fiorilli (Université Paris-Sud)
DTSTART;VALUE=DATE-TIME:20200430T120000Z
DTEND;VALUE=DATE-TIME:20200430T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/2
DESCRIPTION:Title: On the distribution of the error term in Chebotarev's density theorem and
applications\nby Daniel Fiorilli (Université Paris-Sud) as part of A
lgebraic Geometry and Number Theory seminar - ISTA\n\n\nAbstract\nWe will
discuss both extreme and generic values of the error term in Chebotarev's
density theorem. This will allow us to deduce applications on a conjecture
of K. Murty on the least unramified prime ideal in a given Frobenius set
as well as on asymptotic properties of Chebyshev's bias.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov (Caltech / MPI Bonn)
DTSTART;VALUE=DATE-TIME:20200521T160000Z
DTEND;VALUE=DATE-TIME:20200521T180000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/5
DESCRIPTION:Title: From the Generalized Volume Conjecture to Turaev and Ramanujan\nby Se
rgei Gukov (Caltech / MPI Bonn) as part of Algebraic Geometry and Number T
heory seminar - ISTA\n\n\nAbstract\nIn this talk\, intended for a broad au
dience\, we will survey the development of a new 3-manifold invariant that
provides an answer to questions like this: What do Dedekind eta and Alexa
nder polynomial have in common? In fact\, illustrated by this question is
perhaps the most attractive feature of this new invariant: it provides new
and often unexpected connections between different areas of mathematics.
Originating from complex Chern-Simons theory and quantization of $\\operat
orname{SL}(2\,\\mathbb{C})$ character varieties\, it evaluates to $q$-seri
es expressions that are more commonly seen in the theory of mock modular f
orms and in logarithmic Vertex Operator Algebras (VOAs). The goal of the t
alk will be to survey these relations using least amount of technical deta
ils.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Humphries (University College London)
DTSTART;VALUE=DATE-TIME:20200528T120000Z
DTEND;VALUE=DATE-TIME:20200528T130000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/6
DESCRIPTION:Title: Small scale equidistribution of lattice points on the sphere\nby Pete
r Humphries (University College London) as part of Algebraic Geometry and
Number Theory seminar - ISTA\n\n\nAbstract\nConsider the projection onto t
he 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 $\\sqrt{n}$. Duk
e and Schulze-Pillot showed in 1990 that these points equidistribute on th
e sphere as $n \\to \\infty$. We study a small scale refinement of this th
eorem\, where one asks whether these points equidistribute in subsets of t
he sphere whose surface area shrinks as $n$ grows. A particular case of th
is is a conjecture of Linnik\, which states that for all $\\delta > 0$\, t
he 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 toward
s this\, as well as proving an averaged form of this conjecture. This is j
oint work with Maksym Radziwiłł.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junliang Shen (MIT)
DTSTART;VALUE=DATE-TIME:20200618T120000Z
DTEND;VALUE=DATE-TIME:20200618T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
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\nAbstract\nThe
topology of the Hitchin fibrations plays crucial role in geometry\, math
physics\, and representation theory. In this talk\, we will discuss two qu
estions arised naturally in the study of Hitchin fibrations in view of the
P=W conjecture: (a) How to locate the tautological classes in the pervers
e filtration? (b) Is the perverse filtration multiplicative for Hitchin fi
brations? \nI will explain how connnections to the geometry of some specia
l algebraic varieties (Hilbert schemes\, abelian surfaces\, hyper-Kahler m
anifolds) lead to progress to answering these questions.\nBased on joint
work with Mark de Cataldo\, Davesh Maulik\, Qizheng Yin\, Zili Zhang.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitri Wyss (L'Ecole polytechnique fédérale de Lausanne (EPFL))
DTSTART;VALUE=DATE-TIME:20200611T120000Z
DTEND;VALUE=DATE-TIME:20200611T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/9
DESCRIPTION:Title: P-adic integration\, geometry and Higgs bundles\nby Dimitri Wyss (L'E
cole polytechnique fédérale de Lausanne (EPFL)) as part of Algebraic Geo
metry and Number Theory seminar - ISTA\n\n\nAbstract\nIntegration with res
pect to the Haar measure over a non-archimedean local field F shares many
formal properties with integration over the reals while at the same time b
eing closely related to the arithmetic and geometry over the residue 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 zeta fun
ctions and Batyrev's proof of the equality of Hodge numbers for smooth pro
jective birational Calabi-Yau varieties.\n\nIn the second part I explain j
oint work with Michael Groechenig and Paul Ziegler\, where we apply these
ideas to the moduli space of G-Higgs bundles. In quite general situations
we can relate p-adic volumes of Higgs spaces for Langlands-dual groups\, f
rom which we derive two results: the topological mirror symmetry conjectur
e of Hausel-Thaddeus\, which relates Hodge numbers for SL_n and PGL_n Higg
s spaces\, and the geometric stabilization theorem for anisotropic Hitchin
fibers of Ngô. If time permits I will also discuss recent ideas on how t
o effectively compute the p-adic volumes appearing in our argument.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Baird (Memorial University of Newfoundland)
DTSTART;VALUE=DATE-TIME:20201001T120000Z
DTEND;VALUE=DATE-TIME:20201001T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
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 Num
ber Theory seminar - ISTA\n\n\nAbstract\nGiven a Riemann surface $\\Sigma$
denote by $$M_n(\\mathbb{F}) := Hom_{\\xi}( \\pi_1(\\Sigma)\, GL_n(\\math
bb{F}))/GL_n(\\mathbb{F})$$ the $\\xi$-twisted character variety for $\\xi
\\in \\mathbb{F}$ a $n$-th root of unity. An anti-holomorphic involution
$\\tau$ on $\\Sigma$ induces an involution on $M_n(\\mathbb{F})$ such tha
t the fixed point variety $M_n^{\\tau}(\\mathbb{F})$ can be identified wit
h the character variety of ``real representations" for the orbifold fundam
ental group $\\pi_1(\\Sigma\, \\tau)$. When $\\mathbb{F} = \\mathbb{C}$\,
$M_n(\\mathbb{C})$ is a complex symplectic manifold and $M_n^{\\tau}(\\mat
hbb{C})$ embeds as a complex Lagrangian submanifold (or ABA-brane).\nBy co
unting 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 si
milar methods can be used to calculate the E-polynomial of $M_n^\\tau(\\ma
thbb{F}_q)$ using the representation theory of $GL_n(\\mathbb{F}_q)$. We
express our formula as a generating function identity involving the plethy
stic logarithm of a product of sums over Young diagrams. The Pieri's formu
la for multiplying Schur polynomials arises in an interesting way.\n\nThis
is joint work with Michael Lennox Wong.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mirko Mauri (Max Planck Institute\, Bonn)
DTSTART;VALUE=DATE-TIME:20201008T120000Z
DTEND;VALUE=DATE-TIME:20201008T133000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/12
DESCRIPTION:Title: P=W conjectures for character varieties with symplectic resolution\n
by Mirko Mauri (Max Planck Institute\, Bonn) as part of Algebraic Geometry
and Number Theory seminar - ISTA\n\n\nAbstract\nCharacter varieties param
etrise representations of the fundamental group of a curve. They are in ge
neral singular moduli spaces\, and for this reason it is customary to shif
t attention to smooth analogues\, called twisted character varieties. The
P=W conjecture formulated by de Cataldo\, Hausel and Migliorini posits a r
elation between the Hodge theory of twisted character varieties and the ge
ometry of some holomorphic Lagrangian fibrations. In a joint work with Cam
illa Felisetti\, we explore P=W phenomena in the untwisted case. We show t
hat the P=W conjecture holds for character varieties which admit a symplec
tic resolution\, namely in genus 1 and arbitrary rank and in genus 2 and r
ank 2. This involves a careful study of alterations of these character var
ieties. If time permits\, I will discuss new numerical evidence of P=W phe
nomena in higher genus\, when no symplectic resolution exists.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davesh Maulik (MIT Mathematics)
DTSTART;VALUE=DATE-TIME:20201029T130000Z
DTEND;VALUE=DATE-TIME:20201029T143000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/13
DESCRIPTION:Title: Cohomology of the moduli of Higgs bundles and the Hausel-Thaddeus conjec
ture\nby Davesh Maulik (MIT Mathematics) as part of Algebraic Geometry
and Number Theory seminar - ISTA\n\n\nAbstract\nIn this talk\, I will dis
cuss some results on the structure of the cohomology of the moduli space o
f stable SL_n Higgs bundles on a curve. One consequence is a new proof of
he Hausel-Thaddeus conjecture proven previously by Groechenig-Wyss-Ziegle
r via p-adic integration. \nWe will also discuss connections to the P=W co
njecture if time permits. Based on joint work with Junliang Shen.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eloise Hamilton (IMJ-PRG\, University of Paris)
DTSTART;VALUE=DATE-TIME:20201112T130000Z
DTEND;VALUE=DATE-TIME:20201112T143000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/14
DESCRIPTION:Title: Moduli spaces for unstable Higgs bundles of rank 2 and their geometry\nby Eloise Hamilton (IMJ-PRG\, University of Paris) as part of Algebraic
Geometry and Number Theory seminar - ISTA\n\n\nAbstract\nThe moduli space
of semistable Higgs bundles of arbitrary rank and degree on a nonsingular
projective curve was first constructed by Nitsure in 1990\, using Geometr
ic Invariant Theory (GIT). Thanks to its rich geometric structure\, this m
oduli space continues to represent an active area of research. The aim of
this talk is to describe how recent results in Non-Reductive GIT can be us
ed to construct moduli spaces for Higgs bundles which are not semistable\,
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 summ
ary of Nitsure's GIT construction of the moduli space and describing the m
ain geometric features of the moduli space. We will then consider the spec
ial case of (twisted) Higgs bundles over the projective line\, in order to
introduce unstable Higgs bundles and their moduli spaces in an elementary
way. In the second part of the talk we will sketch the Non-Reductive GIT
construction of moduli spaces for unstable Higgs bundles over a smooth pro
jective curve of arbitrary genus. We will then describe how the geometry o
f 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 construction as No
n-Reductive GIT quotients on the other.\nQr image\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ariyan Javanpeykar (Johannes Gutenberg-Universität Mainz)
DTSTART;VALUE=DATE-TIME:20201126T130000Z
DTEND;VALUE=DATE-TIME:20201126T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/15
DESCRIPTION:Title: Hilbert's irreducibility theorem for abelian varieties\nby Ariyan Ja
vanpeykar (Johannes Gutenberg-Universität Mainz) as part of Algebraic Geo
metry and Number Theory seminar - ISTA\n\n\nAbstract\nWe will discuss join
t work with Corvaja\, Demeio\, Lombardo\, and Zannier in which we extend H
ilbert's irreducibility theorem (for rational varieties) to the setting of
abelian varieties. Roughly speaking\, given an abelian variety A over a n
umber field k and a ramified covering X of A\, we show that X has "less" k
-rational points than A.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Feng (MIT Mathematics)
DTSTART;VALUE=DATE-TIME:20201203T130000Z
DTEND;VALUE=DATE-TIME:20201203T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/16
DESCRIPTION:Title: The geometric distribution of Selmer groups over function fields\nby
Tony Feng (MIT Mathematics) as part of Algebraic Geometry and Number Theo
ry seminar - ISTA\n\n\nAbstract\nMany interesting aspects of the arithmeti
c of elliptic curves over global fields are governed by Selmer groups\, wh
ich are cohomological approximations to the group of rational points. The
statistical behavior of Selmer groups has been the focus of much recent st
udy\, and there is a wide gap between what we can prove and what we believ
e is true. On the one hand\, work of Bhargava and Shankar computes the ave
rage size of 2\,3\,4\, and 5-Selmer groups. On the other hand\, Bhargava-K
ane-Lenstra-Poonen-Rains conjecture a precise distribution for n-Selmer gr
oups\, for any n. I will talk about a limiting situation\, in the function
field context\, where the BKLPR distribution can actually be proved to mo
del the distribution of Selmer groups. This is joint work with Aaron Lande
sman and Eric Rains.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sachi Hashimoto (Boston University)
DTSTART;VALUE=DATE-TIME:20201119T130000Z
DTEND;VALUE=DATE-TIME:20201119T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/17
DESCRIPTION:Title: Transcendental Brauer-Manin obstructions on some Calabi-Yau threefolds\nby Sachi Hashimoto (Boston University) as part of Algebraic Geometry a
nd Number Theory seminar - ISTA\n\n\nAbstract\nWe study the arithmetic pro
perties of a family of Calabi-Yau threefolds originally studied by Hosono
and Takagi in the context of mirror symmetry. The geometry of these variet
ies endows them with a 2-torsion Brauer class. Under mild conditions\, we
show this Brauer class prevents the rational points from being dense in th
e adelic points. This is joint work with Katrina Honigs\, Alicia Lamarche\
, and Isabel Vogt.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arielle Leitner (Weizmann Institute of Science)
DTSTART;VALUE=DATE-TIME:20201210T130000Z
DTEND;VALUE=DATE-TIME:20201210T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/18
DESCRIPTION:Title: Limits of the diagonal Cartan subgroup in SL(n\,R) and SL(n\, Q_p)\n
by Arielle Leitner (Weizmann Institute of Science) as part of Algebraic Ge
ometry and Number Theory seminar - ISTA\n\n\nAbstract\nA conjugacy limit g
roup is the limit of a sequence of conjugates of the positive diagonal Car
tan subgroup\, C \\leq SL(n) in the Chabauty topology. Over R\, the grou
p C is naturally associated to a projective n-1 simplex. We can compute t
he 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 hig
her dimensions we show there are infinitely many non-conjugate limits of C
. \nIn the Q_p case\, SL(n\,Q_p) has an associated p+1 regular affine buil
ding. (We'll give a gentle introduction to buildings in the talk). The g
roup C stabilizes an apartment in this building\, and limits are contained
in the parabolic subgroups stabilizing the facets in the spherical buildi
ng at infinity. There is a strong interplay between the conjugacy limit gr
oups 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 Ciobotaru and
Alain Valette.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Márton Hablicsek (Universiteit Leiden\, NL)
DTSTART;VALUE=DATE-TIME:20201015T120000Z
DTEND;VALUE=DATE-TIME:20201015T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/19
DESCRIPTION:Title: Virtual Classes of Representation Varieties of Upper Triangular Matrices
via Topological Quantum Field Theories\nby Márton Hablicsek (Univers
iteit Leiden\, NL) as part of Algebraic Geometry and Number Theory seminar
- ISTA\n\n\nAbstract\nLet $X$ be an oriented closed connected surface. Th
e set of group representations from the fundamental group of $X$ to an alg
ebraic group $G$ has a structure of an algebraic variety. This variety is
called the $G$-representation variety of $X$. In this talk\, I will use a
geometric method developed by González-Prieto\, Logares\, Muñoz\, and Ne
wstead to compute the virtual classes of $G$-representation varieties wher
e $G$ is the group of complex upper-triangular matrices of rank 2\, 3\, or
4. This is joint work with Jesse Vogel.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando R. Villegas (ICTP\, Italy)
DTSTART;VALUE=DATE-TIME:20201022T120000Z
DTEND;VALUE=DATE-TIME:20201022T130000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/20
DESCRIPTION:Title: Character varieties of non-orientable surfaces\nby Fernando R. Ville
gas (ICTP\, Italy) as part of Algebraic Geometry and Number Theory seminar
- ISTA\n\n\nAbstract\nWe will discuss various types of character varietie
s parametrizing representations of the fundamental group of a punctured no
n-orientable surface. We compute the number of points of these spaces ove
r finite fields from which we get a formula for their E-series (a certain
specialization of the mixed Poincare series). For one type of character va
riety we extend this calculation to a conjectural formula for the full mix
ed Poincare series in terms of Macdonald symmetric functions and we provid
e some evidence. Unexpectedly\, the formulas we obtain turn out to be clos
ely related to those arising from the character varieties of punctured com
pact orientable Riemann surfaces. This is joint work with E. Letellier.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lior Bary-Soroker (School of Mathematical Sciences of Tel Aviv Uni
versity)
DTSTART;VALUE=DATE-TIME:20201217T130000Z
DTEND;VALUE=DATE-TIME:20201217T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/21
DESCRIPTION:Title: Random Polynomials\, Probabilistic Galois Theory\, and Finite Field Arit
hmetic\nby Lior Bary-Soroker (School of Mathematical Sciences of Tel A
viv University) as part of Algebraic Geometry and Number Theory seminar -
ISTA\n\n\nAbstract\nWe will discuss recent advances on the following two q
uestion: Let A(X) =Σ ±Xi be a random polynomial of degree n with coeffic
ients taking the values -1\, 1 independently each with probability 1/2.\nQ
1: What is the probability that A is irreducible as the degree goes to inf
inity\nQ2: What is the typical Galois of A?\nOne believes that the answers
are YES and THE FULL SYMMETRIC GROUP\, respectively. These questions were
studied extensively in recent years\, and we will survey the tools develo
ped to attack these problems and partial results.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emmanuel Kowalski (ETH Zürich)
DTSTART;VALUE=DATE-TIME:20210107T130000Z
DTEND;VALUE=DATE-TIME:20210107T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/22
DESCRIPTION:Title: Exponential sums and twisted multiplicativity\nby Emmanuel Kowalski
(ETH Zürich) as part of Algebraic Geometry and Number Theory seminar - IS
TA\n\n\nAbstract\nThe additive exponential sums associated to an integral
polynomial\nsatisfy a property of twisted-multiplicativity. Using this\, i
t is\npossible to exploit properties of these sums over finite fields to g
ain\nsome understanding of the sums modulo all integers. This involves a\n
fine interplay of algebraic methods and analytic techniques. The\nexplain
will describe some of these\, and explain in particular how to\ndeduce tha
t the mean value of these exponential sums vanishes for\nsuitably generic
polynomials.\n\n(Joint work with K. Soundararajan)\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Wang (MIT Mathematics)
DTSTART;VALUE=DATE-TIME:20201105T143000Z
DTEND;VALUE=DATE-TIME:20201105T160000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/23
DESCRIPTION:Title: Spherical varieties and L-functions via geometric Langlands\nby Jona
than Wang (MIT Mathematics) as part of Algebraic Geometry and Number Theor
y seminar - ISTA\n\n\nAbstract\nThe relative Langlands program\, as develo
ped by Sakellaridis and Venkatesh\, conjectures relationships between sphe
rical varieties and automorphic L-functions. In the local setting\, this i
s conjecturally related to the computation of asymptotics\, or more precis
ely nearby cycles\, of an IC complex on the formal arc space of a spherica
l variety. I explain my joint work with Yiannis Sakellaridis where we esta
blish this connection and compute this nearby cycles for a nice class of s
pherical varieties using perverse sheaves and the geometry of semi-infinit
e orbits and affine Grassmannians.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kirsten Wickelgren (Duke University\, North Carolina)
DTSTART;VALUE=DATE-TIME:20210114T140000Z
DTEND;VALUE=DATE-TIME:20210114T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/24
DESCRIPTION:Title: An arithmetic count of rational plane curves\nby Kirsten Wickelgren
(Duke University\, North Carolina) as part of Algebraic Geometry and Numbe
r Theory seminar - ISTA\n\n\nAbstract\nThere are finitely many degree d ra
tional plane curves passing through 3d-1 points\, and over the complex num
bers\, this number is independent of (generically) chosen points. For exam
ple\, there are 12 degree 3 rational curves through 8 points\, one conic p
assing through 5\, and one line passing through 2. Over the real numbers\,
one can obtain a fixed number by weighting real rational curves by their
Welschinger invariant\, and work of Solomon identifies this invariant with
a local degree. It is a feature of A1-homotopy theory that analogous real
and complex results can indicate the presence of a common generalization\
, valid over a general field. We develop and compute an A1-degree\, follow
ing Morel\, of the evaluation map on Kontsevich moduli space to obtain 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\, strengthe
ning a count of Marc Levine. This is joint work with Jesse Kass\, Marc Lev
ine\, and Jake Solomon.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jörg Jahnel (University of Siegen)
DTSTART;VALUE=DATE-TIME:20210128T130000Z
DTEND;VALUE=DATE-TIME:20210128T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
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 Number The
ory seminar - ISTA\n\n\nAbstract\nI will report on investigations\, joint
with Damaris Schindler \n(Göttingen)\, concerning the algebraic and trans
cendental Brauer-Manin \nobstructions to integral points on complements of
a hyperplane section in \ndegree four del Pezzo surfaces. We discuss more
over two concepts of an \nobstruction at an archimedean place. Concrete ex
amples are given of pairs \nof non-homogeneous quadratic polynomials in fo
ur variables representing\n$(0\,0)$ over $\\bbQ$ and over $\\bbZ_p$ for al
l primes $p$\, but not\nover $\\bbZ$. By blow-up\, these yield cubic polyn
omials in three variables \nall integral solutions of which satisfy a gcd
condition.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Otto Overkamp (Leibniz Universität Hannover)
DTSTART;VALUE=DATE-TIME:20210121T130000Z
DTEND;VALUE=DATE-TIME:20210121T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/26
DESCRIPTION:Title: Néron models of pseudo-Abelian varieties\nby Otto Overkamp (Leibniz
Universität Hannover) as part of Algebraic Geometry and Number Theory se
minar - ISTA\n\n\nAbstract\nWe explain Totaro's notion of pseudo-Abelian v
arieties and show that they admit Néron models over excellent discrete va
luation rings. As a next step\, we study those Néron models and generaliz
e the notions of good reduction and semiabelian reduction to such algebrai
c groups. \nWe prove that the well-known representation-theoretic criteri
a for good and semiabelian reduction due to Néron-Ogg-Shafarevich and Gro
thendieck carry over to the pseudo-Abelian case\, and give examples to sho
w that our results are the best possible in most cases.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raf Cluckers (University of Lille\, FR\, KU Leuven\, BE)
DTSTART;VALUE=DATE-TIME:20210311T130000Z
DTEND;VALUE=DATE-TIME:20210311T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/27
DESCRIPTION:Title: A number theoretic characterization of (FRS) morphisms\nby Raf Cluck
ers (University of Lille\, FR\, KU Leuven\, BE) as part of Algebraic Geome
try and Number Theory seminar - ISTA\n\n\nAbstract\nI will present joint w
ork with Glazer and Hendel\, which extends the Lang-Weil estimates to esti
mates working with rings of integers modulo powers of primes rather than w
ith finite fields (see arxiv). These bounds were found by Serre in the smo
oth case\, and by Avni and Aizenbud in the case of rational singularities
(which is close to the smooth case). We render the situation uniform in th
e fibers of an algebraic morphism each of whose fibers has rational singul
arities. Surprizingly\, this relative case with uniform bounds needs rathe
r different methods\, related to motivic integration\, or more precisely u
niform p-adic integration. Subtle new results about formally positive unif
orm p-adic functions needed to be developed for this to work.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uri Onn (Australian National University)
DTSTART;VALUE=DATE-TIME:20210408T120000Z
DTEND;VALUE=DATE-TIME:20210408T130000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/29
DESCRIPTION:Title: Analytic properties of representation zeta functions of arithmetic group
s\nby Uri Onn (Australian National University) as part of Algebraic Ge
ometry and Number Theory seminar - ISTA\n\n\nAbstract\nA group is said to
have polynomial representation growth if the sequence enumerating the isom
orphism classes of finite dimensional irreducible representations accordin
g to their dimension is polynomially bounded. The representation zeta func
tion of such group is the associated Dirichlet generating series. In this
talk I will focus on representation zeta functions of arithmetic groups an
d their analytic properties. I will explain the ideas behind a proof of a
variant of the Larsen-Lubotzky conjecture on the representation growth of
arithmetic lattices in high rank semisimple Lie groups (joint with Nir Avn
i\, Benjamin Klopsch and Christopher Voll). Time permitting\, I will talk
about results on arithmetic groups of type A_2 in positive characteristic
(joint with Amritanshu Prasad and Pooja Singla) and results towards meromo
rphic continuation (joint with Shai Shechter).\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincent Lafforgue (Institute Fournier\, Grenoble)
DTSTART;VALUE=DATE-TIME:20210318T130000Z
DTEND;VALUE=DATE-TIME:20210318T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/30
DESCRIPTION:Title: Classical limits for geometrizations of functoriality kernels and values
of L-functions\nby Vincent Lafforgue (Institute Fournier\, Grenoble)
as part of Algebraic Geometry and Number Theory seminar - ISTA\n\n\nAbstra
ct\nIn the setting of the geometric Langlands program\, it is conjectured
that kernels which should give rise to Langlands functoriality\, and relat
ions between values of L-functions and some periods\, exist. Some cases ar
e known (e.g. the geometric theta correspondence and the geometrization of
Rankin-Selberg integrals\, due to Lysenko)\, the rest is mainly conjectur
al. However the (partly conjectural) classical limits may be described and
their properties studied. In the first hour I will recall some elementary
facts of symplectic geometry and the classical limit of the Langlands co
rrespondence via the Hitchin fibration.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oscar Garcia-Prada (ICMAT\, Spain)
DTSTART;VALUE=DATE-TIME:20210325T130000Z
DTEND;VALUE=DATE-TIME:20210325T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/31
DESCRIPTION:Title: Arakelov–Milnor inequalities and maximal variations of Hodge structure
\nby Oscar Garcia-Prada (ICMAT\, Spain) as part of Algebraic Geometry
and Number Theory seminar - ISTA\n\n\nAbstract\nIn this talk we study the
fixed points under the action of the multiplicative group of non-vanishing
complex numbers on moduli spaces of Higgs bundles over a compact Riemann
surface for complex semisimple Lie groups and their real forms. These fixe
d points are called Hodge bundles and correspond to complex variations of
Hodge structure. We introduce a topological invariant for Hodge bundles th
at generalizes the Toledo invariant appearing for Hermitian Lie groups. A
main result to discuss is a bound on this invariant which generalizes both
the Milnor–Wood inequality of the Hermitian case\, and the Arakelov ine
qualities of classical variations of Hodge structure. When the generalized
Toledo invariant is maximal\, we establish rigidity results for the assoc
iated variations of Hodge structure which generalize known rigidity result
s for maximal Higgs bundles and their associated maximal representations i
n the Hermitian case (based on joint work with Olivier Biquard\, Brian Col
lier and Domingo Toledo).\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Kamnitzer (University of Toronto)
DTSTART;VALUE=DATE-TIME:20210429T120000Z
DTEND;VALUE=DATE-TIME:20210429T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/32
DESCRIPTION:Title: Affine Grassmannian slices and their quantizations\nby Joel Kamnitze
r (University of Toronto) as part of Algebraic Geometry and Number Theory
seminar - ISTA\n\n\nAbstract\nSlices in the affine Grassmannian are geomet
ric incarnations of weight spaces of representations of semisimple complex
groups. These spaces can also be constructed as Coulomb branches of quiv
er gauge theories or in type A\, as bow varieties. They are related to Na
kajima quiver varieties using 3d mirror symmetry\, also known as symplecti
c duality. These spaces are conical symplectic singularities and have na
tural quantizations using algebras called truncated shifted Yangians. I w
ill survey 10 years of research on these wonderful spaces and describe som
e remaining open questions.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mercedes Haiech (University of Rennes)
DTSTART;VALUE=DATE-TIME:20210422T120000Z
DTEND;VALUE=DATE-TIME:20210422T130000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/33
DESCRIPTION:Title: The Fundamental Theorem of Tropical Partial Differential Algebraic Geome
try\nby Mercedes Haiech (University of Rennes) as part of Algebraic Ge
ometry and Number Theory seminar - ISTA\n\n\nAbstract\nGiven a partial dif
ferential equation (PDE)\, its solutions can be difficult\, if not impossi
ble\, to describe.\nThe purpose of the Fundamental theorem of tropical (pa
rtial) differential algebraic geometry is to extract from the equations ce
rtain properties of the solutions. \nMore precisely\, this theorem proves
that the support of the solutions in $k[[t_1\, \\cdots\, t_m]]$ (with $k$
a field of characteristic zero) can be obtained by solving a so-called tro
picalized differential system.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richárd Rimányi (UNC Chapel Hill)
DTSTART;VALUE=DATE-TIME:20210415T120000Z
DTEND;VALUE=DATE-TIME:20210415T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/34
DESCRIPTION:Title: Stable envelopes\, 3d mirror symmetry\, bow varieties\nby Richárd R
imányi (UNC Chapel Hill) as part of Algebraic Geometry and Number Theory
seminar - ISTA\n\n\nAbstract\nThe role played by Schubert classes in the g
eometry of Grassmannians is played by the so-called stable envelopes in th
e geometry of Nakajima quiver varieties. Stable envelopes come in three fl
avors: cohomological\, K theoretic\, and elliptic stable envelopes. We wil
l show examples\, and explore their appearances in enumerative geometry an
d representation theory. In the second part of the talk we will discuss ``
3d mirror symmetry for characteristic classes’’\, namely\, the fact th
at for certain pairs of seemingly unrelated spaces the elliptic stable env
elopes `match’ in some concrete (but non-obvious) sense. We will meet Ch
erkis bow varieties\, a pool of spaces (conjecturally) closed under ``3d m
irror symmetry for characteristic classes’’. The combinatorics necessa
ry to play Schubert calculus on bow varieties includes binary contingency
tables\, tie diagrams\, and the Hanany-Witten transition.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philipp Habegger (University of Basel)
DTSTART;VALUE=DATE-TIME:20210401T120000Z
DTEND;VALUE=DATE-TIME:20210401T130000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/35
DESCRIPTION:Title: Uniformity for the Number of Rational Points on a Curve\nby Philipp
Habegger (University of Basel) as part of Algebraic Geometry and Number Th
eory seminar - ISTA\n\n\nAbstract\nBy Faltings's Theorem\, formerly known
as the Mordell Conjecture\, a smooth projective curve of genus at least 2
that is defined over a number field K has at most finitely many K-rational
points. Votja later gave a second proof. Many authors\, including Bombier
i\, de Diego\, Parshin\, Rémond\, Vojta\, proved upper bounds for the num
ber of K-rational points. I will discuss joint work with Vesselin Dimitrov
and Ziyang Gao where we prove that the number of points on the curve is b
ounded from above as a function of K\, the genus\, and the rank of the Mor
dell-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 boun
d from above the number of points whose height is in the intermediate rang
e.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:NOTE unusual time: Geordie Williamson (University of Sidney)
DTSTART;VALUE=DATE-TIME:20210610T070000Z
DTEND;VALUE=DATE-TIME:20210610T090000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/36
DESCRIPTION:Title: Spectra in representation theory\nby NOTE unusual time: Geordie Will
iamson (University of Sidney) as part of Algebraic Geometry and Number The
ory seminar - ISTA\n\n\nAbstract\nIn geometric representation theory cohom
ology\, intersection cohomology and constructible sheaves show up everywhe
re. This might seem strange to an algebraic topologist\, who might ask: wh
y this emphasis on cohomology\, when there are so many other interesting c
ohomology theories(like K-theory\, elliptic cohomology\, complex cobordism
\, ...) out there? They might also ask: is there something like "intersect
ion K-theory"\, or "intersection complex cobordism"? This is something I'v
e often wondered about. I will describe work in progress with Ben Elias\,
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 an
d B2\, one gets something roughly resembling the quantum group. Speaking v
ery roughly\, the intersection K-theory of Schubert varieties in the affin
e Grassmannian should recover the irreducible representations of the quant
um group. Inspirations for this work include a strange Cartan matrix disco
vered by Ben Elias\, and work of Cautis-Kamnitzer.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhiwei Yun (MIT Mathematics)
DTSTART;VALUE=DATE-TIME:20210520T120000Z
DTEND;VALUE=DATE-TIME:20210520T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/37
DESCRIPTION:Title: Universal global nilpotent cone\nby Zhiwei Yun (MIT Mathematics) as
part of Algebraic Geometry and Number Theory seminar - ISTA\n\nAbstract: T
BA\n\nThe global nilpotent cone is the zero fiber of the Hitchin map in th
e moduli space of Higgs bundles over an algebraic curve. It is a conic Lag
rangian in the ambient symplectic moduli space\, and it plays an important
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 "connection"
among the category of sheaves on Bun_G as the curve varies. I will mentio
n the motivation of the construction from Betti geometric Langlands. This
is joint work with David Nadler.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arul Shankar (University of Toronto)
DTSTART;VALUE=DATE-TIME:20210527T120000Z
DTEND;VALUE=DATE-TIME:20210527T130000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/38
DESCRIPTION:Title: Nonvanishing at the critical point of the Dedekind zeta functions of cub
ic $S_3$-fields\nby Arul Shankar (University of Toronto) as part of Al
gebraic Geometry and Number Theory seminar - ISTA\n\n\nAbstract\nLet $K$ b
e 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 function v
anish at the critical point $s=1/2$? In successive works\, Armitage\, and
then Frohlich\, gave examples of number fields which satisfy $\\zeta_K(s
)=0$. Conversely\, it is believed that certain conditions on $K$ can guara
ntee the nonvanishing of $\\zeta_K(s)$ at the critical point. For example\
, it is believed that $\\zeta_K(s)$ is never $0$ when $K$ is an $S_n$-numb
er field for any $n\\geq 1$.\nWhen $n=1$\, $\\zeta_K(s)$ is simply the Rie
mann zeta function\, and Riemann himself established the non vanishing of
$\\zeta(1/2)$.\nWhen $n=2$\, there has been amazing progress towards under
standing the statistics of $\\zeta_K(1/2)$. Jutila first proved that infin
itely many quadratic fields $K$ satisfy $\\zeta_K(1/2)\\neq 0$\, and Sound
ararajan establishes that this is in fact true for at least $87.5\\%$ of f
ields $K$ in families of quadratic fields. \nIn this talk\, I will discuss
joint work with Anders Södergren and Nicolas Templier\, in which we stud
y the statistics of $\\zeta_K(1/2)$ in families of $S_3$-cubic fields. In
particular\, we will prove that the Dedekind zeta functions of infinitely
many such fields have nonvanishing critical value.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diego Izquierdo (École polytechnique)
DTSTART;VALUE=DATE-TIME:20220113T120000Z
DTEND;VALUE=DATE-TIME:20220113T130000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/41
DESCRIPTION:Title: Milnor K-theory and zero-cycles over p-adic function fields\nby Dieg
o Izquierdo (École polytechnique) as part of Algebraic Geometry and Numbe
r Theory seminar - ISTA\n\n\nAbstract\nIn 1986\, Kato and Kuzumaki introdu
ced a set of conjectures in order to characterize the cohomological dimens
ion of fields in diophantine terms. The conjectures are known to be wrong
in full generality\, but they provide interesting arithmetical problems ov
er various usual fields in arithmetic geometry. The goal of this talk is t
o discuss the case of function fields of p-adic curves. This is an ongoing
work with G. Lucchini Arteche\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Groechenig (University of Toronto)
DTSTART;VALUE=DATE-TIME:20211007T120000Z
DTEND;VALUE=DATE-TIME:20211007T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/42
DESCRIPTION:Title: Complex K-theory of dual Hitchin systems\nby Michael Groechenig (Uni
versity of Toronto) as part of Algebraic Geometry and Number Theory semina
r - 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 gen
eric fibres of the moduli spaces of G-Higgs bundles and G’-Higgs bundles
are dual abelian varieties and are therefore derived equivalent. It is an
interesting open problem to prove existence of a derived equivalence over
the full Hitchin base. I will report on joint work in progress with Shiyu
Shen\, in which we construct a K-theoretic shadow thereof: natural equiva
lences between complex K-theory spectra for certain moduli spaces of Higgs
bundles (in type A).\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Etingof (MIT Mathematics)
DTSTART;VALUE=DATE-TIME:20211111T130000Z
DTEND;VALUE=DATE-TIME:20211111T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/43
DESCRIPTION:Title: Hecke operators over local fields and an analytic approach to the geomet
ric Langlands correspondence\nby Pavel Etingof (MIT Mathematics) as pa
rt of Algebraic Geometry and Number Theory seminar - ISTA\n\n\nAbstract\nI
will review an analytic approach to the geometric Langlands correspondenc
e\, following my work with E. Frenkel and D. Kazhdan\,\narXiv:1908.09677\,
arXiv:2103.01509\, arXiv:2106.05243. This approach was developed by us in
the last couple of years and involves ideas from previous and ongoing wor
ks of a number of mathematicians and mathematical physicists\, Kontsevich\
, Langlands\, Teschner\, and Gaiotto-Witten. One of the goals of this appr
oach is to understand single-valued real analytic eigenfunctions of the qu
antum Hitchin integrable system. The main method of studying these functio
ns is realizing them as the eigenbasis for certain compact normal commutin
g integral operators the Hilbert space of L2 half-densities on the (comple
x points of) the moduli space Bun_G of principal G-bundles on a smooth pro
jective curve X\, possibly with parabolic points. These operators actually
make sense over any local field\, and over non-archimedian fields are a r
eplacement for the quantum Hitchin system. We conjecture them to be compac
t and prove this conjecture in the genus zero case (with parabolic points)
for G=PGL(2). \nI will first discuss the simplest non-trivial example of
Hecke operators over local fields\, namely G=PGL(2) and genus 0 curve with
4 parabolic points. In this case the moduli space of semistable bundles B
un_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 operator wi
th coupling parameter -1/2 (previously studied by Beukers and later in a m
ore functional-analytic sense in our work with Frenkel and Kazhdan). I wil
l consider the corresponding spectral theory and then explain its generali
zation to N>4 points and conjecturally to higher genus curves.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Green (University of Oxford)
DTSTART;VALUE=DATE-TIME:20211104T130000Z
DTEND;VALUE=DATE-TIME:20211104T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/44
DESCRIPTION:Title: Quadratic forms in 8 prime variables\nby Ben Green (University of Ox
ford) as part of Algebraic Geometry and Number Theory seminar - ISTA\n\n\n
Abstract\nI will discuss a recent paper of mine\, the aim of which is to c
ount the number of prime solutions to Q(p_1\,..\,p_8) = N\, for a fixed qu
adratic form Q and varying N. The traditional approach to problems of this
type\, the Hardy-Littlewood circle method\, does not quite suffice. The m
ain new idea is to involve the Weil representation of the symplectic group
s Sp_8(Z/qZ). I will explain what this is\, and what it has to do with the
original problem. I hope to make the talk accessible to a fairly general
audience.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joachim Jelisiejew (University of Warsaw)
DTSTART;VALUE=DATE-TIME:20211021T120000Z
DTEND;VALUE=DATE-TIME:20211021T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/45
DESCRIPTION:Title: Bialynicki-Birula decompositions old and new\nby Joachim Jelisiejew
(University of Warsaw) as part of Algebraic Geometry and Number Theory sem
inar - ISTA\n\n\nAbstract\nBialynicki-Birula decomposition is a powerful t
ool for analysing a smooth variety with a torus action. In the talk\, I wi
ll discuss it and recent developments: the generalization to singular vari
eties and its applications\, as well as an analogue of BB decomposition fo
r additive group actions. This last generalization\, which is connected to
Carrell's rationality conjecture and formal algebraic PDEs\, offers sever
al open questions.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrzej Weber (University of Warsaw)
DTSTART;VALUE=DATE-TIME:20211209T130000Z
DTEND;VALUE=DATE-TIME:20211209T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/46
DESCRIPTION:Title: Elliptic characteristic classes of Schubert varieties and duality\nb
y Andrzej Weber (University of Warsaw) as part of Algebraic Geometry and N
umber Theory seminar - ISTA\n\n\nAbstract\nWe modify the theory of Borisov
and Libgober to define equivariant characteristic classes of Schubert var
ieties in the generalized flag varieties G/B. The resulting classes can be
considered as functions depending on two sets of parameters: equivariant
variables and Kaehler variables. There are two recursions which allow to c
ompute inductively these classes: right recursion corresponding to geometr
ic Demazure-Lusztig operation and left recursion induced by the R-matrix a
ppearing in Yang-Baxter equation. When one passes from a group G to its La
nglands' dual the recursions switch they roles. This allows to show that e
quivariant elliptic classes for Langlands dual groups coincide after a swa
p of equivariant variables with Kaehler variables. This duality is only on
the numerical level. The geometric cause remains mysterious.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joni Teräväinen (University of Turku)
DTSTART;VALUE=DATE-TIME:20211202T130000Z
DTEND;VALUE=DATE-TIME:20211202T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/47
DESCRIPTION:Title: On a hybrid of the Hardy-Littlewood and Chowla conjectures\nby Joni
Teräväinen (University of Turku) as part of Algebraic Geometry and Numbe
r Theory seminar - ISTA\n\n\nAbstract\nI will discuss a hybrid of the Hard
y-Littlewood prime tuples conjecture and Chowla's conjecture on the correl
ations of the Möbius function. In particular\, it is shown that this hybr
id conjecture holds "on average" unconditionally\, and without averaging i
f Siegel zeros exist. This is based on joint works with Jared Lichtman and
Terence Tao.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alina Carmen Cojocaru (University of Illinois at Chicago)
DTSTART;VALUE=DATE-TIME:20211216T150000Z
DTEND;VALUE=DATE-TIME:20211216T160000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/48
DESCRIPTION:Title: A geometric generalization of the square sieve with an application to cy
clic covers over global function fields\nby Alina Carmen Cojocaru (Uni
versity of Illinois at Chicago) as part of Algebraic Geometry and Number T
heory seminar - ISTA\n\n\nAbstract\nWe formulate a geometric generalizatio
n of the square sieve and use it to study the number of points of bounded
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://researchseminars.org/talk/AGNTISTA/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David D Ben-Zvi (University of Texas)
DTSTART;VALUE=DATE-TIME:20220120T190000Z
DTEND;VALUE=DATE-TIME:20220120T210000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/49
DESCRIPTION:Title: Quantization and Duality for Hyperspherical Varieties\nby David D Be
n-Zvi (University of Texas) as part of Algebraic Geometry and Number Theor
y seminar - ISTA\n\n\nAbstract\nI will present joint work with Yiannis Sak
ellaridis and Akshay Venkatesh\, in which we apply a perspective from topo
logical field theory to the relative Langlands program. The main geometric
objects are hyperspherical varieties for a reductive group\, a nonabelian
counterpart of hypertoric varieties which include the cotangent bundles o
f spherical varieties. To a hyperspherical variety one can assign two quan
tization problems\, automorphic and spectral\, both resulting in structure
s borrowed from QFT. The automorphic quantization (or A-side) organizes ob
jects such as periods\, Plancherel measure\, theta series and relative tra
ce formula\, while the spectral quantization (or B-side) organizes L-funct
ions and Langlands parameters. Our conjectures organize the relative Langl
ands program as a duality operation on hyperspherical varieties\, which ex
changes automorphic and spectral quantizations (and may be seen as Langlan
ds duality for boundary conditions in 4d TFT\, a refined form of symplecti
c duality / 3d mirror symmetry).\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mirko Mauri (University of Michigan)
DTSTART;VALUE=DATE-TIME:20211028T110000Z
DTEND;VALUE=DATE-TIME:20211028T130000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/50
DESCRIPTION:Title: On the geometric P = W conjecture\nby Mirko Mauri (University of Mic
higan) as part of Algebraic Geometry and Number Theory seminar - ISTA\n\n\
nAbstract\nThe geometric P = W conjecture is a conjectural description of
the asymptotic behavior of a celebrated correspondence in non-abelian Hodg
e theory. In a joint work with Enrica Mazzon and Matthew Stevenson\, we es
tablish the full geometric conjecture for compact Riemann surfaces of genu
s one\, and obtain partial results in arbitrary genus: this is the first n
on-trivial evidence of the conjecture for compact Riemann surfaces. To thi
s end\, we employ non-Archimedean\, birational and degeneration techniques
to study the topology of the dual boundary complex of certain character v
arieties.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gufang Zhao (University of Melbourne)
DTSTART;VALUE=DATE-TIME:20211118T090000Z
DTEND;VALUE=DATE-TIME:20211118T110000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/51
DESCRIPTION:Title: Frobenii on Morava E-theoretical quantum groups\nby Gufang Zhao (Uni
versity of Melbourne) as part of Algebraic Geometry and Number Theory semi
nar - ISTA\n\n\nAbstract\nThis talk is based on joint work with Yaping Yan
g. We study a family of quantum groups constructed using Morava E-theory o
f Nakajima quiver varieties. We define the quantum Frobenius homomorphisms
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 env
eloping algebras. The main ingredient in constructing these Frobenii is th
e transchromatic character map of Hopkins\, Kuhn\, Ravenal\, and Stapleton
. In the talk we explain the construction of the Frobenius homomorphism\,
as well as an application - a Steinberg type tensor product formula for re
presentations of the quantum groups.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierrick Bousseau
DTSTART;VALUE=DATE-TIME:20211125T130000Z
DTEND;VALUE=DATE-TIME:20211125T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
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 seminar
- ISTA\n\n\nAbstract\nThe Kauffman bracket skein algebra is a quantization
of the algebra of regular functions on the SL_2 character of a topologica
l surface. I will explain how to realize the skein algebra of the 4-punctu
red sphere as the output of a mirror symmetry construction based on higher
genus Gromov-Witten invariants of a log Calabi-Yau cubic surface. This le
ads to the proof of a previously conjectured positivity property of the br
acelets bases of the skein algebras of the 4-punctured sphere and of the 1
-punctured torus.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javier Fresán (École polytechnique\, Palaiseau)
DTSTART;VALUE=DATE-TIME:20220127T120000Z
DTEND;VALUE=DATE-TIME:20220127T130000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/53
DESCRIPTION:Title: Equidistribution of exponential sums over algebraic groups\nby Javie
r Fresán (École polytechnique\, Palaiseau) as part of Algebraic Geometry
and Number Theory seminar - ISTA\n\n\nAbstract\nI will discuss a joint wo
rk with Arthur Forey and Emmanuel Kowalski in which we obtain an equidistr
ibution theorem for discrete Fourier transforms of trace functions of perv
erse sheaves on a commutative algebraic group over a finite field. The pro
of relies on a generic vanishing theorem for twists of perverse sheaves\,
which allows for the construction of a tannakian category with convolution
as tensor operation. If time permits\, I will also explain how to compute
the groups governing the equidistribution in a few interesting examples.\
n
LOCATION:https://researchseminars.org/talk/AGNTISTA/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kien Nguyen Huu (Katholieke Universiteit Leuven)
DTSTART;VALUE=DATE-TIME:20220421T110000Z
DTEND;VALUE=DATE-TIME:20220421T120000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
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://researchseminars.org/talk/AGNTISTA/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quoc P. Ho (Hong Kong University of Science and Technology)
DTSTART;VALUE=DATE-TIME:20220317T120000Z
DTEND;VALUE=DATE-TIME:20220317T140000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/55
DESCRIPTION:Title: Revisiting mixed geometry\nby Quoc P. Ho (Hong Kong University of Sc
ience and Technology) as part of Algebraic Geometry and Number Theory semi
nar - 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 with a s
ix-functor formalism\, a perverse t-structure in the sense of Beilinson--B
ernstein--Deligne--Gabber\, and a weight (or co-t-)structure in the sense
of Bondarko and Pauksztello\, all compatible\, in a precise sense\, with t
he six-functor formalism\, perverse t-structures\, and Frobenius weights o
n ell-adic sheaves. The theory of graded sheaves has a natural interpretat
ion in terms of mixed geometry à la Beilinson--Ginzburg--Soergel and prov
ides a uniform construction thereof. In particular\, it provides a general
construction of graded lifts of many categories arising in geometric repr
esentation theory and categorified knot invariants. Historically\, constru
ctions of graded lifts were done on a case-by-case basis and were technica
lly subtle\, due to Frobenius' non-semisimplicity. Our construction sidest
eps this issue by semi-simplifying the Frobenius action itself. As an appl
ication\, I will conclude the talk by showing that the category of constru
ctible B-equivariant graded sheaves on the flag variety G/B is a geometriz
ation of the DG-category of bounded chain complexes of Soergel bimodules.\
n
LOCATION:https://researchseminars.org/talk/AGNTISTA/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Hilburn (Perimeter Institute for Theoretical Physics)
DTSTART;VALUE=DATE-TIME:20220310T130000Z
DTEND;VALUE=DATE-TIME:20220310T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/56
DESCRIPTION:Title: A survey of (abelian) 3d mirror symmetry\nby Justin Hilburn (Perimet
er Institute for Theoretical Physics) as part of Algebraic Geometry and Nu
mber Theory seminar - ISTA\n\n\nAbstract\nBy now it is well known that dua
lities of 2d and 4d TQFTs\, namely mirror symmetry and electric-magnetic d
uality\, 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 of 3d TQ
FTs associated to hyper-Kahler quotients. To keep things simple I will foc
us on the simplest such quotients\, known variously as toric hyper-Kahler
manifolds or hypertoric varieties.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Landesman (Harvard University)
DTSTART;VALUE=DATE-TIME:20220609T140000Z
DTEND;VALUE=DATE-TIME:20220609T150000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/58
DESCRIPTION:Title: Low degree Hurwitz stacks in the Grothendieck ring\nby Aaron Landesm
an (Harvard University) as part of Algebraic Geometry and Number Theory se
minar - ISTA\n\n\nAbstract\nFor $2 \\leq d \\leq 5$\, we show that the cla
ss of the Hurwitz space of smooth degree $d$\, genus $g$ covers of $\\math
bb P^1$ stabilizes in the Grothendieck ring of stacks as $g \\to \\infty$.
We will survey the connections between this result and related stabilizat
ions occuring in algebraic geometry\, number theory\, and topology. This i
s based on joint work with Ravi Vakil and Melanie Matchett Wood.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daxin Xu (Morningside Center of Mathematics)
DTSTART;VALUE=DATE-TIME:20220428T110000Z
DTEND;VALUE=DATE-TIME:20220428T130000Z
DTSTAMP;VALUE=DATE-TIME:20220927T053330Z
UID:AGNTISTA/59
DESCRIPTION:Title: Bessel equations\, hypergeometric sums and geometric Langlands correspon
dence\nby Daxin Xu (Morningside Center of Mathematics) as part of Alge
braic Geometry and Number Theory seminar - ISTA\n\n\nAbstract\nI will firs
t review the relationship between the Kloosterman sums and the classical B
essel differential equation. Recently\, there are two generalizations of t
his story (corresponding to GL_2-case) for arbitrary reductive groups usin
g ideas from the geometric Langlands program\, due to Frenkel-Gross and He
inloth-Ngô-Yun. I will discuss my joint work with Xinwen Zhu where we uni
fy previous two constructions from the p-adic aspect and identify the expo
nential sums associated to different groups as conjectured by Heinloth-Ng
ô-Yun. I will also talk about my recent joint work with Masoud Kamgarpour
and Lingfei Yi on the generalization of the above story to hypergeometric
sheaves.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/59/
END:VEVENT
END:VCALENDAR