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BEGIN:VEVENT
SUMMARY:Jan Vonk (IAS Princeton)
DTSTART;VALUE=DATE-TIME:20200422T130000Z
DTEND;VALUE=DATE-TIME:20200422T140000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/1
DESCRIPTION:Title: Singular moduli for real quadratic fields\nby Jan Vonk (IAS Pri
nceton) as part of International seminar on automorphic forms\n\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Andersen (Brigham Young University)
DTSTART;VALUE=DATE-TIME:20200429T140000Z
DTEND;VALUE=DATE-TIME:20200429T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/2
DESCRIPTION:Title: Zeros of GL2 L-functions on the critical line\nby Nick Andersen
(Brigham Young University) as part of International seminar on automorphi
c forms\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soma Purkait (Tokyo Institute of Technology)
DTSTART;VALUE=DATE-TIME:20200506T080000Z
DTEND;VALUE=DATE-TIME:20200506T090000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/3
DESCRIPTION:Title: Local Hecke algebras and new forms\nby Soma Purkait (Tokyo Inst
itute of Technology) as part of International seminar on automorphic forms
\n\n\nAbstract\nWe describe local Hecke algebras of $\\GL_2$ and double co
ver of $\\SL_2$\n with certain level structures and use it to give a newfo
rm theory. In the integral weight setting\, our method allows us to give a
characterization of the newspace of any level as a common eigenspace of c
ertain finitely many pair of conjugate operators that we obtain from local
Hecke algebras. In specific cases\, we can completely describe local Whit
taker functions associated to a new form. In the half-integral weight sett
ing\, we give an analogous characterization of the newspace for the full s
pace of half-integral weight forms of level $8M$\, $M$ odd and square-free
and observe that the forms in the newspace space satisfy a Fourier coeffi
cient condition that gives the complement of the plus space. This is a joi
nt work with E.M. Baruch.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Humphries (University College London)
DTSTART;VALUE=DATE-TIME:20200513T130000Z
DTEND;VALUE=DATE-TIME:20200513T140000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/4
DESCRIPTION:Title: Sparse equidistribution of hyperbolic orbifolds\nby Peter Humph
ries (University College London) as part of International seminar on autom
orphic forms\n\n\nAbstract\nDuke\, Imamoḡlu\, and Tóth have recently co
nstructed a new geometric invariant\, a hyperbolic orbifold\, associated t
o each narrow ideal class of a real quadratic field. Furthermore\, they ha
ve shown that the projection of these hyperbolic orbifolds onto the modula
r surface equidistributes on average over a genus of the narrow class grou
p as the fundamental discriminan of the real quadratic field tends to infi
nity. We discuss a refinement of this result\, sparse equidistribution\, w
here one averages over smaller subgroups of the narrow class group: we con
nect this to cycle integrals of automorphic forms and subconvexity for Ran
kin-Selberg L-functions. This is joint work with Asbjørn Nordentoft.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Larry Rolen (Vanderbilt University)
DTSTART;VALUE=DATE-TIME:20200520T130000Z
DTEND;VALUE=DATE-TIME:20200520T140000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/5
DESCRIPTION:Title: Periodicities for Taylor coefficients of half-integral weight modul
ar forms\nby Larry Rolen (Vanderbilt University) as part of Internatio
nal seminar on automorphic forms\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivia Beckwith (University of Illinois)
DTSTART;VALUE=DATE-TIME:20200527T130000Z
DTEND;VALUE=DATE-TIME:20200527T140000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/6
DESCRIPTION:Title: Polyharmonic Maass forms and Hecke L-series\nby Olivia Beckwith
(University of Illinois) as part of International seminar on automorphic
forms\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Fretwell (Bristol University)
DTSTART;VALUE=DATE-TIME:20200603T130000Z
DTEND;VALUE=DATE-TIME:20200603T140000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/7
DESCRIPTION:Title: (Real Quadratic) Arthurian Tales\nby Dan Fretwell (Bristol Univ
ersity) as part of International seminar on automorphic forms\n\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Raum (Chalmers Technical University)
DTSTART;VALUE=DATE-TIME:20200610T130000Z
DTEND;VALUE=DATE-TIME:20200610T140000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/8
DESCRIPTION:Title: Divisibilities of Hurwitz class numbers\nby Martin Raum (Chalme
rs Technical University) as part of International seminar on automorphic f
orms\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sven Möller (Rutgers University)
DTSTART;VALUE=DATE-TIME:20200624T130000Z
DTEND;VALUE=DATE-TIME:20200624T140000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/9
DESCRIPTION:Title: Eisenstein Series\, Dimension Formulae and Generalised Deep Holes o
f the Leech Lattice Vertex Operator Algebra\nby Sven Möller (Rutgers
University) as part of International seminar on automorphic forms\n\nAbstr
act: TBA\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hao Zhang (Sorbonne Université)
DTSTART;VALUE=DATE-TIME:20200701T130000Z
DTEND;VALUE=DATE-TIME:20200701T140000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/10
DESCRIPTION:Title: Elliptic cocycle for $\\mathrm{GL}_N(\\mathbb{Z})$ and Hecke opera
tors\nby Hao Zhang (Sorbonne Université) as part of International sem
inar on automorphic forms\n\n\nAbstract\nA classical result of Eichler\, S
himura and Manin asserts that the map that assigns to a cusp form f its pe
riod polynomial r_f is a Hecke equivariant map. We propose a generalizatio
n of this result to a setting where r_f is replaced by a family of rati
onal function of N variables equipped with the action of GLN(Z). For this
purpose\, we develop a theory of Hecke operators for the elliptic cocycle
recently introduced by Charollois. In particular\, when f is an eigenfor
m\, the corresponding rational function is also an eigenvector respect to
Hecke operator for GLN. Finally\, we give some examples for Eisenstein se
ries and the Ramanujan Delta function.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shaul Zemel (Hebrew University of Jerusalem)
DTSTART;VALUE=DATE-TIME:20200708T130000Z
DTEND;VALUE=DATE-TIME:20200708T140000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/11
DESCRIPTION:Title: Shintani Lifts of Nearly Holomorphic Modular Forms\nby Shaul Z
emel (Hebrew University of Jerusalem) as part of International seminar on
automorphic forms\n\n\nAbstract\nThe Shintani lift is a classical construc
tion of modular\nforms of half-integral weight from modular forms of even
integral\nweight. Soon after its definition it was shown to be related to\
nintegration with respect to theta kernel. The development of the theory\n
of regularized integrals opens the question to what modular forms of\nhalf
-integral weight arise as regularized Shintani lifts of various\nkinds of
integral weight modular forms. We evaluate these lifts for the\ncase of ne
arly holomorphic modular forms\, which in particular shows\nthat when the
depth is smaller than the weight\, the Shintani lift is\nalso nearly holom
orphic. This evaluation requires the determination of\ncertain Fourier tra
nsforms\, which are interesting on their own right.\nThis is joint work wi
th Yingkun Li.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikos Diamantis (University of Nottingham)
DTSTART;VALUE=DATE-TIME:20200715T110000Z
DTEND;VALUE=DATE-TIME:20200715T120000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/12
DESCRIPTION:Title: Twisted L-functions and a conjecture by Mazur\, Rubin and Stein\nby Nikos Diamantis (University of Nottingham) as part of International
seminar on automorphic forms\n\n\nAbstract\nWe will discuss analytic prop
erties of L-functions twisted\nby an additive character. As an implication
\, a full proof of a\nconjecture of Mazur\, Rubin and Stein will be outlin
ed. This is a\nreport on joint work with J. Hoffstein\, M. Kiral and M. Le
e.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna von Pippich (TU Darmstadt)
DTSTART;VALUE=DATE-TIME:20200722T110000Z
DTEND;VALUE=DATE-TIME:20200722T120000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/13
DESCRIPTION:Title: An analytic class number type formula for the Selberg zeta functio
n\nby Anna von Pippich (TU Darmstadt) as part of International seminar
on automorphic forms\n\n\nAbstract\nIn this talk\, we report on an explic
it formula for the special value at $s=1$ of the derivative of the Selberg
zeta function for the modular group $\\Gamma=\\mathrm{PSL}_{2}(\\mathbb{Z
})$. The formula is a consequence of a generalization of the arithmetic Ri
emann--Roch theorem of Deligne and Gillet--Soul\\'e to the case of the tri
vial sheaf on $\\Gamma\\backslash \\mathbb{H}$\, equipped with the hyperbo
lic metric. This is joint work with Gerard Freixas.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haowu Wang (MPIM Bonn)
DTSTART;VALUE=DATE-TIME:20201014T140000Z
DTEND;VALUE=DATE-TIME:20201014T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/14
DESCRIPTION:Title: Root systems and free algebras of modular forms\nby Haowu Wang
(MPIM Bonn) as part of International seminar on automorphic forms\n\n\nAb
stract\nIn this talk we construct some new free algebras of modular forms.
For 25 orthogonal groups of signature $(2\,n)$ related to irreducible roo
t systems\, we prove that the graded algebras of modular forms on type IV
symmetric domains are freely generated. The proof is based on the theory o
f Weyl invariant Jacobi forms. As an application\, we show the modularity
of formal Fourier-Jacobi expansions for these groups. This is joint work w
ith Brandon Williams.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunqing Tang (CNRS & Université Paris-Sud)
DTSTART;VALUE=DATE-TIME:20201021T140000Z
DTEND;VALUE=DATE-TIME:20201021T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/15
DESCRIPTION:Title: Reductions of K3 surfaces via intersections on GSpin Shimura varie
ties\nby Yunqing Tang (CNRS & Université Paris-Sud) as part of Intern
ational seminar on automorphic forms\n\n\nAbstract\nFor a K3 surface X ove
r a number field with potentially good reduction everywhere\, we prove tha
t there are infinitely many primes modulo which the reduction of X has lar
ger geometric Picard rank than that of the generic fiber X. A similar stat
ement still holds true for ordinary K3 surfaces with potentially good redu
ction everywhere over global function fields. In this talk\, I will presen
t the proofs via the (arithmetic) intersection theory on good integral mod
els (and its special fibers) of GSpin Shimura varieties along with a poten
tial application to a certain case of the Hecke orbit conjecture of Chai a
nd Oort. This talk is based on joint work with Ananth Shankar\, Arul Shank
ar\, and Salim Tayou and with Davesh Maulik and Ananth Shankar.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandro Lägeler (ETH)
DTSTART;VALUE=DATE-TIME:20201028T150000Z
DTEND;VALUE=DATE-TIME:20201028T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/16
DESCRIPTION:Title: Continued fractions and Hardy sums\nby Alessandro Lägeler (ET
H) as part of International seminar on automorphic forms\n\n\nAbstract\nAs
was shown by Hickerson in the 70's\, the classical Dedekind sums $s(d\, c
)$ can be represented as sums over the coefficients of the continued fract
ion expansion of the rational $d / c$. Hardy sums\, the analogous integer-
valued objects arising in the transformation of the logarithms of theta fu
nctions under a subgroup of the modular group\, have been shown to satisfy
many properties which mirror the properties of the classical Dedekind sum
s. The representation as coefficients of continued fractions has\, however
\, been missing so far. In this talk\, I will argue how one can fill this
gap. As an application\, I will present a new proof for the fact that the
graph of the Hardy sums is dense in $\\mathbb{R} \\times \\mathbb{Z}$\, wh
ich was previously proved by Meyer.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Griffin (BYU)
DTSTART;VALUE=DATE-TIME:20201104T150000Z
DTEND;VALUE=DATE-TIME:20201104T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/17
DESCRIPTION:Title: Class pairings and elliptic curves\nby Michael Griffin (BYU) a
s part of International seminar on automorphic forms\n\n\nAbstract\nIdeal
class pairings map the rational points an elliptic curve $E/\\mathbb{Q}$ \
nto the ideal class groups $ \\mathrm{CL} (-D)$ of certain imaginary quadr
atic fields\, by means of explicit maps to $\\mathrm{SL}_2(\\mathbb{Z})$-e
quivalence classes of integral binary quadratic forms. Such pairings have
been studied by Buell\, Call\, Soleng and others.\n\nIn recent work with O
no and Tsai\, we used such pairings to study the class group and give expl
icit lowers bounds on the class numbers. In the specific case $E: \\ y^2=x
^3-a$ is a curve of rank $r\,$ and the twist $E_{-D}$ of the elliptic curv
e has a rational point with sufficiently small “$y$-height”\, we find
that \n$$\n h(-D) \\geq \\frac{1}{10}\\cdot \\frac{|E_{\\mathrm{tor}}(\\m
athbb Q)|}{\\sqrt{R_{\\mathbb Q}(E)}}\\cdot \\frac{\\pi^{\\frac{r}{2}}}{2
^{r}\\Gamma\\left (\\frac{r}{2}+1\\right)} \n\\cdot \\frac{\\log(D)^{\\fra
c{r}{2}}}{\\log \\log D}.\n$$\nWhenever the rank is at least $3$\, this re
presents an improvement to the classical lower bound of Goldfeld\, Gross a
nd Zagier.\n\nConversely\, using the classical upper bound on the class nu
mber $\\mathrm{CL}(-D)$ for some discriminant $-D$ represented by the equa
tion of the elliptic curve\, these pairing imply effective lower bounds fo
r the canonical heights $\\widehat{h}(P)$ of non-torsion points\n $P\\in E
(\\mathbb{Q}).$ \n \n\n\nI will also discuss a recent impressive REU proje
ct wherein the authors prove instances where the torsion subgroup of an el
liptic curve injects into the the class group $\\mathrm{CL}(-D)$. Using th
is result\, they are able to demonstrate several infinite families of clas
s groups with subgroups isomorphic to $\\mathbb Z^2\\times \\mathbb Z^2$\,
or whose orders are divisible by the primes $3\,5\,$ or $7$.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christina Röhrig (Uni Köln)
DTSTART;VALUE=DATE-TIME:20201111T150000Z
DTEND;VALUE=DATE-TIME:20201111T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/18
DESCRIPTION:Title: Siegel theta series for indefinite quadratic forms\nby Christi
na Röhrig (Uni Köln) as part of International seminar on automorphic for
ms\n\n\nAbstract\nDue to a result by Vigneras from 1977\, there is a quite
simple way to determine whether a certain theta series admits modular tra
nsformation properties. To be more specific\, she showed that solving a di
fferential equation of second order serves as a criterion for modularity.
We generalize this result for Siegel theta series of arbitrary genus $n$.
In order to do so\, we construct Siegel theta series for indefinite quadra
tic forms by considering functions which solve an $n\\times n$-system of p
artial differential equations. These functions do not only give examples o
f Siegel theta series\, but build a basis of the family of Schwartz functi
ons that generate series which transform like modular forms.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toshiki Matsusaka (Nagoya University)
DTSTART;VALUE=DATE-TIME:20201118T090000Z
DTEND;VALUE=DATE-TIME:20201118T100000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/19
DESCRIPTION:Title: Two analogues of the Rademacher symbol\nby Toshiki Matsusaka (
Nagoya University) as part of International seminar on automorphic forms\n
\n\nAbstract\nThe Rademacher symbol is a classical object related to the t
ransformation formula of the Dedekind eta function. In 2007\, Ghys showed
that the Rademacher symbol is equal to the linking number of a modular kno
t and the trefoil knot. In this talk\, we consider two analogues of Ghys'
theorem. One is a hyperbolic analogue of the Rademacher symbol introduced
by Duke-Imamoglu-Toth. As they showed\, the hyperbolic Rademacher symbol g
ives the linking number of two modular knots. I will give here some explic
it formulas for this symbol. The other is the Rademacher symbol on the tri
angle group. This symbol is defined from the transformation formula of the
logarithm of a cusp form on the triangle group\, and gives the linking nu
mber of a (triangle) modular knot and the (p\,q)-torus knot. The latter pa
rt is a joint work (in progress) with Jun Ueki (Tokyo Denki University).\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kathrin Maurischat (RWTH Aachen)
DTSTART;VALUE=DATE-TIME:20201125T150000Z
DTEND;VALUE=DATE-TIME:20201125T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/20
DESCRIPTION:Title: Explicit construction of Ramanujan bigraphs\nby Kathrin Mauris
chat (RWTH Aachen) as part of International seminar on automorphic forms\n
\n\nAbstract\nRamanujan bigraphs are known to arise as quotients of Bruhat
-Tits buildings for non-split unitary groups $U_3$. However\, these are on
ly implicitly defined. We show that one also obtains Ramanujan bigraphs in
special split cases\, and we give explicit constructions. The proof is ob
tained by inspecting the automorphic spectrum for temperedness\, and for t
he construction we introduce the notion of bi-Cayley graphs. This is joint
work with C. Ballantine\, S. Evra\, B. Feigon\, O. Parzanchevski.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriele Bogo (TU Darmstadt)
DTSTART;VALUE=DATE-TIME:20201202T150000Z
DTEND;VALUE=DATE-TIME:20201202T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/21
DESCRIPTION:Title: Extended modularity arising from the deformation of Riemann surfac
es\nby Gabriele Bogo (TU Darmstadt) as part of International seminar o
n automorphic forms\n\n\nAbstract\nModular forms appear in Poincaré's wor
k as solutions of certain differential equations related to the uniformiza
tion of Riemann surfaces. In the talk I will consider certain perturbation
s of these differential equations and prove that their solutions are given
by combinations of quasimodular forms and Eichler integrals. The relation
between these ODEs and the deformation theory of Riemann surfaces will be
discussed. By considering the monodromy representation of the perturbed O
DEs one can describe their solutions as components of vector-valued modula
r forms. This leads to the general study of functions arising as component
s of vector-valued modular forms attached to extensions of symmetric tenso
r representations (extended modular forms). If time permits I will discuss
some examples\, including certain functions arising in the study of scatt
ering amplitudes.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ariel Pacetti (Universidad de Cordoba)
DTSTART;VALUE=DATE-TIME:20201209T150000Z
DTEND;VALUE=DATE-TIME:20201209T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/22
DESCRIPTION:Title: $\\mathbb{Q}$-curves\, Hecke characters and some Diophantine equat
ions\nby Ariel Pacetti (Universidad de Cordoba) as part of Internation
al seminar on automorphic forms\n\n\nAbstract\nIn this talk we will invest
igate integral solutions of the equation $x^2+dy^2=z^p$\, for positive val
ues of \n$d$. To a solution\, one can attach a Frey curve\, which happens
to be a $\\mathbb{Q}$-curve. A result of Ribet implies that such a curve i
s related to a weight $2$ modular form in $S_2(Γ_0(N)\,\\varepsilon)$. Us
ing Hecke characters we will give a precise formula for $N$ and $\\varepsi
lon$ and prove non-existence of solutions in some cases. If time allows\,
we will show how a similar idea applies to the equation $x^2+dy^6=z^p$.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenia Rosu (University of Regensburg)
DTSTART;VALUE=DATE-TIME:20201216T150000Z
DTEND;VALUE=DATE-TIME:20201216T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/23
DESCRIPTION:Title: Twists of elliptic curves with CM\nby Eugenia Rosu (University
of Regensburg) as part of International seminar on automorphic forms\n\n\
nAbstract\nWe consider certain families of sextic twists of the elliptic c
urve\n $y^2=x^3+1$ that are not defined over $\\mathb
b{Q}$\, but over $\\mathbb{Q}(\\sqrt{-3})$. We compute a formula\n
that relates the value of the $L$-function $L(E_D\, 1)$ to t
he square of a trace of a\n modular function at a CM
point. Assuming the Birch and Swinnerton-Dyer conjecture\,\n
when the value above is non-zero\, we should recover the order of
the\n Tate-Shafarevich group\, and under certain cond
itions\, we show that the value is\n indeed a square.
\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johann Franke (University of Cologne)
DTSTART;VALUE=DATE-TIME:20210113T150000Z
DTEND;VALUE=DATE-TIME:20210113T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/24
DESCRIPTION:Title: Rational functions\, modular forms and cotangent sums\nby Joha
nn Franke (University of Cologne) as part of International seminar on auto
morphic forms\n\n\nAbstract\nThere are two elementary methods for construc
ting elliptic modular forms that dominate in literature. One of them uses
automorphic Poincare series and the other one theta functions. We start a
third elementary approach to modular forms using rational functions that h
ave certain properties regarding pole distribution and growth. One can pro
ve modularity with contour integration methods and Weil's converse theorem
\, without using the classical formalism of Eisenstein series and L-functi
ons. This approach to modular forms has several applications\, for example
to Eisenstein series\, L-functions and Eichler integrals. In this talk we
focus on some applications to cotangent sums.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jolanta Marzec (University of Kazimierz Wielki)
DTSTART;VALUE=DATE-TIME:20210120T150000Z
DTEND;VALUE=DATE-TIME:20210120T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/25
DESCRIPTION:Title: Algebraicity of special L-values attached to Jacobi forms of highe
r index\nby Jolanta Marzec (University of Kazimierz Wielki) as part of
International seminar on automorphic forms\n\n\nAbstract\nThe special val
ues of motivic L-functions have obtained a lot of attention due to their a
rithmetic consequences. In particular\, they are expected to be algebraic
up to certain factors. The Jacobi forms may also be related to a geometric
object (mixed motive)\, but their L-functions are much less understood. D
uring the talk we associate to Jacobi forms (of higher degree\, index and
level) a standard L-function and mention some of its analytic properties.
We will focus on the ingredients that come into a proof of algebraicity (u
p to certain factors) of its special values. The talk is based on joint wo
rk with Thanasis Bouganis: https://link.springer.com/article/10.1007/s0022
9-020-01243-w\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Oliver (University of Nottingham)
DTSTART;VALUE=DATE-TIME:20210127T150000Z
DTEND;VALUE=DATE-TIME:20210127T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/26
DESCRIPTION:Title: Twisting moduli\, meromorphy and zeros\nby Tom Oliver (Univers
ity of Nottingham) as part of International seminar on automorphic forms\n
\n\nAbstract\nThe zeros of automorphic L-functions are central to certain
famous conjectures in arithmetic. In this talk we will discuss the charact
erization of Dirichlet coefficients\, with a particular emphasis on applic
ations to vanishing. The primary focus will be GL(2)\, but we will also me
ntion higher rank groups - namely\, GL(m) and GL(n) such that m-n=2.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tiago Fonseca (University of Oxford)
DTSTART;VALUE=DATE-TIME:20210413T130000Z
DTEND;VALUE=DATE-TIME:20210413T140000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/27
DESCRIPTION:Title: The algebraic geometry of Fourier coefficients of Poincaré series
\nby Tiago Fonseca (University of Oxford) as part of International sem
inar on automorphic forms\n\n\nAbstract\nThe main goal of this talk is to
explain how to characterise Fourier coefficients of Poincaré series\, of
positive and negative index\, as certain algebro-geometric invariants atta
ched to the cohomology of modular curves\, namely their `single-valued per
iods'. This is achieved by a suitable geometric reformulation of classic r
esults in the theory of harmonic Maass forms. Some applications to algebra
icity questions will also be discussed.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Mono (University of Cologne)
DTSTART;VALUE=DATE-TIME:20210420T130000Z
DTEND;VALUE=DATE-TIME:20210420T140000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/28
DESCRIPTION:Title: On a twisted version of Zagier's $f_{k\, D}$ function\nby Andr
eas Mono (University of Cologne) as part of International seminar on autom
orphic forms\n\n\nAbstract\nWe present a twisting of Zagier's $f_{k\, D}$
function by a sign\nfunction and a genus character. Assuming even and posi
tive integral\nweight\, we inspect its obstruction to modularity\, and com
pute its Fourier\nexpansion. This involves twisted hyperbolic Eisenstein s
eries\, locally\nharmonic Maass forms\, and modular cycle integrals\, whic
h were studied by\nDuke\, Imamoglu\, Toth.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amanda Folsom (Amherst)
DTSTART;VALUE=DATE-TIME:20210427T130000Z
DTEND;VALUE=DATE-TIME:20210427T140000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/29
DESCRIPTION:Title: Eisenstein series\, cotangent-zeta sums\, and quantum modular form
s\nby Amanda Folsom (Amherst) as part of International seminar on auto
morphic forms\n\n\nAbstract\nQuantum modular forms\, defined in the ration
als\, transform like modular forms do on the upper half plane\, up to suit
ably analytic error functions. After introducing the subject\, in this tal
k\, we extend work of Bettin and Conrey and define twisted Eisenstein seri
es\, study their period functions\, and establish quantum modularity of ce
rtain cotangent-zeta sums. The Dedekind sum\, discussed by Zagier in his o
riginal paper on quantum modular forms\, is a motivating example.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Moni Kumari (Bar-Ilan University)
DTSTART;VALUE=DATE-TIME:20210504T130000Z
DTEND;VALUE=DATE-TIME:20210504T140000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/30
DESCRIPTION:Title: Non-vanishing of Hilbert-Poincaré series\nby Moni Kumari (Bar
-Ilan University) as part of International seminar on automorphic forms\n\
n\nAbstract\nModular forms play a prominent role in the classical as well
as in modern number theory. In the theory of modular forms\, there is an i
mportant class of functions called Poincaré series. These functions are v
ery mysterious and there are many unsolved problems about them. In particu
lar\, the vanishing or non-vanishing of such functions is still unknown in
full generality. In a special case\, the latter problem is equivalent to
the famous Lehmer's conjecture which is one of the classical open problems
in the theory. In this talk\, I will speak about when these functions are
non-zero for Hilbert modular forms\, a natural generalization of modular
forms for totally real number fields.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Mertens (University of Liverpool)
DTSTART;VALUE=DATE-TIME:20210511T130000Z
DTEND;VALUE=DATE-TIME:20210511T140000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/31
DESCRIPTION:Title: Weierstrass mock modular forms and vertex operator algebras\nb
y Michael Mertens (University of Liverpool) as part of International semin
ar on automorphic forms\n\n\nAbstract\nUsing techniques from the theory of
mock modular forms and harmonic Maass forms\, especially Weierstrass mock
modular forms\, we establish several dimension formulas for certain holom
orphic\, strongly rational vertex operator algebras\, complementing previo
us work by van Ekeren\, Möller\, and Scheithauer. As an application\, we
show that certain special values of the completed Weierstrass zeta functio
n are rational. This talk is based on joint work with Lea Beneish.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastián Herrero (Pontifical Catholic University of Valparaiso)
DTSTART;VALUE=DATE-TIME:20210518T130000Z
DTEND;VALUE=DATE-TIME:20210518T140000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/32
DESCRIPTION:Title: There are at most finitely many singular moduli that are S-units\nby Sebastián Herrero (Pontifical Catholic University of Valparaiso) a
s part of International seminar on automorphic forms\n\n\nAbstract\nIn 201
5 P. Habegger proved that there are at most finitely many singular moduli
that are algebraic units. In 2018 this result was made explicit by Y. Bilu
\, P. Habegger and L. Kühne\, by proving that there is actually no singul
ar modulus that is an algebraic unit. Later\, this result was extended by
Y. Li to values of modular polynomials at pairs of singular moduli. In thi
s talk I will report on joint work with R. Menares and J. Rivera-Letelier\
, where we prove that for any finite set of prime numbers S\, there are at
most finitely many singular moduli that are S-units. We use Habegger's or
iginal strategy together with the new ingredient that for every prime numb
er p\, singular moduli are p-adically disperse.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Rickards (McGill University)
DTSTART;VALUE=DATE-TIME:20210525T130000Z
DTEND;VALUE=DATE-TIME:20210525T140000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/33
DESCRIPTION:Title: Counting intersection numbers on Shimura curves\nby James Rick
ards (McGill University) as part of International seminar on automorphic f
orms\n\n\nAbstract\nIn this talk\, we give a formula for the total interse
ction number of optimal embeddings of a pair of real quadratic orders with
respect to an indefinite quaternion algebra over Q. We recall the classic
al Gross-Zagier formula for the factorization of the difference of singula
r moduli\, and note that our formula resembles an indefinite version of th
is factorization. This lends support to the work of Darmon-Vonk\, who conj
ecturally construct a real quadratic analogue of the difference of singula
r moduli.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuya Murakami (Tohoku University)
DTSTART;VALUE=DATE-TIME:20210601T130000Z
DTEND;VALUE=DATE-TIME:20210601T140000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/34
DESCRIPTION:Title: Extended-cycle integrals of the $j$-function for badly approximabl
e numbers\nby Yuya Murakami (Tohoku University) as part of Internation
al seminar on automorphic forms\n\n\nAbstract\nCycle integrals of the $j$-
function are expected to play a role in the real quadratic analog of singu
lar moduli. However\, it is not clear how one can consider cycle integrals
as a "continuous" function on real quadratic numbers. In this talk\, we e
xtend the definition of cycle integrals of the $j$-function from real quad
ratic numbers to badly approximable numbers to seek an appropriate continu
ity. We also give some explicit representations for extended-cycle integra
ls in some cases which can be considered as a partial result of continuity
of cycle integrals.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claire Burrin (ETH)
DTSTART;VALUE=DATE-TIME:20210608T130000Z
DTEND;VALUE=DATE-TIME:20210608T140000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/35
DESCRIPTION:Title: Rademacher symbols on Fuchsian groups\nby Claire Burrin (ETH)
as part of International seminar on automorphic forms\n\n\nAbstract\nThe R
ademacher symbol is algebraically expressed as a conjugacy class invariant
quasimorphism $\\mathrm{PSL}(2\,\\mathbb{Z}) \\to \\mathbb{Z}$. It was fi
rst studied in connection to Dedekind's eta-function\, but soon enough app
eared to be connected to class numbers of real quadratic fields\, the Hirz
ebruch signature theorem\, or linking numbers of knots. I will explain \n(
1) how\, using continued fractions\, Psi can be realized as the winding nu
mber for closed curves on the modular surface around the cusp\; \n(2) how\
, using Eisenstein series\, one can naturally construct a Rademacher symbo
l for any cusp of a general noncocompact Fuchsian group\; \n(3) and discus
s some new connections to arithmetic geometry.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chao Li (Columbia University)
DTSTART;VALUE=DATE-TIME:20210615T130000Z
DTEND;VALUE=DATE-TIME:20210615T140000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/36
DESCRIPTION:Title: Beilinson-Bloch conjecture and arithmetic inner product formula\nby Chao Li (Columbia University) as part of International seminar on au
tomorphic forms\n\n\nAbstract\nFor certain automorphic representations $\\
pi$ on unitary groups\, we show\nthat if $L(s\, \\pi)$ vanishes to order o
ne at the center $s=1/2$\, then the\nassociated $\\pi$-localized Chow grou
p of a unitary Shimura variety is\nnontrivial. This proves part of the Bei
linson-Bloch conjecture for unitary\nShimura varieties\, which generalizes
the BSD conjecture. Assuming Kudla's\nmodularity conjecture\, we further
prove the arithmetic inner product\nformula for $L'(1/2\, \\pi)$\, which g
eneralizes the Gross-Zagier formula. We\nwill motivate these conjectures a
nd discuss some aspects of the proof. We\nwill also mention recent extensi
ons applicable to symmetric power\nL-functions of elliptic curves. This is
joint work with Yifeng Liu.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:YoungJu Choie (Postech)
DTSTART;VALUE=DATE-TIME:20210622T080000Z
DTEND;VALUE=DATE-TIME:20210622T090000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/37
DESCRIPTION:Title: A generating function of periods of automorphic forms\nby Youn
gJu Choie (Postech) as part of International seminar on automorphic forms\
n\n\nAbstract\nA closed formula for the sum of all Hecke eigenforms on $\\
Gamma_0(N)$\, multiplied by their odd period polynomials in two variables\
, as a single product of Jacobi theta series for any squarefree level $N$
is known. When $N = 1$ this was result given by Zagier in 1991. We discuss
more general result regarding on this direction.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudia Alfes-Neumann (Universität Bielefeld)
DTSTART;VALUE=DATE-TIME:20210629T130000Z
DTEND;VALUE=DATE-TIME:20210629T140000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/38
DESCRIPTION:Title: Some theta liftings and applications\nby Claudia Alfes-Neumann
(Universität Bielefeld) as part of International seminar on automorphic
forms\n\n\nAbstract\nIn this talk we give an introduction to the study of
generating series of the traces\nof CM values and geodesic cycle integrals
of different modular functions. \nFirst we define modular forms and harmo
nic Maass forms. Then we briefly discuss the\ntheory of theta lifts that g
ives a conceptual framework for such generating series.\nWe end with some
applications of the theory.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lennart Gehrmann (Universität Duisburg-Essen)
DTSTART;VALUE=DATE-TIME:20210706T130000Z
DTEND;VALUE=DATE-TIME:20210706T140000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/39
DESCRIPTION:Title: Rigid meromorphic cocycles for orthogonal groups\nby Lennart G
ehrmann (Universität Duisburg-Essen) as part of International seminar on
automorphic forms\n\n\nAbstract\nI will talk about a generalization of Dar
mon and Vonk's notion of rigid meromorphic cocycles to the setting of orth
ogonal groups. After giving an overview over the general setting I will di
scuss the case of orthogonal groups attached to quadratic spaces of signat
ure (3\,1) in more detail. This is joint work with Henri Darmon and Mike L
ipnowski.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Bruinier (TU Darmstadt)
DTSTART;VALUE=DATE-TIME:20211026T130000Z
DTEND;VALUE=DATE-TIME:20211026T140000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/40
DESCRIPTION:Title: Arithmetic volumes of unitary Shimura varieties\nby Jan Bruini
er (TU Darmstadt) as part of International seminar on automorphic forms\n\
n\nAbstract\nThe geometric volume of a unitary Shimura variety can be defi
ned as the self-intersection number of the Hodge line bundle on it. It rep
resents an important invariant\, which can be explicitly computed in terms
of special values of Dirichlet L-functions. Analogously\, the arithmetic
volume is defined as the arithmetic self-intersection number of the Hodge
bundle\, equipped with the Petersson metric\, on an integral model of the
unitary Shimura variety. We show that such arithmetic volumes can be expre
ssed in terms of logarithmic derivatives of Dirichlet L-functions. This is
joint work with Ben Howard.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nils Matthes (Oxford)
DTSTART;VALUE=DATE-TIME:20211102T140000Z
DTEND;VALUE=DATE-TIME:20211102T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/41
DESCRIPTION:Title: Meromorphic modular forms and their iterated integrals\nby Nil
s Matthes (Oxford) as part of International seminar on automorphic forms\n
\n\nAbstract\nMeromorphic modular forms are generalizations of modular for
ms which are allowed to have poles. Part of the motivation for their study
comes from recent work of Li-Neururer\, Pasol-Zudilin\, and others\, whic
h shows that integrals of certain meromorphic modular forms have integer F
ourier coefficients -- an arithmetic phenomenon which does not seem to exi
st for holomorphic modular forms. In this talk we will study iterated inte
grals of meromorphic modular forms and describe some general algebraic ind
ependence results\, generalizing results of Pasol-Zudilin. If time permits
we will also mention an algebraic geometric interpretation of meromorphic
modular forms which generalizes the classical fact that modular forms are
sections of certain line bundles\, and describe the occurrence of iterate
d integrals of meromorphic modular forms in computations of Feynman integr
als in quantum field theory.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lindsay Dever (Bryn Mawr)
DTSTART;VALUE=DATE-TIME:20211109T140000Z
DTEND;VALUE=DATE-TIME:20211109T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/42
DESCRIPTION:Title: Distribution of Holonomy on Compact Hyperbolic 3-Manifolds\nby
Lindsay Dever (Bryn Mawr) as part of International seminar on automorphic
forms\n\n\nAbstract\nThe study of hyperbolic 3-manifolds draws deep conne
ctions between number theory\, geometry\, topology\, and quantum mechanics
. Specifically\, the closed geodesics on a manifold are intrinsically rela
ted to the eigenvalues of Maass forms via the Selberg trace formula and ar
e parametrized by their length and holonomy\, which describes the angle of
rotation by parallel transport along the geodesic. The trace formula for
spherical Maass forms can be used to prove the Prime Geodesic Theorem\, wh
ich provides an asymptotic count of geodesics up to a certain length. I wi
ll present an asymptotic count of geodesics (obtained via the non-spherica
l trace formula) by length and holonomy in prescribed intervals which are
allowed to shrink independently. This count implies effective equidistribu
tion of holonomy and substantially sharpens the result of Sarnak and Wakay
ama in the context of compact hyperbolic 3-manifolds. I will then discuss
new results regarding biases in the finer distribution of holonomy.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Kiefer (TU Darmstadt)
DTSTART;VALUE=DATE-TIME:20211116T140000Z
DTEND;VALUE=DATE-TIME:20211116T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/43
DESCRIPTION:Title: Orthogonal Eisenstein Series of Singular Weight\nby Paul Kiefe
r (TU Darmstadt) as part of International seminar on automorphic forms\n\n
\nAbstract\nWe will study (non-)holomorphic orthogonal Eisenstein series u
sing Borcherds' additive theta lift. It turns out that the lifts of vector
-valued non-holomorphic Eisenstein series with respect to the Weil represe
ntation of an even lattice are linear combinations of non-holomorphic orth
ogonal Eisenstein series. This yields their meromorphic continuation and f
unctional equation. Moreover we will determine the image of this construct
ion. Afterwards we evaluate the non-holomorphic orthogonal Eisenstein seri
es at certain special values to obtain holomorphic orthogonal Eisenstein s
eries and determine all holomorphic orthogonal modular forms that can be o
btained in this way.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Chen (IAS)
DTSTART;VALUE=DATE-TIME:20211123T140000Z
DTEND;VALUE=DATE-TIME:20211123T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/44
DESCRIPTION:Title: Connectivity of Hurwitz spaces and the conjecture of Bourgain\, Ga
mburd\, and Sarnak\nby William Chen (IAS) as part of International sem
inar on automorphic forms\n\n\nAbstract\nA Hurwitz space is a moduli space
of coverings of algebraic varieties. After fixing certain topological inv
ariants\, it is a classical problem to classify the connected components o
f the resulting moduli space. For example\, the connectivity of the space
of coverings of the projective line with simple branching and fixed degree
led to the first proof of the irreducibility of $M_g$. In this talk I wil
l explain a similar connectedness result\, this time in the context of SL(
2\,p)-covers of elliptic curves\, only branched above the origin. The conn
ectedness result comes from combining asymptotic results of Bourgain\, Gam
burd\, and Sarnak with a new combinatorial 'rigidity' coming from algebrai
c geometry. This rigidity result can also be viewed as a divisibility theo
rem on the cardinalities of Nielsen equivalence classes of generating pair
s of finite groups. The connectedness is a key piece of information that u
nlocks a number of applications\, including a conjecture of Bourgain\, Gam
burd and Sarnak on a strong approximation property of the Markoff equation
$x^2 + y^2 + z^2 - xyz$ = 0\, a noncongruence analog of Rademacher's conj
ecture of the genus of modular curves\, tamely ramified 3-point covers in
characteristic p\, and counting flat geodesics on a certain family of cong
ruence modular curves.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Riccardo Zuffetti (GU Frankfurt)
DTSTART;VALUE=DATE-TIME:20211130T140000Z
DTEND;VALUE=DATE-TIME:20211130T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/45
DESCRIPTION:Title: Cones of codimension two special cycles\nby Riccardo Zuffetti
(GU Frankfurt) as part of International seminar on automorphic forms\n\n\n
Abstract\nIn the literature\, there are several results on cones generated
by (effective\, ample\, nef...) divisors on (quasi-)projective varieties.
However\, a little is known on cones generated by cycles of codimension g
reater than one. Let X be an orthogonal Shimura variety. In this talk\, we
consider the cone $C_X$ generated by rational classes of codimension two
special cycles of X. We illustrate how to prove properties of $C_X$ by mea
ns of Fourier coefficients of Siegel modular forms.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manami Roy (Fordham)
DTSTART;VALUE=DATE-TIME:20211207T140000Z
DTEND;VALUE=DATE-TIME:20211207T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/46
DESCRIPTION:Title: Dimensions for the spaces of Siegel cusp forms of level 4\nby
Manami Roy (Fordham) as part of International seminar on automorphic forms
\n\n\nAbstract\nMany mathematicians have studied dimension and codimension
formulas for the spaces of Siegel cusp forms of degree 2. The dimensions
of the spaces of Siegel cusp forms of non-squarefree levels are mostly now
available in the literature. This talk will present new dimension formula
s of Siegel cusp forms of degree 2\, weight k\, and level 4 for three cong
ruence subgroups. One of these dimension formulas is obtained using the Sa
take compactification. However\, our primary method relies on counting a p
articular set of cuspidal automorphic representations of GSp(4) and explor
ing its connection to dimensions of spaces of Siegel cusp forms of degree
2. This work is joint with Ralf Schmidt and Shaoyun Yi.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrick Bieker (TU Darmstadt)
DTSTART;VALUE=DATE-TIME:20211214T140000Z
DTEND;VALUE=DATE-TIME:20211214T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/47
DESCRIPTION:Title: Modular units for orthogonal groups of signature (2\,2) and invari
ants for the Weil representation\nby Patrick Bieker (TU Darmstadt) as
part of International seminar on automorphic forms\n\n\nAbstract\nWe const
ruct modular units for certain orthogonal groups in signature (2\, 2) usin
g Borcherds products. As an input to the construction we show that the spa
ce of invariants for the Weil representation for discriminant groups which
contain self-dual isotropic subgroups is spanned by the characteristic fu
nctions of the self-dual isotropic subgroups. This allows us to determine
all modular units arising as Borcherds products in examples.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Garcia (UCL)
DTSTART;VALUE=DATE-TIME:20220111T130000Z
DTEND;VALUE=DATE-TIME:20220111T140000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/48
DESCRIPTION:Title: Eisenstein cocycles and values of L-functions\nby Luis Garcia
(UCL) as part of International seminar on automorphic forms\n\n\nAbstract\
nThere are several recent constructions by many authors of Eisenstein cocy
cles of arithmetic groups. I will discuss a point of view on these constru
ctions using equivariant cohomology and equivariant differential forms. Th
e resulting objects behave like theta kernels relating the homology of ari
thmetic groups to algebraic objects. As an application\, I will explain th
e proof of some conjectures of Sczech and Colmez on critical values of Hec
ke L-functions. The talk is based on joint work with Nicolas Bergeron and
Pierre Charollois.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Márton Erdélyi (Budapest University of Technology and Economics)
DTSTART;VALUE=DATE-TIME:20220125T140000Z
DTEND;VALUE=DATE-TIME:20220125T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/49
DESCRIPTION:Title: Matrix Kloosterman sums\nby Márton Erdélyi (Budapest Univers
ity of Technology and Economics) as part of International seminar on autom
orphic forms\n\n\nAbstract\nWe study exponential sums arosing in the work
of Lee and Marklof about the horocyclic flow on the group $GL_n$. In many
cases this sum can be expressed with the help of classical Kloosterman sum
s. We give effective bounds using the very basics of cohomological methods
and get a nice illustration of the general purity theorem of Fouvry and K
atz. Joint work with Árpád Tóth.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isabella Negrini (McGill)
DTSTART;VALUE=DATE-TIME:20220118T140000Z
DTEND;VALUE=DATE-TIME:20220118T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/50
DESCRIPTION:Title: A Shimura-Shintani correspondence for rigid analytic cocycles\
nby Isabella Negrini (McGill) as part of International seminar on automorp
hic forms\n\n\nAbstract\nIn their paper Singular moduli for real quadratic
fields: a rigid analytic approach\,\nDarmon and Vonk introduced rigid mer
omorphic cocycles\, i.e. elements of\n$H^1(\\mathrm{SL}_2(\\mathbb{Z}[1/p]
)\, M^\\times)$ where $M^\\times$ is the multiplicative group of rigid mer
omorphic functions on the p-adic upper-half plane. Their values at RM poin
ts belong to narrow ring class fields of real quadratic fiends and behave
analogously to CM values of\nmodular functions on $\\mathrm{SL}_2(\\mathbb
{Z})\\backslash\\mathbf{H}$. In this talk I will present some progress to
wards developing a Shimura-Shintani correspondence in this setting.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vesselin Dimitrov (Toronto)
DTSTART;VALUE=DATE-TIME:20220201T140000Z
DTEND;VALUE=DATE-TIME:20220201T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/51
DESCRIPTION:Title: The unbounded denominators conjecture\nby Vesselin Dimitrov (T
oronto) as part of International seminar on automorphic forms\n\n\nAbstrac
t\nI will explain the ideas of the proof of the following recent theorem\,
joint with Frank Calegari and Yunqing Tang: A modular form for a finite i
ndex subgroup of $SL_2(\\mathbb{Z})$ has a $q$-expansion\nwith bounded den
ominators if and only if it is a modular form for a congruence subgroup. I
will also discuss some related open problems such as a hypothetical $SL_2
(\\mathbb{F}_q[t])$ analog of the theorem.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weibo Fu (Princeton)
DTSTART;VALUE=DATE-TIME:20220426T140000Z
DTEND;VALUE=DATE-TIME:20220426T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/52
DESCRIPTION:Title: Growth of Bianchi modular forms\nby Weibo Fu (Princeton) as pa
rt of International seminar on automorphic forms\n\n\nAbstract\nIn this ta
lk\, I will establish a sharp bound on the growth of cuspidal Bianchi modu
lar forms. By the Eichler-Shimura isomorphism\, we actually give a sharp b
ound of the second cohomology of a hyperbolic three manifold (Bianchi mani
fold) with local system arising from the representation $Sym^k \\otimes \\
overline{Sym^k}$ of $SL_2(\\mathbb{C})$. I will explain how a p-adic algeb
raic method is used for deriving our result.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brandon Williams (RWTH Aachen)
DTSTART;VALUE=DATE-TIME:20220503T140000Z
DTEND;VALUE=DATE-TIME:20220503T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/53
DESCRIPTION:Title: Free algebras of modular forms on ball quotients\nby Brandon W
illiams (RWTH Aachen) as part of International seminar on automorphic form
s\n\n\nAbstract\nWe study algebras of modular forms on unitary groups of s
ignature $(n\, 1)$. We give a\nsufficient criterion for the ring of unitar
y modular forms to be freely generated in\nterms of the divisor of a modul
ar Jacobian determinant. We use this to prove that a\nnumber of rings of u
nitary modular forms associated to Hermitian lattices over the\nrings of i
ntegers of $\\mathbb{Q}(\\sqrt{ d})$ for $d = −1\, −2\, −3$ are poly
nomial algebras without\nrelations. This is joint work with Haowu Wang.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaclyn Lang (Temple University)
DTSTART;VALUE=DATE-TIME:20220510T140000Z
DTEND;VALUE=DATE-TIME:20220510T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/54
DESCRIPTION:Title: A modular construction of unramified p-extensions of $\\mathbb{Q}(
N^{1/p})$\nby Jaclyn Lang (Temple University) as part of International
seminar on automorphic forms\n\n\nAbstract\nIn his 1976 proof of the conv
erse of Herbrand's theorem\, Ribet used Eisenstein-cuspidal congruences to
produce unramified degree-p extensions of the p-th cyclotomic field when
p is an odd prime. After reviewing Ribet's strategy\, we will discuss rece
nt work with Preston Wake in which we apply similar techniques to produce
unramified degree-p extensions of $\\mathbb{Q}(N^{1/p})$ when N is a prime
that is congruent to -1 mod p. This answers a question posed on Frank Cal
egari's blog.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sudhir Pujahari (NISER)
DTSTART;VALUE=DATE-TIME:20220517T070000Z
DTEND;VALUE=DATE-TIME:20220517T080000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/55
DESCRIPTION:Title: Sato-Tate conjecture in arithmetic progressions for certain famili
es of elliptic curves\nby Sudhir Pujahari (NISER) as part of Internati
onal seminar on automorphic forms\n\n\nAbstract\nIn this talk we will stud
y moments of the trace of Frobenius of elliptic curves if the trace is res
tricted to a fixed arithmetic progression. In conclusion\, we will obtain
the Sato-Tate distribution for the trace of certain families of Elliptic c
urves. As a special case we will recover a result of Birch proving Sato-Ta
te distribution for certain family of elliptic curves. Moreover\, we will
see that these results follow from asymptotic formulas relating sums and m
oments of Hurwitz class numbers where the sums are restricted to certain a
rithmetic progressions. This is a joint work with Kathrin Bringmann and Be
n Kane.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arvind Kumar (IIT Jamu)
DTSTART;VALUE=DATE-TIME:20220607T070000Z
DTEND;VALUE=DATE-TIME:20220607T080000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/57
DESCRIPTION:Title: Distinguishing Siegel eigenforms from Hecke eigenvalues\nby Ar
vind Kumar (IIT Jamu) as part of International seminar on automorphic form
s\n\n\nAbstract\nDetermination of modular forms is one of the fundamental
and\ninteresting problems in number theory. It is known that if the Hecke\
neigenvalues of two newforms agree for all but finitely many primes\, then
\nboth the forms are the same. In other words\, the set of Hecke eigenvalu
es\nat primes determines the newform uniquely and this result is known as
the\nmultiplicity one theorem. In the case of Siegel cuspidal eigenforms o
f\ndegree two\, the multiplicity one theorem has been proved only recently
in\n2018 by Schmidt. In this talk\, we refine the result of Schmidt by sh
owing\nthat if the Hecke eigenvalues of two Siegel eigenforms of level 1 a
gree at\na set of primes of positive density\, then the eigenforms are the
same (up\nto a constant). We also distinguish Siegel eigenforms from the
signs of\ntheir Hecke eigenvalues. The main ingredient to prove these resu
lts are\nGalois representations attached to Siegel eigenforms\, the Chebot
arev\ndensity theorem and some analytic properties of associated L-functio
ns.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Nelson (IAS)
DTSTART;VALUE=DATE-TIME:20220614T140000Z
DTEND;VALUE=DATE-TIME:20220614T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/58
DESCRIPTION:Title: The orbit method\, microlocal analysis and applications to L-funct
ions\nby Paul Nelson (IAS) as part of International seminar on automor
phic forms\n\n\nAbstract\nL-functions are generalizations of the Riemann z
eta function. Their analytic properties control the asymptotic behavior of
prime numbers in various refined senses. Conjecturally\, every L-function
is a "standard L-function" arising from an automorphic form. A problem of
recurring interest\, with widespread applications\, has been to establish
nontrivial bounds for L-functions. I will survey some recent results addr
essing this problem. The proofs involve the analysis of integrals of autom
orphic forms\, approached through the lens of representation theory. I wil
l emphasize the role played by the orbit method\, developed in a quantitat
ive form along the lines of microlocal analysis. The results/methods to be
surveyed are the subject of the following papers/preprints: \n\nhttps://a
rxiv.org/abs/1805.07750 \n\nhttps://arxiv.org/abs/2012.02187 \n\nhttps://a
rxiv.org/abs/2109.15230\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Manning (MPIM Bonn)
DTSTART;VALUE=DATE-TIME:20220621T140000Z
DTEND;VALUE=DATE-TIME:20220621T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/59
DESCRIPTION:Title: The Wiles-Lenstra-Diamond numerical criterion over imaginary quadr
atic fields\nby Jeff Manning (MPIM Bonn) as part of International semi
nar on automorphic forms\n\n\nAbstract\nWiles' modularity lifting theorem
was the central argument in his proof of modularity of (semistable) ellipt
ic curves over $\\mathbb{Q}$\, and hence of Fermat's Last Theorem. His pro
of relied on two key components: his "patching" argument (developed in col
laboration with Taylor) and his numerical isomorphism criterion. In the ti
me since Wiles' proof\, the patching argument has been generalized extensi
vely to prove a wide variety of modularity lifting results. In particular
Calegari and Geraghty have found a way to generalize it to prove potential
modularity of elliptic curves over imaginary quadratic fields (contingent
on some standard conjectures). The numerical criterion on the other hand
has proved far more difficult to generalize\, although in situations where
it can be used it can prove stronger results than what can be proven pure
ly via patching. In this talk I will present joint work with Srikanth Iyen
gar and Chandrashekhar Khare which proves a generalization of the numerica
l criterion to the context considered by Calegari and Geraghty (and contin
gent on the same conjectures). This allows us to prove integral "R=T" theo
rems at non-minimal levels over imaginary quadratic fields\, which are ina
ccessible by Calegari and Geraghty's method. The results provide new evide
nce in favor of a torsion analog of the classical Langlands correspondence
.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yichao Zhang (Harbin Institute of Technology)
DTSTART;VALUE=DATE-TIME:20220628T140000Z
DTEND;VALUE=DATE-TIME:20220628T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/60
DESCRIPTION:Title: Rationality of the Petersson Inner Product of Generally Twisted Co
hen Kernels\nby Yichao Zhang (Harbin Institute of Technology) as part
of International seminar on automorphic forms\n\n\nAbstract\nKohnen and Za
gier showed that the Petersson inner product of Cohen kernels at integers
of opposite parity is rational in the critical strip. Later Diamantis and
O'Sullivan generalized such rationality to the Petersson inner product wit
h one of the two Cohen kernels acted by a Hecke operator. In this talk\, u
sing Diamantis and O'Sullivan's twisted double Eisenstein series\, we twis
t one of the two Cohen kernels by a general rational number and prove a si
milar rationality result. This is a joint work with Yuanyi You.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikos Diamantis (University of Nottingham)
DTSTART;VALUE=DATE-TIME:20220531T140000Z
DTEND;VALUE=DATE-TIME:20220531T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/61
DESCRIPTION:Title: L-series associated with harmonic Maass forms and their values
\nby Nikos Diamantis (University of Nottingham) as part of International s
eminar on automorphic forms\n\n\nAbstract\nWe define a L-series for harmon
ic Maass forms and discuss their functional equations. A converse theorem
for these L-series is given. As an application\, we interpret as proper va
lues of our L-functions certain important quantities that arose in works b
y Bruinier-Funke-Imamoglu and Alfes-Schwagenscheidt\, and which they had p
hilosophically viewed as "central L-values". This is joint work with M. Le
e\, W. Raji and L. Rolen.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel Müller (TU Darmstadt)
DTSTART;VALUE=DATE-TIME:20221101T150000Z
DTEND;VALUE=DATE-TIME:20221101T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/62
DESCRIPTION:Title: The invariants of the Weil representation of $\\mathrm{SL}_2(\\mat
hbb{Z})$\nby Manuel Müller (TU Darmstadt) as part of International se
minar on automorphic forms\n\n\nAbstract\nThe transformation behaviour of
the vector valued theta function of a positive definite even lattice under
the metaplectic group $\\mathrm{Mp}_2(\\mathbb{Z})$ is described by the W
eil representation. This representation plays an important role in the the
ory of automorphic forms. We show that its invariants are induced from 5 f
undamental invariants.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Congling Qiu (Yale University)
DTSTART;VALUE=DATE-TIME:20221115T150000Z
DTEND;VALUE=DATE-TIME:20221115T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/64
DESCRIPTION:Title: Modularity and automorphy of cycles on Shimura varieties\nby C
ongling Qiu (Yale University) as part of International seminar on automorp
hic forms\n\n\nAbstract\nAlgebraic cycles are central objects in algebraic
/arithmetic geometry and problems around them are very difficult. For Shim
ura varieties modularity of generating series with coefficients being alge
braic cycles has been proved useful in the of study of algebraic cycles. A
closely related problem is the automorphy of representations spanned by a
lgebraic cycles. I will discuss the history of these problems some progres
s and applications.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eran Assaf (Dartmouth College)
DTSTART;VALUE=DATE-TIME:20221122T150000Z
DTEND;VALUE=DATE-TIME:20221122T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/65
DESCRIPTION:Title: Orthogonal modular forms\, Siegel modular forms and Eisenstein con
gruences\nby Eran Assaf (Dartmouth College) as part of International s
eminar on automorphic forms\n\n\nAbstract\nThe theta correspondence betwee
n the orthogonal group and the symplectic group provides a cornerstone for
studying Siegel modular forms via orthogonal modular forms. \nIn this wor
k\, we make this correspondence completely explicit\, with precise level s
tructure for low to moderate even rank and nontrivial discriminant.\nGuide
d by computational discoveries\, we prove congruences between eigenvalues
of classical modular forms and eigenvalues of genuine Siegel modular forms
\, obtain formulas for the number of neighbors in terms of eigenvalues of
classical modular forms\, and formulate some conjectures that arise natura
lly from the data.\nThis is joint work with Dan Fretwell\, Colin Ingalls\,
Adam Logan\, Spencer Secord\, and John Voight\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shouhei Ma (Tokyo Institute of Technology)
DTSTART;VALUE=DATE-TIME:20221129T080000Z
DTEND;VALUE=DATE-TIME:20221129T090000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/66
DESCRIPTION:Title: Vector-valued orthogonal modular forms\nby Shouhei Ma (Tokyo I
nstitute of Technology) as part of International seminar on automorphic fo
rms\n\n\nAbstract\nI will talk about the theory of vector-valued modular f
orms on domains of type IV\, with some emphasis on its algebro-geometric a
spects.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bingrong Huang (Shandong University)
DTSTART;VALUE=DATE-TIME:20221206T080000Z
DTEND;VALUE=DATE-TIME:20221206T090000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/67
DESCRIPTION:Title: Arithmetic Quantum Chaos and L-functions\nby Bingrong Huang (S
handong University) as part of International seminar on automorphic forms\
n\n\nAbstract\nIn this talk\, I will introduce some aspects of the theory
of arithmetic quantum chaos\, focusing on the quantum unique ergodicity th
eorem for automorphic forms on the modular surface. Then I will give some
results on effective decorrelation of Hecke eigenforms and the cubic momen
t of Hecke-Maass cusp forms. The proofs are based on the analytic theory o
f L-functions.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Dunn (Caltech)
DTSTART;VALUE=DATE-TIME:20221213T150000Z
DTEND;VALUE=DATE-TIME:20221213T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/68
DESCRIPTION:Title: Bias in cubic Gauss sums: Patterson's conjecture\nby Alex Dunn
(Caltech) as part of International seminar on automorphic forms\n\n\nAbst
ract\nWe prove\, in this joint work with Maksym Radziwill\, a 1978 conject
ure of S. Patterson (conditional on the Generalised Riemann hypothesis)\nc
oncerning the bias of cubic Gauss sums.\nThis explains a well-known numeri
cal bias in the distribution of cubic Gauss sums first observed by Kummer
in 1846.\n\nOne important byproduct of our proof is that we show\nHeath-Br
own's cubic large sieve is sharp under GRH. \nThis disproves the popular b
elief that the cubic large sieve can be\nimproved.\n\n An important ingred
ient in our proof is a dispersion estimate for cubic\n Gauss sums. It can
be interpreted as a cubic large sieve with correction by a non-trivial asy
mptotic main term.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Morten Risager (University of Copenhagen)
DTSTART;VALUE=DATE-TIME:20221220T150000Z
DTEND;VALUE=DATE-TIME:20221220T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/69
DESCRIPTION:Title: Distributions of Manin's iterated integrals\nby Morten Risager
(University of Copenhagen) as part of International seminar on automorphi
c forms\n\n\nAbstract\nWe recall the definition of Manin's iterated integr
als of a given length. We then explain how these generalise modular symbol
s and certain aspects of the theory of multiple zeta-values. In length one
and two we determine the limiting distribution of these iterated integral
s. Maybe surprisingly\, even if we can compute all moments also in higher
length we cannot in general determine a distribution for length three or h
igher. This is joint work with Y. Petridis and with N. Matthes.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yota Maeda (Kyoto University)
DTSTART;VALUE=DATE-TIME:20230110T080000Z
DTEND;VALUE=DATE-TIME:20230110T090000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/70
DESCRIPTION:Title: Deligne-Mostow theory and beyond\nby Yota Maeda (Kyoto Univers
ity) as part of International seminar on automorphic forms\n\n\nAbstract\n
Ball quotients have been studied extensively in algebraic geometry from th
e aspect of moduli spaces\, and in number theory with emphasis on the rela
tion with modular forms. The Deligne-Mostow theory gives them moduli inter
pretation through the isomorphism between the Baily-Borel compactification
s of them and certain GIT quotients.\nIn this talk\, I will discuss whethe
r the isomorphisms given by the Deligne-Mostow theory are lifted to other
compactifications from the viewpoint of modular forms and pursue ''better'
' compactifications. Moreover\, I will also clarify their connection with
the recent development in the minimal model program. This work is based on
a joint work with Klaus Hulek (Leibniz University Hannover)\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soumya Das (Indian Institute of Science\, Bangalore)
DTSTART;VALUE=DATE-TIME:20230117T080000Z
DTEND;VALUE=DATE-TIME:20230117T090000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/71
DESCRIPTION:Title: Sup-norms of automorphic forms on average\nby Soumya Das (Indi
an Institute of Science\, Bangalore) as part of International seminar on a
utomorphic forms\n\n\nAbstract\nBounding the sup-norms of automorphic form
s has been a very active area in research in recent times. Whereas lot of
nice results are known for small rank groups\, like $\\operatorname{GL}(2)
$\, almost nothing is known for\, say\, Siegel or Jacobi modular forms of
higher degrees. In this talk we aim to discuss some conjectures and result
s in this area. We use either the theory of Poincare series or averages of
central values of $L$-functions to tackle this problem. Our methods have
the benefit of having a hands-on approach and fits into many situations.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Riccardo Salvati Manni (Sapienza University of Rome)
DTSTART;VALUE=DATE-TIME:20230124T150000Z
DTEND;VALUE=DATE-TIME:20230124T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/72
DESCRIPTION:Title: Slope of Siegel modular forms: some geometric applications\nb
y Riccardo Salvati Manni (Sapienza University of Rome) as part of Internat
ional seminar on automorphic forms\n\n\nAbstract\nWe study the slope of mo
dular forms on the Siegel space. We will recover known divisors of minimal
slope for $g\\leq5$ and we discuss the Kodaira dimension of the moduli sp
ace of principally polarized abelian varieties $A_g$ (and eventually of th
e generalized Kuga's varieties). Moreover we illustrate the cone of moving
divisors on $A_g$. Partly motivated by the generalized Rankin-Cohen brack
et\, we construct a non-linear holomorphic differential operator that send
s Siegel modular forms to Siegel cusp forms\, and we apply it to produce n
ew modular forms. Our construction recovers the known divisors of minimal
moving slope on $A_g$ for $g\\leq5$.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandro Bettin (University of Genova)
DTSTART;VALUE=DATE-TIME:20230131T150000Z
DTEND;VALUE=DATE-TIME:20230131T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/73
DESCRIPTION:Title: Continuity and value distribution of quantum modular forms\nby
Sandro Bettin (University of Genova) as part of International seminar on
automorphic forms\n\n\nAbstract\nQuantum modular forms are functions f def
ined on the rationals whose period functions\, such as psi(x):= f(x) - x^(
-k) f(-1/x) (for level 1)\, satisfy some continuity properties. In the cas
e of k=0\, f can be interpreted as a Birkhoff sums associated with the Gau
ss map. In particular\, under mild hypotheses on G\, one can show converge
nce to a stable law. If k is non-zero\, the situation is rather different
and we can show that mild conditions on psi imply that f itself has to exh
ibit some continuity property. Finally\, we discuss the convergence in dis
tribution also in this case. This is a joint work with Sary Drappeau.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulia Cesana (University of Cologne)
DTSTART;VALUE=DATE-TIME:20230207T150000Z
DTEND;VALUE=DATE-TIME:20230207T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/74
DESCRIPTION:Title: Asymptotic equidistribution for partition statistics and topologic
al invariants\nby Giulia Cesana (University of Cologne) as part of Int
ernational seminar on automorphic forms\n\n\nAbstract\nThroughout mathemat
ics\, the equidistribution properties of certain objects are a central the
me studied by many authors. In my talk I am going to speak about a joint p
roject with William Craig and Joshua Males\, where we provide a general fr
amework for proving asymptotic equidistribution\, convexity\, and log-conc
avity of coefficients of generating functions on arithmetic progressions.\
n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abhishek Saha (Queen Mary University (London))
DTSTART;VALUE=DATE-TIME:20230502T140000Z
DTEND;VALUE=DATE-TIME:20230502T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/75
DESCRIPTION:Title: Mass equidistribution for Saito-Kurokawa lifts\nby Abhishek Sa
ha (Queen Mary University (London)) as part of International seminar on au
tomorphic forms\n\n\nAbstract\nThe Quantum Unique Ergodicity (QUE) conject
ure was proved in the classical case for Maass forms of full level in the
eigenvalue aspect by Lindenstrauss and Soundararajan\, and for holomorphic
forms in the weight aspect by Holowinsky and Soundararajan. In this talk
\, I will discuss some joint work with Jesse Jaasaari and Steve Lester on
the analogue of the QUE conjecture in the weight aspect for holomorphic Si
egel cusp forms of degree 2 and full level. Assuming the Generalized Riema
nn Hypothesis (GRH) we establish QUE for Saito–Kurokawa lifts as the wei
ght tends to infinity. As an application\, we prove the equidistribution o
f zero divisors of Saito-Kurokawa lifts.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabrizio Andreatta (University of Milan)
DTSTART;VALUE=DATE-TIME:20230516T140000Z
DTEND;VALUE=DATE-TIME:20230516T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/76
DESCRIPTION:Title: Endoscopy for GSp(4) and rational points on elliptic curves\nb
y Fabrizio Andreatta (University of Milan) as part of International semina
r on automorphic forms\n\n\nAbstract\nI report on a joint project with M.
Bertolini \, M.A. Seveso and R. Venerucci\, aimed at studying the equivari
ant BSD conjecture for rational elliptic curves twisted by certain self-du
al 4-dimensional Artin representations in situations of odd analytic rank.
We use the endoscopy for GSp(4) to construct Selmer classes related to th
e relevant (complex and p-adic) L-values via explicit reciprocity laws.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oguz Gezmis (Heidelberg University)
DTSTART;VALUE=DATE-TIME:20230425T140000Z
DTEND;VALUE=DATE-TIME:20230425T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/77
DESCRIPTION:Title: Almost holomorphic Drinfeld modular forms\nby Oguz Gezmis (Hei
delberg University) as part of International seminar on automorphic forms\
n\n\nAbstract\nIn his series of papers from 1970s\, Shimura analyzed a non
-holomorphic operator\, nowadays called the Maass-Shimura operator\, and l
ater extensively studied almost holomorphic modular forms. He also discove
red their role on constructing class fields as well as the connection with
periods of CM elliptic curves. In this talk\, our first goal is to introd
uce their positive characteristic counterpart\, almost holomorphic Drinfel
d modular forms. We further relate them to Drinfeld quasi-modular forms wh
ich leads us to generalize the work of Bosser and Pellarin to a certain ex
tend. Moreover\, we introduce the Maass-Shimura operator $\\delta_k$ in ou
r setting for any nonnegative integer k and investigate the relation betwe
en the periods of CM Drinfeld modules and the values at CM points of arith
metic Drinfeld modular forms under the image of $\\delta_k$. If time per
mits\, we also reveal how to construct class fields by using such values.
This is a joint work with Yen-Tsung Chen.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sachi Hashimoto (MPI Leipzig)
DTSTART;VALUE=DATE-TIME:20230509T140000Z
DTEND;VALUE=DATE-TIME:20230509T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/78
DESCRIPTION:Title: p-adic Gross-Zagier and rational points on modular curves\nby
Sachi Hashimoto (MPI Leipzig) as part of International seminar on automorp
hic forms\n\n\nAbstract\nFaltings' theorem states that there are finitely
many rational points on a nice projective curve defined over the rationals
of genus at least 2. The quadratic Chabauty method makes explicit some ca
ses of Faltings' theorem. Quadratic Chabauty has recent notable success in
determining the rational points of some modular curves. In this talk\, I
will explain how we can leverage information from p-adic Gross-Zagier form
ulas to give a new quadratic Chabauty method for certain modular curves. G
ross-Zagier formulas relate analytic quantities (special values of p-adic
L-functions) to invariants of algebraic cycles (the p-adic height and loga
rithm of Heegner points). By using p-adic Gross-Zagier formulas\, this new
quadratic Chabauty method makes essential use of modular forms to determi
ne rational points.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Salim Tayou (Harvard)
DTSTART;VALUE=DATE-TIME:20230620T140000Z
DTEND;VALUE=DATE-TIME:20230620T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/79
DESCRIPTION:Title: Mixed mock modularity of special divisors\nby Salim Tayou (Har
vard) as part of International seminar on automorphic forms\n\n\nAbstract\
nKudla-Millson and Borcherds have proved some time ago that the generating
series of special divisors in orthogonal Shimura varieties are modular fo
rms. In this talk\, I will explain an extension of these results to toroid
al compactifications where we prove that the generating series is a mixed
mock modular form. More precisely\, we find an explicit completion using t
heta series associated to rays in the cone decomposition. The proof relies
on intersection theory at the boundary of the Shimura variety. This recov
ers and refines recent results of Bruinier and Zemel. The result of this t
alk are joint work with Philip Engel and François Greer.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toshiki Matsusaka (Kyushu)
DTSTART;VALUE=DATE-TIME:20230530T070000Z
DTEND;VALUE=DATE-TIME:20230530T080000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/80
DESCRIPTION:Title: Discontinuity property of a certain Habiro series at roots of unit
y\nby Toshiki Matsusaka (Kyushu) as part of International seminar on a
utomorphic forms\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ezra Waxman (Haifa)
DTSTART;VALUE=DATE-TIME:20230606T140000Z
DTEND;VALUE=DATE-TIME:20230606T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/81
DESCRIPTION:Title: Artin's primitive root conjecture: classically and over Fq[T]\
nby Ezra Waxman (Haifa) as part of International seminar on automorphic fo
rms\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nina Zubrilina (Princeton)
DTSTART;VALUE=DATE-TIME:20230627T140000Z
DTEND;VALUE=DATE-TIME:20230627T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/82
DESCRIPTION:Title: Root Number Correlation Bias of Fourier Coefficients of Modular Fo
rms\nby Nina Zubrilina (Princeton) as part of International seminar on
automorphic forms\n\n\nAbstract\nIn a recent machine learning based study
\, He\, Lee\, Oliver\, and Pozdnyakov observed a striking\noscillating pat
tern in the average value of the P-th Frobenius trace of elliptic curves o
f\nprescribed rank and conductor in an interval range. Sutherland discover
ed that this bias\nextends to Dirichlet coefficients of a much broader cla
ss of arithmetic L-functions when\nsplit by root number. In my talk\, I wi
ll discuss this root number correlation bias when\nthe average is taken ov
er all weight 2 modular newforms. I will point to a source of this\nphenom
enon in this case and compute the correlation function exactly.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sander Zwegers (University of Cologne)
DTSTART;VALUE=DATE-TIME:20230613T070000Z
DTEND;VALUE=DATE-TIME:20230613T080000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/83
DESCRIPTION:Title: Indefinite Theta Functions: something old\, something new\nby
Sander Zwegers (University of Cologne) as part of International seminar on
automorphic forms\n\n\nAbstract\nIn this talk we give an overview of the
theory of indefinite theta functions and discuss some recent results.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan-Willem van Ittersum (MPIM Bonn)
DTSTART;VALUE=DATE-TIME:20230418T140000Z
DTEND;VALUE=DATE-TIME:20230418T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/84
DESCRIPTION:Title: On quasimodular forms associated to projective representations of
symmetric groups\nby Jan-Willem van Ittersum (MPIM Bonn) as part of In
ternational seminar on automorphic forms\n\n\nAbstract\nWe explain how one
can naturally associate a quasimodular form to a representation of a symm
etric group. We determine its growth and explain how this construction is
applied to several problems in enumerative geometry. Finally\, we discuss
the difference between linear and projective representations. This is base
d on joint work with Adrien Sauvaget.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Annika Burmester (Bielefeld University)
DTSTART;VALUE=DATE-TIME:20230704T140000Z
DTEND;VALUE=DATE-TIME:20230704T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/85
DESCRIPTION:Title: A general view on multiple zeta values\, modular forms and related
q-series\nby Annika Burmester (Bielefeld University) as part of Inter
national seminar on automorphic forms\n\n\nAbstract\nMultiple zeta values
and modular forms have a deep\, partly \nmysterious\, connection. This can
be seen in the Broadhurst-Kreimer \nconjecture\, which was made partly ex
plicit by Gangl-Kaneko-Zagier in \n2006. Further\, multiple zeta values oc
cur in the Fourier expansion of \nmultiple Eisenstein series as computed b
y Bachmann. We will study this \nconnection in more details on a formal le
vel. This means\, we review \nformal multiple zeta values and then introdu
ce the algebra G^f\, which \nshould be seen as a formal version of multipl
e Eisenstein series\, and \nalso multiple q-zeta values and polynomial fun
ctions on partitions \nsimultaneously. We will give a surjective algebra m
orphism from G^f into \nthe algebra of formal multiple zeta values.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathilde Gerbelli-Gauthier (McGill University)
DTSTART;VALUE=DATE-TIME:20230711T140000Z
DTEND;VALUE=DATE-TIME:20230711T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/86
DESCRIPTION:Title: Counting non-tempered automorphic forms using endoscopy\nby Ma
thilde Gerbelli-Gauthier (McGill University) as part of International semi
nar on automorphic forms\n\n\nAbstract\nHow many automorphic representatio
ns of level n have a specified local factor at the infinite places? When t
his local factor is a discrete series representation\, this question is as
ymptotically well-undersertood as $n$ grows. Non-tempered local factors\,
on the other hand\, violate the Ramanujan conjecture and should be very ra
re. We use the endoscopic classification for representations to quantify t
his rarity in the case of cohomological representations of unitary groups\
, and discuss some applications to the growth of cohomology of Shimura var
ieties.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksander Horawa (University of Oxford)
DTSTART;VALUE=DATE-TIME:20231024T140000Z
DTEND;VALUE=DATE-TIME:20231024T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/87
DESCRIPTION:Title: Siegel modular forms and higher algebraic cycles\nby Aleksande
r Horawa (University of Oxford) as part of International seminar on automo
rphic forms\n\n\nAbstract\nIn recent work with Kartik Prasanna\, we propos
e an explicit relationship between the cohomology of vector bundles on Sie
gel modular threefolds and higher Chow groups (aka motivic cohomology grou
ps). For Yoshida lifts of Hilbert modular forms\, we a result of Ramakrish
nan to prove our conjecture. For Yoshida lifts off Bianchi modular forms\,
we show that our conjecture implies the conjecture of Prasanna—Venkates
h.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Pollack (UCSD)
DTSTART;VALUE=DATE-TIME:20231031T150000Z
DTEND;VALUE=DATE-TIME:20231031T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/88
DESCRIPTION:Title: Arithmeticity of modular forms on $G_2$\nby Aaron Pollack (UCS
D) as part of International seminar on automorphic forms\n\n\nAbstract\nHo
lomorphic modular forms on Hermitian tube domains have a good notion of Fo
urier expansion and Fourier coefficients. These Fourier coefficients give
the holomorphic modular forms an arithmetic structure: there is a basis o
f the space of holomorphic modular forms for which all Fourier coefficient
s of all elements of the basis are algebraic numbers. The group $G_2$ doe
s not have an associated Shimura variety\, but nevertheless there is a cla
ss of automorphic functions on $G_2$ which possess a semi-classical Fourie
r expansion\, called the quaternionic modular forms. I will explain the p
roof that (in even weight at least 6) the cuspidal quaternionic modular fo
rms possess an arithmetic structure\, defined in terms of Fourier coeffici
ents.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaoyu Zhang (University Duisburg-Essen)
DTSTART;VALUE=DATE-TIME:20231107T150000Z
DTEND;VALUE=DATE-TIME:20231107T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/89
DESCRIPTION:Title: Global theta correspondence mod p for unitary groups\nby Xiaoy
u Zhang (University Duisburg-Essen) as part of International seminar on au
tomorphic forms\n\n\nAbstract\nTheta correspondence is a very important to
ol in Langlands program. A fundamental problem in theta correspondence is
the non-vanishing of the theta lifting of an automorphic representation. I
n this talk\, we would like to consider a mod p version of the non-vanishi
ng problem for global theta correspondence for certain reductive dual pair
s of unitary groups. We approach this by looking at the Fourier coefficien
ts of the theta lifting and reduce the problem to the equidistribution of
unipotent orbits.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robin Zhang (MIT)
DTSTART;VALUE=DATE-TIME:20231114T150000Z
DTEND;VALUE=DATE-TIME:20231114T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/90
DESCRIPTION:Title: Harris–Venkatesh plus Stark\nby Robin Zhang (MIT) as part of
International seminar on automorphic forms\n\n\nAbstract\nThe class numbe
r formula describes the behavior of the Dedekind zeta function at $s = 0$
and $s = 1$. The Stark and Gross conjectures extend the class number formu
la\, describing the behavior of Artin $L$-functions and $p$-adic $L$-funct
ions at $s = 0$ and $s = 1$ in terms of units. The Harris–Venkatesh conj
ecture describes the residue of Stark units modulo $p$\, giving a modular
analogue to the Stark and Gross conjectures while also serving as the firs
t verifiable part of the broader conjectures of Venkatesh\, Prasanna\, and
Galatius. In this talk\, I will draw an introductory picture\, formulate
a unified conjecture combining Harris–Venkatesh and Stark for weight one
modular forms\, and describe the proof of this in the imaginary dihedral
case.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steve Lester (King's College London)
DTSTART;VALUE=DATE-TIME:20231121T150000Z
DTEND;VALUE=DATE-TIME:20231121T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/91
DESCRIPTION:Title: Around the Gauss circle problem\nby Steve Lester (King's Colle
ge London) as part of International seminar on automorphic forms\n\n\nAbst
ract\nHardy conjectured that the error term arising from approximating the
number of lattice points lying in a radius-R disc by its area is $O(R^{1/
2+o(1)})$. One source of support for this conjecture is a folklore heurist
ic that uses i.i.d. random variables to model the lattice points lying nea
r the boundary and square-root cancellation of sums of these random variab
les. In this talk I will examine this heuristic and discuss how lattice po
ints near the circle interact with one another. This is joint work with Ig
or Wigman.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Humphries (University of Virginia)
DTSTART;VALUE=DATE-TIME:20231128T150000Z
DTEND;VALUE=DATE-TIME:20231128T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/92
DESCRIPTION:Title: Restricted Arithmetic Quantum Unique Ergodicity\nby Peter Hump
hries (University of Virginia) as part of International seminar on automor
phic forms\n\n\nAbstract\nThe quantum unique ergodicity conjecture of Rudn
ick and Sarnak concerns the mass equidistribution in the large eigenvalue
limit of Laplacian eigenfunctions on negatively curved manifolds. This con
jecture has been resolved by Lindenstrauss when this manifold is the modul
ar surface assuming these eigenfunctions are additionally Hecke eigenfunct
ions\, namely Hecke-Maass cusp forms. I will discuss a variant of this pro
blem in this arithmetic setting concerning the mass equidistribution of He
cke-Maass cusp forms on submanifolds of the modular surface.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Min Lee (University of Bristol)
DTSTART;VALUE=DATE-TIME:20231205T150000Z
DTEND;VALUE=DATE-TIME:20231205T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/93
DESCRIPTION:Title: Murmurations of holomorphic modular forms in the weight aspect
\nby Min Lee (University of Bristol) as part of International seminar on a
utomorphic forms\n\n\nAbstract\nIn April 2022\, He\, Lee\, Oliver\, and Po
zdnyakov made an interesting discovery using machine learning – a surpri
sing correlation between the root numbers of elliptic curves and the coeff
icients of their L-functions. They coined this correlation 'murmurations o
f elliptic curves.' Naturally\, one might wonder whether we can identify a
common thread of 'murmurations' in other families of L-functions. In this
talk\, I will introduce a joint work with Jonathan Bober\, Andrew R. Book
er and David Lowry-Duda\, demonstrating murmurations in holomorphic modula
r forms.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anke Pohl (University of Bremen)
DTSTART;VALUE=DATE-TIME:20231212T150000Z
DTEND;VALUE=DATE-TIME:20231212T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/94
DESCRIPTION:Title: Resonances of Schottky surfaces\nby Anke Pohl (University of B
remen) as part of International seminar on automorphic forms\n\n\nAbstract
\nThe investigation of $L^2$-Laplace eigenvalues and eigenfunctions for hy
perbolic surfaces of finite area is a classical and exciting topic at the
intersection of number theory\, harmonic analysis and mathematical physics
. In stark contrast\, for (geometrically finite) hyperbolic surfaces of in
finite area\, the discrete $L^2$-spectrum is finite. A natural replacement
are the resonances of the considered hyperbolic surface\, which are the p
oles of the meromorphically continued resolvent of the Laplacian.\nThese s
pectral entities also play an important role in number theory and various
other fields\, and many fascinating results about them have already been f
ound\; the generalization of Selberg's $3/16$-theorem by Bourgain\, Gambur
d and Sarnak is a well-known example. However\, an enormous amount of the
properties of such resonances\, also some very elementary ones\, is still
undiscovered. A few years ago\, by means of numerical experiments\, Borthw
ick noticed for some classes of Schottky surfaces (hyperbolic surfaces of
infinite area without cusps and conical singularities) that their sets of
resonances exhibit unexcepted and nice patterns\, which are not yet fully
understood.\nAfter a brief survey of some parts of this field\, we will di
scuss an alternative numerical method\, combining tools from dynamics\, ze
ta functions\, transfer operators and thermodynamic formalism\, functional
analysis and approximation theory. The emphasis of the presentation will
be on motivation\, heuristics and pictures. This is joint work with Oscar
Bandtlow\, Torben Schick and Alex Weisse.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pietro Mercuri (University of Rome - La Sapienza)
DTSTART;VALUE=DATE-TIME:20240116T150000Z
DTEND;VALUE=DATE-TIME:20240116T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/95
DESCRIPTION:Title: Automorphism group of Cartan modular curves\nby Pietro Mercuri
(University of Rome - La Sapienza) as part of International seminar on au
tomorphic forms\n\n\nAbstract\nWe consider the modular curves associated t
o a Cartan subgroup of $GL(2\,\\mathbb{Z}/n\\mathbb{Z})$ or to a particula
r class of subgroups of $GL(2\,\\mathbb{Z}/n\\mathbb{Z})$ containing the C
artan subgroup as a normal subgroup. We describe the automorphism group of
these curves when the level is large enough. If time permits\, we give a
sketch of the proof.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wee Teck Gan (National University of Singapore)
DTSTART;VALUE=DATE-TIME:20240123T080000Z
DTEND;VALUE=DATE-TIME:20240123T090000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/96
DESCRIPTION:Title: The BZSV duality and the relative Langlands program\nby Wee Te
ck Gan (National University of Singapore) as part of International seminar
on automorphic forms\n\n\nAbstract\nI will discuss a duality of Hamiltoni
an group varieties proposed in a recent preprint of Ben-Zvi\, Sakellaridis
and Venkatesh\, which gives a new paradigm for the relative Langlands pro
gram.\nI will then discuss a joint work with Bryan Wang on instances of th
is duality for certain Hamiltonian varieties which quantize to generalized
Whittaker models.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew de Courcy-Ireland (Stockholm University)
DTSTART;VALUE=DATE-TIME:20240130T150000Z
DTEND;VALUE=DATE-TIME:20240130T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/97
DESCRIPTION:Title: Six-dimensional sphere packing and linear programming\nby Matt
hew de Courcy-Ireland (Stockholm University) as part of International semi
nar on automorphic forms\n\n\nAbstract\nThis talk is based on joint work w
ith Maria Dostert and Maryna Viazovska. We prove that the Cohn--Elkies lin
ear programming bound is not sharp for sphere packing in dimension 6. This
is in contrast to Viazovska's sharp bound in dimension 8\, even though it
is believed that closely related lattices achieve the optimal densities i
n both dimensions. The proof uses modular forms to construct feasible poin
ts in a dual program\, generalizing a construction of Cohn and Triantafill
ou to the case of odd weight and non-trivial Dirichlet character. Non-shar
pness of linear programming is demonstrated by comparing this dual bound t
o a stronger upper bound obtained from semidefinite programming by Cohn\,
de Laat\, and Salmon. Our construction has vanishing Fourier coefficients
along an arithmetic progression\, which can be explained using skew self-a
djointness of Hecke operators.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Newton (King’s College London)
DTSTART;VALUE=DATE-TIME:20240206T150000Z
DTEND;VALUE=DATE-TIME:20240206T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/98
DESCRIPTION:Title: Evaluating the wild Brauer group\nby Rachel Newton (King’s C
ollege London) as part of International seminar on automorphic forms\n\n\n
Abstract\nThe local-global approach to the study of rational points on var
ieties over number fields begins by embedding the set of rational points o
n a variety X into the set of its adelic points. The Brauer--Manin pairing
cuts out a subset of the adelic points\, called the Brauer--Manin set\, t
hat contains the rational points. If the set of adelic points is non-empty
but the Brauer--Manin set is empty then we say there's a Brauer--Manin ob
struction to the existence of rational points on X. Computing the Brauer--
Manin pairing involves evaluating elements of the Brauer group of X at loc
al points. If an element of the Brauer group has order coprime to p\, then
its evaluation at a p-adic point factors via reduction of the point modul
o p. For p-torsion elements this is no longer the case: in order to comput
e the evaluation map one must know the point to a higher p-adic precision.
Classifying Brauer group elements according to the precision required to
evaluate them at p-adic points gives a filtration which we describe using
work of Bloch and Kato. Applications of our work include addressing Swinne
rton-Dyer's question about which places can play a role in the Brauer--Man
in obstruction. This is joint work with Martin Bright.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elisa Lorenzo Garcia (Université de Neuchâtel)
DTSTART;VALUE=DATE-TIME:20240213T150000Z
DTEND;VALUE=DATE-TIME:20240213T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/99
DESCRIPTION:Title: On the conductor of Ciani plane quartics\nby Elisa Lorenzo Gar
cia (Université de Neuchâtel) as part of International seminar on automo
rphic forms\n\n\nAbstract\nIn this talk we will discuss the determination
of the conductor exponent of non-special Ciani quartics at primes of poten
tially good reduction in terms of their Ciani invariants. As an intermedia
te step\, we will provide a reconstruction algorithm to construct Ciani qu
artics with given invariants. During the talk we will consider many partic
ular examples and extensions of the presented results. (j.w.w. I. Bouw\, N
. Coppola and A. Somoza)\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesse Thorner (UIUC)
DTSTART;VALUE=DATE-TIME:20240430T140000Z
DTEND;VALUE=DATE-TIME:20240430T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/100
DESCRIPTION:Title: A new zero-free region for Rankin-Selberg L-functions\nby Jes
se Thorner (UIUC) as part of International seminar on automorphic forms\n\
n\nAbstract\nI will present a new zero-free region for GL(m) x GL(n) Ranki
n--Selberg L-functions in the GL(1) twist aspect. The proof is inspired by
Siegel's lower bound for Dirichlet L-functions at s = 1. This is joint wo
rk with Gergely Harcos.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Duke (UCLA)
DTSTART;VALUE=DATE-TIME:20240507T140000Z
DTEND;VALUE=DATE-TIME:20240507T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/101
DESCRIPTION:Title: Quadratic reciprocity in a polynomial ring\nby William Duke (
UCLA) as part of International seminar on automorphic forms\n\n\nAbstract\
nI will give a characterization of when a kind of quadratic reciprocity h
olds for irreducible polynomials whose coefficients are in a number field.
\nThe method is based on Gauss’s second proof of classical quadratic rec
iprocity using binary quadratic forms.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Disegni (Aix-Marseille University)
DTSTART;VALUE=DATE-TIME:20240514T140000Z
DTEND;VALUE=DATE-TIME:20240514T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/102
DESCRIPTION:Title: Gan-Gross-Prasad cycles and derivatives of p-adic L-functions
\nby Daniel Disegni (Aix-Marseille University) as part of International se
minar on automorphic forms\n\n\nAbstract\nCertain Rankin-Selberg motives o
f rank n(n+1) are endowed with algebraic cycles arising from maps of unita
ry Shimura varieties. Gan-Gross-Prasad conjectured that these cycles are a
nalogous to Heegner points\, in the sense that their nontriviality should
be detected by derivatives of L-functions.\nI will propose another nontriv
iality criterion\, based on p-adic L-functions. Under some local condition
s\, this variant can be established in a refined quantitative form\, via t
he construction and comparison two p-adic relative-trace formulas. (Joint
work with Wei Zhang.)\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fu-Tsun Wei (National Tsing Hua University)
DTSTART;VALUE=DATE-TIME:20240521T140000Z
DTEND;VALUE=DATE-TIME:20240521T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/103
DESCRIPTION:Title: Chowla-Selberg phenomenon over function fields\nby Fu-Tsun We
i (National Tsing Hua University) as part of International seminar on auto
morphic forms\n\n\nAbstract\nIn this talk\, I will first determine the alg
ebraic relations among various special gamma values over function fields.
The result is based on the intrinsic relations between gamma values\nin qu
estion and periods of CM dual t-motives\, which are interpreted in terms o
f their “distributions”. This enables us to express every "abelian" CM
period by a suitable product of special gamma values (up to an algebraic
multiple)\, and derive a Chowla–Selberg-type formula in the function fie
ld case.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hohto Bekki (MPIM Bonn)
DTSTART;VALUE=DATE-TIME:20240611T140000Z
DTEND;VALUE=DATE-TIME:20240611T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/104
DESCRIPTION:Title: On the denominators of the special values of the partial zeta fun
ctions of real quadratic fields\nby Hohto Bekki (MPIM Bonn) as part of
International seminar on automorphic forms\n\nInteractive livestream: htt
ps://tu-darmstadt.zoom.us/j/68048280736\nPassword hint: First Fourier coef
ficient of the modular j -function\n\nAbstract\nIt is classically known t
hat the special values of the partial zeta functions of real quadratic fie
lds\, or more generally\, of totally real fields at negative integers are
rational numbers. In this talk\, I would like to discuss the denominators
of these rational numbers in the case of real quadratic fields. \nMore pre
cisely\, Duke recently presented a conjecture which gives a universal uppe
r bound for the denominators of these special values of the partial zeta f
unctions of real quadratic fields. I would like to explain that by using H
arder's theory on the denominator of the Eisenstein class for $\\operatorn
ame{SL}(2\,\\mathbb Z)$\, we can prove the conjecture of Duke and moreover
the sharpness of his upper bound. This is a joint work with Ryotaro Sakam
oto.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/104/
URL:https://tu-darmstadt.zoom.us/j/68048280736
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miao Gu (University of Michigan)
DTSTART;VALUE=DATE-TIME:20240618T140000Z
DTEND;VALUE=DATE-TIME:20240618T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/105
DESCRIPTION:by Miao Gu (University of Michigan) as part of International s
eminar on automorphic forms\n\nInteractive livestream: https://tu-darmstad
t.zoom.us/j/68048280736\nPassword hint: First Fourier coefficient of the m
odular j -function\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/105/
URL:https://tu-darmstadt.zoom.us/j/68048280736
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lola Thompson (Utrecht University)
DTSTART;VALUE=DATE-TIME:20240625T140000Z
DTEND;VALUE=DATE-TIME:20240625T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/106
DESCRIPTION:by Lola Thompson (Utrecht University) as part of International
seminar on automorphic forms\n\nInteractive livestream: https://tu-darmst
adt.zoom.us/j/68048280736\nPassword hint: First Fourier coefficient of the
modular j -function\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/106/
URL:https://tu-darmstadt.zoom.us/j/68048280736
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Möller (Goethe University Frankfurt)
DTSTART;VALUE=DATE-TIME:20240702T140000Z
DTEND;VALUE=DATE-TIME:20240702T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T042021Z
UID:IntSemAutForms/107
DESCRIPTION:by Martin Möller (Goethe University Frankfurt) as part of Int
ernational seminar on automorphic forms\n\nInteractive livestream: https:/
/tu-darmstadt.zoom.us/j/68048280736\nPassword hint: First Fourier coeffici
ent of the modular j -function\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/107/
URL:https://tu-darmstadt.zoom.us/j/68048280736
END:VEVENT
END:VCALENDAR