BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Yuuji Tanaka (Oxford)
DTSTART;VALUE=DATE-TIME:20200423T120000Z
DTEND;VALUE=DATE-TIME:20200423T140000Z
DTSTAMP;VALUE=DATE-TIME:20210419T101427Z
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:20210419T101427Z
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:20210419T101427Z
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:20210419T101427Z
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:20210419T101427Z
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:20210419T101427Z
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:20210419T101427Z
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:20210419T101427Z
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:20210419T101427Z
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:20210419T101427Z
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:20210419T101427Z
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:20210419T101427Z
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:20210419T101427Z
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:20210419T101427Z
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:20210419T101427Z
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:20210419T101427Z
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:20210419T101427Z
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:20210419T101427Z
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:20210419T101427Z
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:20210419T101427Z
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:20210419T101427Z
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:20210419T101427Z
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:20210419T101427Z
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:Maria Yakerson (ETH Zürich)
DTSTART;VALUE=DATE-TIME:20210506T120000Z
DTEND;VALUE=DATE-TIME:20210506T130000Z
DTSTAMP;VALUE=DATE-TIME:20210419T101427Z
UID:AGNTISTA/28
DESCRIPTION:by Maria Yakerson (ETH Zürich) as part of Algebraic Geometry
and Number Theory seminar - ISTA\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uri Onn (Australian National University)
DTSTART;VALUE=DATE-TIME:20210408T120000Z
DTEND;VALUE=DATE-TIME:20210408T130000Z
DTSTAMP;VALUE=DATE-TIME:20210419T101427Z
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:20210419T101427Z
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:20210419T101427Z
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:20210419T101427Z
UID:AGNTISTA/32
DESCRIPTION:by Joel Kamnitzer (University of Toronto) as part of Algebraic
Geometry and Number Theory seminar - ISTA\n\nAbstract: TBA\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:20210419T101427Z
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:20210419T101427Z
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:20210419T101427Z
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:Geordie Williamson (University of Sidney)
DTSTART;VALUE=DATE-TIME:20210610T120000Z
DTEND;VALUE=DATE-TIME:20210610T140000Z
DTSTAMP;VALUE=DATE-TIME:20210419T101427Z
UID:AGNTISTA/36
DESCRIPTION:by Geordie Williamson (University of Sidney) as part of Algebr
aic Geometry and Number Theory seminar - ISTA\n\nAbstract: TBA\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:20210419T101427Z
UID:AGNTISTA/37
DESCRIPTION:by Zhiwei Yun (MIT Mathematics) as part of Algebraic Geometry
and Number Theory seminar - ISTA\n\nAbstract: TBA\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:20210419T101427Z
UID:AGNTISTA/38
DESCRIPTION:by Arul Shankar (University of Toronto) as part of Algebraic G
eometry and Number Theory seminar - ISTA\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/38/
END:VEVENT
END:VCALENDAR