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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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
UID:IntSemAutForms/44
DESCRIPTION:by William Chen (IAS) as part of International seminar on auto
morphic forms\n\nAbstract: TBA\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:20220528T204107Z
UID:IntSemAutForms/45
DESCRIPTION:by Riccardo Zuffetti (GU Frankfurt) as part of International s
eminar on automorphic forms\n\nAbstract: TBA\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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
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:20220528T204107Z
UID:IntSemAutForms/57
DESCRIPTION:by Arvind Kumar (IIT Jamu) as part of International seminar on
automorphic forms\n\nInteractive livestream: https://ethz.zoom.us/j/68930
894558\nPassword hint: First Fourier coefficient of the modular j -functi
on\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/57/
URL:https://ethz.zoom.us/j/68930894558
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Nelson (IAS)
DTSTART;VALUE=DATE-TIME:20220614T140000Z
DTEND;VALUE=DATE-TIME:20220614T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204107Z
UID:IntSemAutForms/58
DESCRIPTION:by Paul Nelson (IAS) as part of International seminar on autom
orphic forms\n\nInteractive livestream: https://ethz.zoom.us/j/68930894558
\nPassword hint: First Fourier coefficient of the modular j -function\nAb
stract: TBA\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/58/
URL:https://ethz.zoom.us/j/68930894558
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Manning (MPIM Bonn)
DTSTART;VALUE=DATE-TIME:20220621T140000Z
DTEND;VALUE=DATE-TIME:20220621T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204107Z
UID:IntSemAutForms/59
DESCRIPTION:by Jeff Manning (MPIM Bonn) as part of International seminar o
n automorphic forms\n\nInteractive livestream: https://ethz.zoom.us/j/6893
0894558\nPassword hint: First Fourier coefficient of the modular j -funct
ion\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/59/
URL:https://ethz.zoom.us/j/68930894558
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:20220528T204107Z
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\nInteractive livestream: h
ttps://ethz.zoom.us/j/68930894558\nPassword hint: First Fourier coefficien
t of the modular j -function\n\nAbstract\nKohnen and Zagier showed that t
he Petersson inner product of Cohen kernels at integers of opposite parity
is rational in the critical strip. Later Diamantis and O'Sullivan general
ized such rationality to the Petersson inner product with one of the two C
ohen kernels acted by a Hecke operator. In this talk\, using Diamantis and
O'Sullivan's twisted double Eisenstein series\, we twist one of the two C
ohen kernels by a general rational number and prove a similar rationality
result. This is a joint work with Yuanyi You.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/60/
URL:https://ethz.zoom.us/j/68930894558
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikos Diamantis (University of Nottingham)
DTSTART;VALUE=DATE-TIME:20220531T140000Z
DTEND;VALUE=DATE-TIME:20220531T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204107Z
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\nInteractive livestream: https://ethz.zoom.u
s/j/68930894558\nPassword hint: First Fourier coefficient of the modular
j -function\n\nAbstract\nWe define a L-series for harmonic Maass forms and
discuss their functional equations. A converse theorem for these L-series
is given. As an application\, we interpret as proper values of our L-func
tions certain important quantities that arose in works by Bruinier-Funke-I
mamoglu and Alfes-Schwagenscheidt\, and which they had philosophically vie
wed as "central L-values". This is joint work with M. Lee\, W. Raji and L.
Rolen.\n
LOCATION:https://researchseminars.org/talk/IntSemAutForms/61/
URL:https://ethz.zoom.us/j/68930894558
END:VEVENT
END:VCALENDAR