BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Jan Vonk (IAS Princeton)
DTSTART:20200422T130000Z
DTEND:20200422T140000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/1
DESCRIPTION:Title: Singular moduli for real quadratic fields\nby Jan Vonk (
IAS Princeton) as part of International seminar on automorphic forms\n\nAb
stract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Andersen (Brigham Young University)
DTSTART:20200429T140000Z
DTEND:20200429T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/2
DESCRIPTION:Title: Zeros of GL2 L-functions on the critical line\nby Nick A
ndersen (Brigham Young University) as part of International seminar on aut
omorphic forms\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soma Purkait (Tokyo Institute of Technology)
DTSTART:20200506T080000Z
DTEND:20200506T090000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/3
DESCRIPTION:Title: Local Hecke algebras and new forms\nby Soma Purkait (Tok
yo Institute of Technology) as part of International seminar on automorphi
c forms\n\n\nAbstract\nWe describe local Hecke algebras of $\\GL_2$ and do
uble cover of $\\SL_2$\n with certain level structures and use it to give
a newform theory. In the integral weight setting\, our method allows us to
give a characterization of the newspace of any level as a common eigenspa
ce of certain finitely many pair of conjugate operators that we obtain fro
m local Hecke algebras. In specific cases\, we can completely describe loc
al Whittaker functions associated to a new form. In the half-integral weig
ht setting\, we give an analogous characterization of the newspace for the
full space of half-integral weight forms of level $8M$\, $M$ odd and squa
re-free and observe that the forms in the newspace space satisfy a Fourier
coefficient condition that gives the complement of the plus space. This i
s a joint work with E.M. Baruch.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Humphries (University College London)
DTSTART:20200513T130000Z
DTEND:20200513T140000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/4
DESCRIPTION:Title: Sparse equidistribution of hyperbolic orbifolds\nby Pete
r Humphries (University College London) as part of International seminar o
n automorphic forms\n\n\nAbstract\nDuke\, Imamoḡlu\, and Tóth have rece
ntly constructed a new geometric invariant\, a hyperbolic orbifold\, assoc
iated to each narrow ideal class of a real quadratic field. Furthermore\,
they have shown that the projection of these hyperbolic orbifolds onto the
modular surface equidistributes on average over a genus of the narrow cla
ss group as the fundamental discriminan of the real quadratic field tends
to infinity. We discuss a refinement of this result\, sparse equidistribut
ion\, where one averages over smaller subgroups of the narrow class group:
we connect this to cycle integrals of automorphic forms and subconvexity
for Rankin-Selberg L-functions. This is joint work with Asbjørn Nordentof
t.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Larry Rolen (Vanderbilt University)
DTSTART:20200520T130000Z
DTEND:20200520T140000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/5
DESCRIPTION:Title: Periodicities for Taylor coefficients of half-integral weigh
t modular forms\nby Larry Rolen (Vanderbilt University) as part of Int
ernational seminar on automorphic forms\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivia Beckwith (University of Illinois)
DTSTART:20200527T130000Z
DTEND:20200527T140000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/6
DESCRIPTION:Title: Polyharmonic Maass forms and Hecke L-series\nby Olivia B
eckwith (University of Illinois) as part of International seminar on autom
orphic forms\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Fretwell (Bristol University)
DTSTART:20200603T130000Z
DTEND:20200603T140000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/7
DESCRIPTION:Title: (Real Quadratic) Arthurian Tales\nby Dan Fretwell (Brist
ol University) as part of International seminar on automorphic forms\n\nAb
stract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Raum (Chalmers Technical University)
DTSTART:20200610T130000Z
DTEND:20200610T140000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/8
DESCRIPTION:Title: Divisibilities of Hurwitz class numbers\nby Martin Raum
(Chalmers Technical University) as part of International seminar on automo
rphic forms\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sven Möller (Rutgers University)
DTSTART:20200624T130000Z
DTEND:20200624T140000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/9
DESCRIPTION:Title: Eisenstein Series\, Dimension Formulae and Generalised Deep
Holes of the Leech Lattice Vertex Operator Algebra\nby Sven Möller (R
utgers University) as part of International seminar on automorphic forms\n
\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hao Zhang (Sorbonne Université)
DTSTART:20200701T130000Z
DTEND:20200701T140000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/10
DESCRIPTION:Title: Elliptic cocycle for $\\mathrm{GL}_N(\\mathbb{Z})$ and Heck
e operators\nby Hao Zhang (Sorbonne Université) as part of Internatio
nal seminar on automorphic forms\n\n\nAbstract\nA classical result of Eich
ler\, Shimura and Manin asserts that the map that assigns to a cusp form f
its period polynomial r_f is a Hecke equivariant map. We propose a genera
lization of this result to a setting where r_f is replaced by a family
of rational function of N variables equipped with the action of GLN(Z). Fo
r this purpose\, we develop a theory of Hecke operators for the elliptic c
ocycle recently introduced by Charollois. In particular\, when f is an e
igenform\, the corresponding rational function is also an eigenvector resp
ect to Hecke operator for GLN. Finally\, we give some examples for Eisens
tein series and the Ramanujan Delta function.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shaul Zemel (Hebrew University of Jerusalem)
DTSTART:20200708T130000Z
DTEND:20200708T140000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/11
DESCRIPTION:Title: Shintani Lifts of Nearly Holomorphic Modular Forms\nby
Shaul Zemel (Hebrew University of Jerusalem) as part of International semi
nar on automorphic forms\n\n\nAbstract\nThe Shintani lift is a classical c
onstruction of modular\nforms of half-integral weight from modular forms o
f even integral\nweight. Soon after its definition it was shown to be rela
ted to\nintegration with respect to theta kernel. The development of the t
heory\nof regularized integrals opens the question to what modular forms o
f\nhalf-integral weight arise as regularized Shintani lifts of various\nki
nds of integral weight modular forms. We evaluate these lifts for the\ncas
e of nearly holomorphic modular forms\, which in particular shows\nthat wh
en the depth is smaller than the weight\, the Shintani lift is\nalso nearl
y holomorphic. This evaluation requires the determination of\ncertain Four
ier transforms\, which are interesting on their own right.\nThis is joint
work with Yingkun Li.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikos Diamantis (University of Nottingham)
DTSTART:20200715T110000Z
DTEND:20200715T120000Z
DTSTAMP:20260404T110644Z
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 Intern
ational seminar on automorphic forms\n\n\nAbstract\nWe will discuss analyt
ic properties of L-functions twisted\nby an additive character. As an impl
ication\, a full proof of a\nconjecture of Mazur\, Rubin and Stein will be
outlined. This is a\nreport on joint work with J. Hoffstein\, M. Kiral an
d M. Lee.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna von Pippich (TU Darmstadt)
DTSTART:20200722T110000Z
DTEND:20200722T120000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/13
DESCRIPTION:Title: An analytic class number type formula for the Selberg zeta
function\nby Anna von Pippich (TU Darmstadt) as part of International
seminar on automorphic forms\n\n\nAbstract\nIn this talk\, we report on an
explicit formula for the special value at $s=1$ of the derivative of the
Selberg zeta function for the modular group $\\Gamma=\\mathrm{PSL}_{2}(\\m
athbb{Z})$. The formula is a consequence of a generalization of the arithm
etic Riemann--Roch theorem of Deligne and Gillet--Soul\\'e to the case of
the trivial sheaf on $\\Gamma\\backslash \\mathbb{H}$\, equipped with the
hyperbolic metric. This is joint work with Gerard Freixas.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haowu Wang (MPIM Bonn)
DTSTART:20201014T140000Z
DTEND:20201014T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/14
DESCRIPTION:Title: Root systems and free algebras of modular forms\nby Hao
wu Wang (MPIM Bonn) as part of International seminar on automorphic forms\
n\n\nAbstract\nIn this talk we construct some new free algebras of modular
forms. For 25 orthogonal groups of signature $(2\,n)$ related to irreduci
ble root systems\, we prove that the graded algebras of modular forms on t
ype IV symmetric domains are freely generated. The proof is based on the t
heory of Weyl invariant Jacobi forms. As an application\, we show the modu
larity of formal Fourier-Jacobi expansions for these groups. This is joint
work with Brandon Williams.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunqing Tang (CNRS & Université Paris-Sud)
DTSTART:20201021T140000Z
DTEND:20201021T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/15
DESCRIPTION:Title: Reductions of K3 surfaces via intersections on GSpin Shimur
a varieties\nby Yunqing Tang (CNRS & Université Paris-Sud) as part of
International seminar on automorphic forms\n\n\nAbstract\nFor a K3 surfac
e X over a number field with potentially good reduction everywhere\, we pr
ove that there are infinitely many primes modulo which the reduction of X
has larger geometric Picard rank than that of the generic fiber X. A simil
ar statement still holds true for ordinary K3 surfaces with potentially go
od reduction everywhere over global function fields. In this talk\, I will
present the proofs via the (arithmetic) intersection theory on good integ
ral models (and its special fibers) of GSpin Shimura varieties along with
a potential application to a certain case of the Hecke orbit conjecture of
Chai and Oort. This talk is based on joint work with Ananth Shankar\, Aru
l Shankar\, and Salim Tayou and with Davesh Maulik and Ananth Shankar.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandro Lägeler (ETH)
DTSTART:20201028T150000Z
DTEND:20201028T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/16
DESCRIPTION:Title: Continued fractions and Hardy sums\nby Alessandro Läge
ler (ETH) as part of International seminar on automorphic forms\n\n\nAbstr
act\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 continue
d fraction expansion of the rational $d / c$. Hardy sums\, the analogous i
nteger-valued objects arising in the transformation of the logarithms of t
heta functions under a subgroup of the modular group\, have been shown to
satisfy many properties which mirror the properties of the classical Dedek
ind sums. The representation as coefficients of continued fractions has\,
however\, been missing so far. In this talk\, I will argue how one can fil
l this gap. As an application\, I will present a new proof for the fact th
at the graph of the Hardy sums is dense in $\\mathbb{R} \\times \\mathbb{Z
}$\, which was previously proved by Meyer.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Griffin (BYU)
DTSTART:20201104T150000Z
DTEND:20201104T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/17
DESCRIPTION:Title: Class pairings and elliptic curves\nby Michael Griffin
(BYU) as part of International seminar on automorphic forms\n\n\nAbstract\
nIdeal class pairings map the rational points an elliptic curve $E/\\mathb
b{Q}$ \nto the ideal class groups $ \\mathrm{CL} (-D)$ of certain imaginar
y quadratic fields\, by means of explicit maps to $\\mathrm{SL}_2(\\mathbb
{Z})$-equivalence classes of integral binary quadratic forms. Such pairing
s have been studied by Buell\, Call\, Soleng and others.\n\nIn recent work
with Ono and Tsai\, we used such pairings to study the class group and gi
ve explicit 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 ellipt
ic curve has a rational point with sufficiently small “$y$-height”\, w
e find that \n$$\n h(-D) \\geq \\frac{1}{10}\\cdot \\frac{|E_{\\mathrm{to
r}}(\\mathbb Q)|}{\\sqrt{R_{\\mathbb Q}(E)}}\\cdot \\frac{\\pi^{\\frac{r}
{2}}}{2^{r}\\Gamma\\left (\\frac{r}{2}+1\\right)} \n\\cdot \\frac{\\log(D)
^{\\frac{r}{2}}}{\\log \\log D}.\n$$\nWhenever the rank is at least $3$\,
this represents an improvement to the classical lower bound of Goldfeld\,
Gross and Zagier.\n\nConversely\, using the classical upper bound on the c
lass number $\\mathrm{CL}(-D)$ for some discriminant $-D$ represented by t
he equation of the elliptic curve\, these pairing imply effective lower bo
unds for 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 RE
U project wherein the authors prove instances where the torsion subgroup o
f an elliptic curve injects into the the class group $\\mathrm{CL}(-D)$. U
sing this result\, they are able to demonstrate several infinite families
of class 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://stable.researchseminars.org/talk/IntSemAutForms/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christina Röhrig (Uni Köln)
DTSTART:20201111T150000Z
DTEND:20201111T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/18
DESCRIPTION:Title: Siegel theta series for indefinite quadratic forms\nby
Christina Röhrig (Uni Köln) as part of International seminar on automorp
hic forms\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 modu
lar transformation properties. To be more specific\, she showed that solvi
ng a differential equation of second order serves as a criterion for modul
arity. We generalize this result for Siegel theta series of arbitrary genu
s $n$. In order to do so\, we construct Siegel theta series for indefinite
quadratic forms by considering functions which solve an $n\\times n$-syst
em of partial differential equations. These functions do not only give exa
mples of Siegel theta series\, but build a basis of the family of Schwartz
functions that generate series which transform like modular forms.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toshiki Matsusaka (Nagoya University)
DTSTART:20201118T090000Z
DTEND:20201118T100000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/19
DESCRIPTION:Title: Two analogues of the Rademacher symbol\nby Toshiki Mats
usaka (Nagoya University) as part of International seminar on automorphic
forms\n\n\nAbstract\nThe Rademacher symbol is a classical object related t
o the transformation formula of the Dedekind eta function. In 2007\, Ghys
showed that the Rademacher symbol is equal to the linking number of a modu
lar knot and the trefoil knot. In this talk\, we consider two analogues of
Ghys' theorem. One is a hyperbolic analogue of the Rademacher symbol intr
oduced by Duke-Imamoglu-Toth. As they showed\, the hyperbolic Rademacher s
ymbol gives the linking number of two modular knots. I will give here some
explicit formulas for this symbol. The other is the Rademacher symbol on
the triangle group. This symbol is defined from the transformation formula
of the logarithm of a cusp form on the triangle group\, and gives the lin
king number of a (triangle) modular knot and the (p\,q)-torus knot. The la
tter part is a joint work (in progress) with Jun Ueki (Tokyo Denki Univers
ity).\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kathrin Maurischat (RWTH Aachen)
DTSTART:20201125T150000Z
DTEND:20201125T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/20
DESCRIPTION:Title: Explicit construction of Ramanujan bigraphs\nby Kathrin
Maurischat (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 only implicitly defined. We show that one also obtains Ramanujan bigr
aphs in special split cases\, and we give explicit constructions. The proo
f is obtained by inspecting the automorphic spectrum for temperedness\, an
d for the construction we introduce the notion of bi-Cayley graphs. This i
s joint work with C. Ballantine\, S. Evra\, B. Feigon\, O. Parzanchevski.\
n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriele Bogo (TU Darmstadt)
DTSTART:20201202T150000Z
DTEND:20201202T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/21
DESCRIPTION:Title: Extended modularity arising from the deformation of Riemann
surfaces\nby Gabriele Bogo (TU Darmstadt) as part of International se
minar on automorphic forms\n\n\nAbstract\nModular forms appear in Poincar
é's work as solutions of certain differential equations related to the un
iformization of Riemann surfaces. In the talk I will consider certain pert
urbations of these differential equations and prove that their solutions a
re 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 per
turbed ODEs one can describe their solutions as components of vector-value
d modular forms. This leads to the general study of functions arising as c
omponents of vector-valued modular forms attached to extensions of symmetr
ic tensor representations (extended modular forms). If time permits I will
discuss some examples\, including certain functions arising in the study
of scattering amplitudes.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ariel Pacetti (Universidad de Cordoba)
DTSTART:20201209T150000Z
DTEND:20201209T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/22
DESCRIPTION:Title: $\\mathbb{Q}$-curves\, Hecke characters and some Diophantin
e equations\nby Ariel Pacetti (Universidad de Cordoba) as part of Inte
rnational seminar on automorphic forms\n\n\nAbstract\nIn this talk we will
investigate integral solutions of the equation $x^2+dy^2=z^p$\, for posit
ive values of \n$d$. To a solution\, one can attach a Frey curve\, which h
appens to be a $\\mathbb{Q}$-curve. A result of Ribet implies that such a
curve is related to a weight $2$ modular form in $S_2(Γ_0(N)\,\\varepsilo
n)$. Using Hecke characters we will give a precise formula for $N$ and $\\
varepsilon$ and prove non-existence of solutions in some cases. If time al
lows\, we will show how a similar idea applies to the equation $x^2+dy^6=
z^p$.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenia Rosu (University of Regensburg)
DTSTART:20201216T150000Z
DTEND:20201216T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/23
DESCRIPTION:Title: Twists of elliptic curves with CM\nby Eugenia Rosu (Uni
versity of Regensburg) as part of International seminar on automorphic for
ms\n\n\nAbstract\nWe consider certain families of sextic twists of the ell
iptic curve\n $y^2=x^3+1$ that are not defined over $
\\mathbb{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 the square of a trace of a\n modular function a
t a CM point. Assuming the Birch and Swinnerton-Dyer conjecture\,\n
when the value above is non-zero\, we should recover the or
der of the\n Tate-Shafarevich group\, and under certa
in conditions\, we show that the value is\n indeed a
square.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johann Franke (University of Cologne)
DTSTART:20210113T150000Z
DTEND:20210113T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/24
DESCRIPTION:Title: Rational functions\, modular forms and cotangent sums\n
by Johann Franke (University of Cologne) as part of International seminar
on automorphic forms\n\n\nAbstract\nThere are two elementary methods for c
onstructing elliptic modular forms that dominate in literature. One of the
m uses automorphic Poincare series and the other one theta functions. We s
tart a third elementary approach to modular forms using rational functions
that have certain properties regarding pole distribution and growth. One
can prove modularity with contour integration methods and Weil's converse
theorem\, without using the classical formalism of Eisenstein series and L
-functions. 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://stable.researchseminars.org/talk/IntSemAutForms/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jolanta Marzec (University of Kazimierz Wielki)
DTSTART:20210120T150000Z
DTEND:20210120T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/25
DESCRIPTION:Title: Algebraicity of special L-values attached to Jacobi forms o
f higher index\nby Jolanta Marzec (University of Kazimierz Wielki) as
part of International seminar on automorphic forms\n\n\nAbstract\nThe spec
ial values of motivic L-functions have obtained a lot of attention due to
their arithmetic consequences. In particular\, they are expected to be alg
ebraic up to certain factors. The Jacobi forms may also be related to a ge
ometric object (mixed motive)\, but their L-functions are much less unders
tood. During the talk we associate to Jacobi forms (of higher degree\, ind
ex and level) a standard L-function and mention some of its analytic prope
rties. We will focus on the ingredients that come into a proof of algebrai
city (up to certain factors) of its special values. The talk is based on j
oint work with Thanasis Bouganis: https://link.springer.com/article/10.100
7/s00229-020-01243-w\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Oliver (University of Nottingham)
DTSTART:20210127T150000Z
DTEND:20210127T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/26
DESCRIPTION:Title: Twisting moduli\, meromorphy and zeros\nby Tom Oliver (
University of Nottingham) as part of International seminar on automorphic
forms\n\n\nAbstract\nThe zeros of automorphic L-functions are central to c
ertain famous conjectures in arithmetic. In this talk we will discuss the
characterization of Dirichlet coefficients\, with a particular emphasis on
applications to vanishing. The primary focus will be GL(2)\, but we will
also mention higher rank groups - namely\, GL(m) and GL(n) such that m-n=2
.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tiago Fonseca (University of Oxford)
DTSTART:20210413T130000Z
DTEND:20210413T140000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/27
DESCRIPTION:Title: The algebraic geometry of Fourier coefficients of Poincaré
series\nby Tiago Fonseca (University of Oxford) as part of Internatio
nal seminar on automorphic forms\n\n\nAbstract\nThe main goal of this talk
is to explain how to characterise Fourier coefficients of Poincaré serie
s\, of positive and negative index\, as certain algebro-geometric invarian
ts attached to the cohomology of modular curves\, namely their `single-val
ued periods'. This is achieved by a suitable geometric reformulation of cl
assic results in the theory of harmonic Maass forms. Some applications to
algebraicity questions will also be discussed.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Mono (University of Cologne)
DTSTART:20210420T130000Z
DTEND:20210420T140000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/28
DESCRIPTION:Title: On a twisted version of Zagier's $f_{k\, D}$ function\n
by Andreas Mono (University of Cologne) as part of International seminar o
n automorphic 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 a
nd positive integral\nweight\, we inspect its obstruction to modularity\,
and compute its Fourier\nexpansion. This involves twisted hyperbolic Eisen
stein series\, locally\nharmonic Maass forms\, and modular cycle integrals
\, which were studied by\nDuke\, Imamoglu\, Toth.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amanda Folsom (Amherst)
DTSTART:20210427T130000Z
DTEND:20210427T140000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/29
DESCRIPTION:Title: Eisenstein series\, cotangent-zeta sums\, and quantum modul
ar forms\nby Amanda Folsom (Amherst) as part of International seminar
on automorphic forms\n\n\nAbstract\nQuantum modular forms\, defined in the
rationals\, transform like modular forms do on the upper half plane\, up
to suitably analytic error functions. After introducing the subject\, in t
his talk\, we extend work of Bettin and Conrey and define twisted Eisenste
in series\, study their period functions\, and establish quantum modularit
y of certain cotangent-zeta sums. The Dedekind sum\, discussed by Zagier i
n his original paper on quantum modular forms\, is a motivating example.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Moni Kumari (Bar-Ilan University)
DTSTART:20210504T130000Z
DTEND:20210504T140000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/30
DESCRIPTION:Title: Non-vanishing of Hilbert-Poincaré series\nby Moni Kuma
ri (Bar-Ilan University) as part of International seminar on automorphic f
orms\n\n\nAbstract\nModular forms play a prominent role in the classical a
s well as in modern number theory. In the theory of modular forms\, there
is an important class of functions called Poincaré series. These function
s are very mysterious and there are many unsolved problems about them. In
particular\, the vanishing or non-vanishing of such functions is still unk
nown in full generality. In a special case\, the latter problem is equival
ent to the famous Lehmer's conjecture which is one of the classical open p
roblems in the theory. In this talk\, I will speak about when these functi
ons are non-zero for Hilbert modular forms\, a natural generalization of m
odular forms for totally real number fields.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Mertens (University of Liverpool)
DTSTART:20210511T130000Z
DTEND:20210511T140000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/31
DESCRIPTION:Title: Weierstrass mock modular forms and vertex operator algebras
\nby Michael Mertens (University of Liverpool) as part of Internationa
l seminar on automorphic forms\n\n\nAbstract\nUsing techniques from the th
eory of mock modular forms and harmonic Maass forms\, especially Weierstra
ss mock modular forms\, we establish several dimension formulas for certai
n holomorphic\, strongly rational vertex operator algebras\, complementing
previous work by van Ekeren\, Möller\, and Scheithauer. As an applicatio
n\, we show that certain special values of the completed Weierstrass zeta
function are rational. This talk is based on joint work with Lea Beneish.\
n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastián Herrero (Pontifical Catholic University of Valparaiso)
DTSTART:20210518T130000Z
DTEND:20210518T140000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/32
DESCRIPTION:Title: There are at most finitely many singular moduli that are S-
units\nby Sebastián Herrero (Pontifical Catholic University of Valpar
aiso) as part of International seminar on automorphic forms\n\n\nAbstract\
nIn 2015 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
singular modulus that is an algebraic unit. Later\, this result was exten
ded by Y. Li to values of modular polynomials at pairs of singular moduli.
In this talk I will report on joint work with R. Menares and J. Rivera-Le
telier\, 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 Habegg
er's original strategy together with the new ingredient that for every pri
me number p\, singular moduli are p-adically disperse.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Rickards (McGill University)
DTSTART:20210525T130000Z
DTEND:20210525T140000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/33
DESCRIPTION:Title: Counting intersection numbers on Shimura curves\nby Jam
es Rickards (McGill University) as part of International seminar on automo
rphic forms\n\n\nAbstract\nIn this talk\, we give a formula for the total
intersection number of optimal embeddings of a pair of real quadratic orde
rs with respect to an indefinite quaternion algebra over Q. We recall the
classical Gross-Zagier formula for the factorization of the difference of
singular moduli\, and note that our formula resembles an indefinite versio
n of this factorization. This lends support to the work of Darmon-Vonk\, w
ho conjecturally construct a real quadratic analogue of the difference of
singular moduli.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuya Murakami (Tohoku University)
DTSTART:20210601T130000Z
DTEND:20210601T140000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/34
DESCRIPTION:Title: Extended-cycle integrals of the $j$-function for badly appr
oximable numbers\nby Yuya Murakami (Tohoku University) as part of Inte
rnational seminar on automorphic forms\n\n\nAbstract\nCycle integrals of t
he $j$-function are expected to play a role in the real quadratic analog o
f singular moduli. However\, it is not clear how one can consider cycle in
tegrals as a "continuous" function on real quadratic numbers. In this talk
\, we extend the definition of cycle integrals of the $j$-function from re
al quadratic numbers to badly approximable numbers to seek an appropriate
continuity. We also give some explicit representations for extended-cycle
integrals in some cases which can be considered as a partial result of con
tinuity of cycle integrals.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claire Burrin (ETH)
DTSTART:20210608T130000Z
DTEND:20210608T140000Z
DTSTAMP:20260404T110644Z
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 Rademacher symbol is algebraically expressed as a conjugacy class in
variant quasimorphism $\\mathrm{PSL}(2\,\\mathbb{Z}) \\to \\mathbb{Z}$. It
was first studied in connection to Dedekind's eta-function\, but soon eno
ugh appeared to be connected to class numbers of real quadratic fields\, t
he Hirzebruch signature theorem\, or linking numbers of knots. I will expl
ain \n(1) how\, using continued fractions\, Psi can be realized as the win
ding number for closed curves on the modular surface around the cusp\; \n(
2) how\, using Eisenstein series\, one can naturally construct a Rademache
r symbol for any cusp of a general noncocompact Fuchsian group\; \n(3) and
discuss some new connections to arithmetic geometry.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chao Li (Columbia University)
DTSTART:20210615T130000Z
DTEND:20210615T140000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/36
DESCRIPTION:Title: Beilinson-Bloch conjecture and arithmetic inner product for
mula\nby Chao Li (Columbia University) as part of International semina
r on automorphic forms\n\n\nAbstract\nFor certain automorphic representati
ons $\\pi$ on unitary groups\, we show\nthat if $L(s\, \\pi)$ vanishes to
order one at the center $s=1/2$\, then the\nassociated $\\pi$-localized Ch
ow group of a unitary Shimura variety is\nnontrivial. This proves part of
the Beilinson-Bloch conjecture for unitary\nShimura varieties\, which gene
ralizes the BSD conjecture. Assuming Kudla's\nmodularity conjecture\, we f
urther prove the arithmetic inner product\nformula for $L'(1/2\, \\pi)$\,
which generalizes the Gross-Zagier formula. We\nwill motivate these conjec
tures and discuss some aspects of the proof. We\nwill also mention recent
extensions applicable to symmetric power\nL-functions of elliptic curves.
This is joint work with Yifeng Liu.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:YoungJu Choie (Postech)
DTSTART:20210622T080000Z
DTEND:20210622T090000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/37
DESCRIPTION:Title: A generating function of periods of automorphic forms\n
by YoungJu 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 var
iables\, as a single product of Jacobi theta series for any squarefree lev
el $N$ 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://stable.researchseminars.org/talk/IntSemAutForms/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudia Alfes-Neumann (Universität Bielefeld)
DTSTART:20210629T130000Z
DTEND:20210629T140000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/38
DESCRIPTION:Title: Some theta liftings and applications\nby Claudia Alfes-
Neumann (Universität Bielefeld) as part of International seminar on autom
orphic forms\n\n\nAbstract\nIn this talk we give an introduction to the st
udy of generating series of the traces\nof CM values and geodesic cycle in
tegrals of different modular functions. \nFirst we define modular forms an
d harmonic Maass forms. Then we briefly discuss the\ntheory of theta lifts
that gives a conceptual framework for such generating series.\nWe end wit
h some applications of the theory.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lennart Gehrmann (Universität Duisburg-Essen)
DTSTART:20210706T130000Z
DTEND:20210706T140000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/39
DESCRIPTION:Title: Rigid meromorphic cocycles for orthogonal groups\nby Le
nnart Gehrmann (Universität Duisburg-Essen) as part of International semi
nar on automorphic forms\n\n\nAbstract\nI will talk about a generalization
of Darmon and Vonk's notion of rigid meromorphic cocycles to the setting
of orthogonal groups. After giving an overview over the general setting I
will discuss the case of orthogonal groups attached to quadratic spaces of
signature (3\,1) in more detail. This is joint work with Henri Darmon and
Mike Lipnowski.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Bruinier (TU Darmstadt)
DTSTART:20211026T130000Z
DTEND:20211026T140000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/40
DESCRIPTION:Title: Arithmetic volumes of unitary Shimura varieties\nby Jan
Bruinier (TU Darmstadt) as part of International seminar on automorphic f
orms\n\n\nAbstract\nThe geometric volume of a unitary Shimura variety can
be defined as the self-intersection number of the Hodge line bundle on it.
It represents an important invariant\, which can be explicitly computed i
n terms of special values of Dirichlet L-functions. Analogously\, the arit
hmetic 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 b
e expressed in terms of logarithmic derivatives of Dirichlet L-functions.
This is joint work with Ben Howard.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nils Matthes (Oxford)
DTSTART:20211102T140000Z
DTEND:20211102T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/41
DESCRIPTION:Title: Meromorphic modular forms and their iterated integrals\
nby Nils Matthes (Oxford) as part of International seminar on automorphic
forms\n\n\nAbstract\nMeromorphic modular forms are generalizations of modu
lar forms which are allowed to have poles. Part of the motivation for thei
r study comes from recent work of Li-Neururer\, Pasol-Zudilin\, and others
\, which shows that integrals of certain meromorphic modular forms have in
teger Fourier coefficients -- an arithmetic phenomenon which does not seem
to exist for holomorphic modular forms. In this talk we will study iterat
ed integrals of meromorphic modular forms and describe some general algebr
aic independence results\, generalizing results of Pasol-Zudilin. If time
permits we will also mention an algebraic geometric interpretation of mero
morphic modular forms which generalizes the classical fact that modular fo
rms are sections of certain line bundles\, and describe the occurrence of
iterated integrals of meromorphic modular forms in computations of Feynman
integrals in quantum field theory.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lindsay Dever (Bryn Mawr)
DTSTART:20211109T140000Z
DTEND:20211109T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/42
DESCRIPTION:Title: Distribution of Holonomy on Compact Hyperbolic 3-Manifolds<
/a>\nby Lindsay Dever (Bryn Mawr) as part of International seminar on auto
morphic forms\n\n\nAbstract\nThe study of hyperbolic 3-manifolds draws dee
p connections between number theory\, geometry\, topology\, and quantum me
chanics. Specifically\, the closed geodesics on a manifold are intrinsical
ly related to the eigenvalues of Maass forms via the Selberg trace formula
and are parametrized by their length and holonomy\, which describes the a
ngle of rotation by parallel transport along the geodesic. The trace formu
la for spherical Maass forms can be used to prove the Prime Geodesic Theor
em\, which provides an asymptotic count of geodesics up to a certain lengt
h. I will present an asymptotic count of geodesics (obtained via the non-s
pherical trace formula) by length and holonomy in prescribed intervals whi
ch are allowed to shrink independently. This count implies effective equid
istribution of holonomy and substantially sharpens the result of Sarnak an
d Wakayama in the context of compact hyperbolic 3-manifolds. I will then d
iscuss new results regarding biases in the finer distribution of holonomy.
\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Kiefer (TU Darmstadt)
DTSTART:20211116T140000Z
DTEND:20211116T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/43
DESCRIPTION:Title: Orthogonal Eisenstein Series of Singular Weight\nby Pau
l Kiefer (TU Darmstadt) as part of International seminar on automorphic fo
rms\n\n\nAbstract\nWe will study (non-)holomorphic orthogonal Eisenstein s
eries using Borcherds' additive theta lift. It turns out that the lifts of
vector-valued non-holomorphic Eisenstein series with respect to the Weil
representation of an even lattice are linear combinations of non-holomorph
ic orthogonal Eisenstein series. This yields their meromorphic continuatio
n and functional equation. Moreover we will determine the image of this co
nstruction. Afterwards we evaluate the non-holomorphic orthogonal Eisenste
in series at certain special values to obtain holomorphic orthogonal Eisen
stein series and determine all holomorphic orthogonal modular forms that c
an be obtained in this way.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Chen (IAS)
DTSTART:20211123T140000Z
DTEND:20211123T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/44
DESCRIPTION:Title: Connectivity of Hurwitz spaces and the conjecture of Bourga
in\, Gamburd\, and Sarnak\nby William Chen (IAS) as part of Internatio
nal seminar on automorphic forms\n\n\nAbstract\nA Hurwitz space is a modul
i space of coverings of algebraic varieties. After fixing certain topologi
cal invariants\, it is a classical problem to classify the connected compo
nents of 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 tal
k I will explain a similar connectedness result\, this time in the context
of SL(2\,p)-covers of elliptic curves\, only branched above the origin. T
he connectedness result comes from combining asymptotic results of Bourgai
n\, Gamburd\, and Sarnak with a new combinatorial 'rigidity' coming from a
lgebraic geometry. This rigidity result can also be viewed as a divisibili
ty theorem on the cardinalities of Nielsen equivalence classes of generati
ng pairs of finite groups. The connectedness is a key piece of information
that unlocks a number of applications\, including a conjecture of Bourgai
n\, Gamburd and Sarnak on a strong approximation property of the Markoff e
quation $x^2 + y^2 + z^2 - xyz$ = 0\, a noncongruence analog of Rademacher
's conjecture of the genus of modular curves\, tamely ramified 3-point cov
ers in characteristic p\, and counting flat geodesics on a certain family
of congruence modular curves.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Riccardo Zuffetti (GU Frankfurt)
DTSTART:20211130T140000Z
DTEND:20211130T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/45
DESCRIPTION:Title: Cones of codimension two special cycles\nby Riccardo Zu
ffetti (GU Frankfurt) as part of International seminar on automorphic form
s\n\n\nAbstract\nIn the literature\, there are several results on cones ge
nerated by (effective\, ample\, nef...) divisors on (quasi-)projective var
ieties. However\, a little is known on cones generated by cycles of codime
nsion greater than one. Let X be an orthogonal Shimura variety. In this ta
lk\, we consider the cone $C_X$ generated by rational classes of codimensi
on two special cycles of X. We illustrate how to prove properties of $C_X$
by means of Fourier coefficients of Siegel modular forms.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manami Roy (Fordham)
DTSTART:20211207T140000Z
DTEND:20211207T150000Z
DTSTAMP:20260404T110644Z
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 automorphi
c forms\n\n\nAbstract\nMany mathematicians have studied dimension and codi
mension formulas for the spaces of Siegel cusp forms of degree 2. The dime
nsions of the spaces of Siegel cusp forms of non-squarefree levels are mos
tly now available in the literature. This talk will present new dimension
formulas of Siegel cusp forms of degree 2\, weight k\, and level 4 for thr
ee congruence subgroups. One of these dimension formulas is obtained using
the Satake compactification. However\, our primary method relies on count
ing a particular set of cuspidal automorphic representations of GSp(4) and
exploring 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://stable.researchseminars.org/talk/IntSemAutForms/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrick Bieker (TU Darmstadt)
DTSTART:20211214T140000Z
DTEND:20211214T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/47
DESCRIPTION:Title: Modular units for orthogonal groups of signature (2\,2) and
invariants for the Weil representation\nby Patrick Bieker (TU Darmsta
dt) as part of International seminar on automorphic forms\n\n\nAbstract\nW
e construct modular units for certain orthogonal groups in signature (2\,
2) using Borcherds products. As an input to the construction we show that
the space of invariants for the Weil representation for discriminant group
s which contain self-dual isotropic subgroups is spanned by the characteri
stic functions of the self-dual isotropic subgroups. This allows us to det
ermine all modular units arising as Borcherds products in examples.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Garcia (UCL)
DTSTART:20220111T130000Z
DTEND:20220111T140000Z
DTSTAMP:20260404T110644Z
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\nAb
stract\nThere are several recent constructions by many authors of Eisenste
in cocycles of arithmetic groups. I will discuss a point of view on these
constructions using equivariant cohomology and equivariant differential fo
rms. The resulting objects behave like theta kernels relating the homology
of arithmetic groups to algebraic objects. As an application\, I will exp
lain the proof of some conjectures of Sczech and Colmez on critical values
of Hecke L-functions. The talk is based on joint work with Nicolas Berger
on and Pierre Charollois.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Márton Erdélyi (Budapest University of Technology and Economics)
DTSTART:20220125T140000Z
DTEND:20220125T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/49
DESCRIPTION:Title: Matrix Kloosterman sums\nby Márton Erdélyi (Budapest
University of Technology and Economics) as part of International seminar o
n automorphic forms\n\n\nAbstract\nWe study exponential sums arosing in th
e work of Lee and Marklof about the horocyclic flow on the group $GL_n$. I
n many cases this sum can be expressed with the help of classical Klooster
man sums. We give effective bounds using the very basics of cohomological
methods and get a nice illustration of the general purity theorem of Fouvr
y and Katz. Joint work with Árpád Tóth.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isabella Negrini (McGill)
DTSTART:20220118T140000Z
DTEND:20220118T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/50
DESCRIPTION:Title: A Shimura-Shintani correspondence for rigid analytic cocycl
es\nby Isabella Negrini (McGill) as part of International seminar on a
utomorphic forms\n\n\nAbstract\nIn their paper Singular moduli for real qu
adratic fields: a rigid analytic approach\,\nDarmon and Vonk introduced ri
gid meromorphic 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 ri
gid meromorphic functions on the p-adic upper-half plane. Their values at
RM points 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 prog
ress towards developing a Shimura-Shintani correspondence in this setting.
\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vesselin Dimitrov (Toronto)
DTSTART:20220201T140000Z
DTEND:20220201T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/51
DESCRIPTION:Title: The unbounded denominators conjecture\nby Vesselin Dimi
trov (Toronto) as part of International seminar on automorphic forms\n\n\n
Abstract\nI will explain the ideas of the proof of the following recent th
eorem\, joint with Frank Calegari and Yunqing Tang: A modular form for a f
inite index subgroup of $SL_2(\\mathbb{Z})$ has a $q$-expansion\nwith boun
ded denominators if and only if it is a modular form for a congruence subg
roup. I will also discuss some related open problems such as a hypothetica
l $SL_2(\\mathbb{F}_q[t])$ analog of the theorem.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weibo Fu (Princeton)
DTSTART:20220426T140000Z
DTEND:20220426T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/52
DESCRIPTION:Title: Growth of Bianchi modular forms\nby Weibo Fu (Princeton
) as part of International seminar on automorphic forms\n\n\nAbstract\nIn
this talk\, I will establish a sharp bound on the growth of cuspidal Bianc
hi modular forms. By the Eichler-Shimura isomorphism\, we actually give a
sharp bound of the second cohomology of a hyperbolic three manifold (Bianc
hi manifold) with local system arising from the representation $Sym^k \\ot
imes \\overline{Sym^k}$ of $SL_2(\\mathbb{C})$. I will explain how a p-adi
c algebraic method is used for deriving our result.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brandon Williams (RWTH Aachen)
DTSTART:20220503T140000Z
DTEND:20220503T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/53
DESCRIPTION:Title: Free algebras of modular forms on ball quotients\nby Br
andon Williams (RWTH Aachen) as part of International seminar on automorph
ic forms\n\n\nAbstract\nWe study algebras of modular forms on unitary grou
ps of signature $(n\, 1)$. We give a\nsufficient criterion for the ring of
unitary modular forms to be freely generated in\nterms of the divisor of
a modular Jacobian determinant. We use this to prove that a\nnumber of rin
gs of unitary modular forms associated to Hermitian lattices over the\nrin
gs of integers of $\\mathbb{Q}(\\sqrt{ d})$ for $d = −1\, −2\, −3$ a
re polynomial algebras without\nrelations. This is joint work with Haowu W
ang.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaclyn Lang (Temple University)
DTSTART:20220510T140000Z
DTEND:20220510T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/54
DESCRIPTION:Title: A modular construction of unramified p-extensions of $\\mat
hbb{Q}(N^{1/p})$\nby Jaclyn Lang (Temple University) as part of Intern
ational seminar on automorphic forms\n\n\nAbstract\nIn his 1976 proof of t
he converse of Herbrand's theorem\, Ribet used Eisenstein-cuspidal congrue
nces to produce unramified degree-p extensions of the p-th cyclotomic fiel
d when p is an odd prime. After reviewing Ribet's strategy\, we will discu
ss recent work with Preston Wake in which we apply similar techniques to p
roduce 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 Fr
ank Calegari's blog.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sudhir Pujahari (NISER)
DTSTART:20220517T070000Z
DTEND:20220517T080000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/55
DESCRIPTION:Title: Sato-Tate conjecture in arithmetic progressions for certain
families of elliptic curves\nby Sudhir Pujahari (NISER) as part of In
ternational seminar on automorphic forms\n\n\nAbstract\nIn this talk we wi
ll study moments of the trace of Frobenius of elliptic curves if the trace
is restricted to a fixed arithmetic progression. In conclusion\, we will
obtain the Sato-Tate distribution for the trace of certain families of Ell
iptic curves. As a special case we will recover a result of Birch proving
Sato-Tate distribution for certain family of elliptic curves. Moreover\, w
e will see that these results follow from asymptotic formulas relating sum
s and moments of Hurwitz class numbers where the sums are restricted to ce
rtain arithmetic progressions. This is a joint work with Kathrin Bringmann
and Ben Kane.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arvind Kumar (IIT Jamu)
DTSTART:20220607T070000Z
DTEND:20220607T080000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/57
DESCRIPTION:Title: Distinguishing Siegel eigenforms from Hecke eigenvalues
\nby Arvind Kumar (IIT Jamu) as part of International seminar on automorph
ic forms\n\n\nAbstract\nDetermination of modular forms is one of the funda
mental 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 ei
genvalues\nat primes determines the newform uniquely and this result is kn
own as the\nmultiplicity one theorem. In the case of Siegel cuspidal eigen
forms of\ndegree two\, the multiplicity one theorem has been proved only r
ecently in\n2018 by Schmidt. In this talk\, we refine the result of Schmid
t by showing\nthat if the Hecke eigenvalues of two Siegel eigenforms of le
vel 1 agree at\na set of primes of positive density\, then the eigenforms
are the same (up\nto a constant). We also distinguish Siegel eigenforms fr
om the signs of\ntheir Hecke eigenvalues. The main ingredient to prove the
se results are\nGalois representations attached to Siegel eigenforms\, the
Chebotarev\ndensity theorem and some analytic properties of associated L-
functions.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Nelson (IAS)
DTSTART:20220614T140000Z
DTEND:20220614T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/58
DESCRIPTION:Title: The orbit method\, microlocal analysis and applications to
L-functions\nby Paul Nelson (IAS) as part of International seminar on
automorphic forms\n\n\nAbstract\nL-functions are generalizations of the Ri
emann zeta function. Their analytic properties control the asymptotic beha
vior of prime numbers in various refined senses. Conjecturally\, every L-f
unction is a "standard L-function" arising from an automorphic form. A pro
blem of recurring interest\, with widespread applications\, has been to es
tablish nontrivial bounds for L-functions. I will survey some recent resul
ts addressing this problem. The proofs involve the analysis of integrals o
f automorphic forms\, approached through the lens of representation theory
. I will emphasize the role played by the orbit method\, developed in a qu
antitative form along the lines of microlocal analysis. The results/method
s to be surveyed are the subject of the following papers/preprints: \n\nht
tps://arxiv.org/abs/1805.07750 \n\nhttps://arxiv.org/abs/2012.02187 \n\nht
tps://arxiv.org/abs/2109.15230\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Manning (MPIM Bonn)
DTSTART:20220621T140000Z
DTEND:20220621T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/59
DESCRIPTION:Title: The Wiles-Lenstra-Diamond numerical criterion over imaginar
y quadratic fields\nby Jeff Manning (MPIM Bonn) as part of Internation
al seminar on automorphic forms\n\n\nAbstract\nWiles' modularity lifting t
heorem was the central argument in his proof of modularity of (semistable)
elliptic curves over $\\mathbb{Q}$\, and hence of Fermat's Last Theorem.
His proof relied on two key components: his "patching" argument (developed
in collaboration with Taylor) and his numerical isomorphism criterion. In
the time since Wiles' proof\, the patching argument has been generalized
extensively to prove a wide variety of modularity lifting results. In part
icular Calegari and Geraghty have found a way to generalize it to prove po
tential modularity of elliptic curves over imaginary quadratic fields (con
tingent on some standard conjectures). The numerical criterion on the othe
r hand has proved far more difficult to generalize\, although in situation
s where it can be used it can prove stronger results than what can be prov
en purely via patching. In this talk I will present joint work with Srikan
th Iyengar and Chandrashekhar Khare which proves a generalization of the n
umerical criterion to the context considered by Calegari and Geraghty (and
contingent on the same conjectures). This allows us to prove integral "R=
T" theorems at non-minimal levels over imaginary quadratic fields\, which
are inaccessible by Calegari and Geraghty's method. The results provide ne
w evidence in favor of a torsion analog of the classical Langlands corresp
ondence.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yichao Zhang (Harbin Institute of Technology)
DTSTART:20220628T140000Z
DTEND:20220628T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/60
DESCRIPTION:Title: Rationality of the Petersson Inner Product of Generally Twi
sted Cohen Kernels\nby Yichao Zhang (Harbin Institute of Technology) a
s part of International seminar on automorphic forms\n\n\nAbstract\nKohnen
and Zagier showed that the Petersson inner product of Cohen kernels at in
tegers of opposite parity is rational in the critical strip. Later Diamant
is and O'Sullivan generalized such rationality to the Petersson inner prod
uct with one of the two Cohen kernels acted by a Hecke operator. In this t
alk\, using Diamantis and O'Sullivan's twisted double Eisenstein series\,
we twist one of the two Cohen kernels by a general rational number and pro
ve a similar rationality result. This is a joint work with Yuanyi You.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikos Diamantis (University of Nottingham)
DTSTART:20220531T140000Z
DTEND:20220531T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/61
DESCRIPTION:Title: L-series associated with harmonic Maass forms and their val
ues\nby Nikos Diamantis (University of Nottingham) as part of Internat
ional seminar on automorphic forms\n\n\nAbstract\nWe define a L-series for
harmonic Maass forms and discuss their functional equations. A converse t
heorem for these L-series is given. As an application\, we interpret as pr
oper values of our L-functions certain important quantities that arose in
works by Bruinier-Funke-Imamoglu and Alfes-Schwagenscheidt\, and which the
y had philosophically viewed as "central L-values". This is joint work wit
h M. Lee\, W. Raji and L. Rolen.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel Müller (TU Darmstadt)
DTSTART:20221101T150000Z
DTEND:20221101T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/62
DESCRIPTION:Title: The invariants of the Weil representation of $\\mathrm{SL}_
2(\\mathbb{Z})$\nby Manuel Müller (TU Darmstadt) as part of Internati
onal seminar on automorphic forms\n\n\nAbstract\nThe transformation behavi
our of the vector valued theta function of a positive definite even lattic
e under the metaplectic group $\\mathrm{Mp}_2(\\mathbb{Z})$ is described b
y the Weil representation. This representation plays an important role in
the theory of automorphic forms. We show that its invariants are induced f
rom 5 fundamental invariants.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Congling Qiu (Yale University)
DTSTART:20221115T150000Z
DTEND:20221115T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/64
DESCRIPTION:Title: Modularity and automorphy of cycles on Shimura varieties\nby Congling Qiu (Yale University) as part of International seminar on a
utomorphic forms\n\n\nAbstract\nAlgebraic cycles are central objects in al
gebraic/arithmetic geometry and problems around them are very difficult. F
or Shimura varieties modularity of generating series with coefficients bei
ng algebraic cycles has been proved useful in the of study of algebraic cy
cles. A closely related problem is the automorphy of representations spann
ed by algebraic cycles. I will discuss the history of these problems some
progress and applications.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eran Assaf (Dartmouth College)
DTSTART:20221122T150000Z
DTEND:20221122T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/65
DESCRIPTION:Title: Orthogonal modular forms\, Siegel modular forms and Eisenst
ein congruences\nby Eran Assaf (Dartmouth College) as part of Internat
ional seminar on automorphic forms\n\n\nAbstract\nThe theta correspondence
between the orthogonal group and the symplectic group provides a cornerst
one for studying Siegel modular forms via orthogonal modular forms. \nIn t
his work\, we make this correspondence completely explicit\, with precise
level structure for low to moderate even rank and nontrivial discriminant.
\nGuided by computational discoveries\, we prove congruences between eigen
values of classical modular forms and eigenvalues of genuine Siegel modula
r forms\, obtain formulas for the number of neighbors in terms of eigenval
ues of classical modular forms\, and formulate some conjectures that arise
naturally from the data.\nThis is joint work with Dan Fretwell\, Colin In
galls\, Adam Logan\, Spencer Secord\, and John Voight\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shouhei Ma (Tokyo Institute of Technology)
DTSTART:20221129T080000Z
DTEND:20221129T090000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/66
DESCRIPTION:Title: Vector-valued orthogonal modular forms\nby Shouhei Ma (
Tokyo Institute of Technology) as part of International seminar on automor
phic forms\n\n\nAbstract\nI will talk about the theory of vector-valued mo
dular forms on domains of type IV\, with some emphasis on its algebro-geom
etric aspects.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bingrong Huang (Shandong University)
DTSTART:20221206T080000Z
DTEND:20221206T090000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/67
DESCRIPTION:Title: Arithmetic Quantum Chaos and L-functions\nby Bingrong H
uang (Shandong 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 ergodi
city theorem for automorphic forms on the modular surface. Then I will giv
e some results on effective decorrelation of Hecke eigenforms and the cubi
c moment of Hecke-Maass cusp forms. The proofs are based on the analytic t
heory of L-functions.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Dunn (Caltech)
DTSTART:20221213T150000Z
DTEND:20221213T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/68
DESCRIPTION:Title: Bias in cubic Gauss sums: Patterson's conjecture\nby Al
ex Dunn (Caltech) as part of International seminar on automorphic forms\n\
n\nAbstract\nWe prove\, in this joint work with Maksym Radziwill\, a 1978
conjecture of S. Patterson (conditional on the Generalised Riemann hypothe
sis)\nconcerning the bias of cubic Gauss sums.\nThis explains a well-known
numerical 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\nH
eath-Brown's cubic large sieve is sharp under GRH. \nThis disproves the po
pular belief that the cubic large sieve can be\nimproved.\n\n An important
ingredient 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-triv
ial asymptotic main term.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Morten Risager (University of Copenhagen)
DTSTART:20221220T150000Z
DTEND:20221220T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/69
DESCRIPTION:Title: Distributions of Manin's iterated integrals\nby Morten
Risager (University of Copenhagen) as part of International seminar on aut
omorphic forms\n\n\nAbstract\nWe recall the definition of Manin's iterated
integrals of a given length. We then explain how these generalise modular
symbols and certain aspects of the theory of multiple zeta-values. In len
gth one and two we determine the limiting distribution of these iterated i
ntegrals. Maybe surprisingly\, even if we can compute all moments also in
higher length we cannot in general determine a distribution for length thr
ee or higher. This is joint work with Y. Petridis and with N. Matthes.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yota Maeda (Kyoto University)
DTSTART:20230110T080000Z
DTEND:20230110T090000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/70
DESCRIPTION:Title: Deligne-Mostow theory and beyond\nby Yota Maeda (Kyoto
University) as part of International seminar on automorphic forms\n\n\nAbs
tract\nBall quotients have been studied extensively in algebraic geometry
from the aspect of moduli spaces\, and in number theory with emphasis on t
he relation with modular forms. The Deligne-Mostow theory gives them modul
i interpretation through the isomorphism between the Baily-Borel compactif
ications of them and certain GIT quotients.\nIn this talk\, I will discuss
whether 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 connectio
n with the recent development in the minimal model program. This work is b
ased on a joint work with Klaus Hulek (Leibniz University Hannover)\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soumya Das (Indian Institute of Science\, Bangalore)
DTSTART:20230117T080000Z
DTEND:20230117T090000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/71
DESCRIPTION:Title: Sup-norms of automorphic forms on average\nby Soumya Da
s (Indian Institute of Science\, Bangalore) as part of International semin
ar on automorphic forms\n\n\nAbstract\nBounding the sup-norms of automorph
ic forms 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 fo
rms of higher degrees. In this talk we aim to discuss some conjectures and
results in this area. We use either the theory of Poincare series or aver
ages of central values of $L$-functions to tackle this problem. Our method
s have the benefit of having a hands-on approach and fits into many situat
ions.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Riccardo Salvati Manni (Sapienza University of Rome)
DTSTART:20230124T150000Z
DTEND:20230124T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/72
DESCRIPTION:Title: Slope of Siegel modular forms: some geometric applications
\nby Riccardo Salvati Manni (Sapienza University of Rome) as part of I
nternational seminar on automorphic forms\n\n\nAbstract\nWe study the slop
e of modular forms on the Siegel space. We will recover known divisors of
minimal slope for $g\\leq5$ and we discuss the Kodaira dimension of the mo
duli space of principally polarized abelian varieties $A_g$ (and eventuall
y of the generalized Kuga's varieties). Moreover we illustrate the cone of
moving divisors on $A_g$. Partly motivated by the generalized Rankin-Cohe
n bracket\, we construct a non-linear holomorphic differential operator th
at sends Siegel modular forms to Siegel cusp forms\, and we apply it to pr
oduce new modular forms. Our construction recovers the known divisors of m
inimal moving slope on $A_g$ for $g\\leq5$.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandro Bettin (University of Genova)
DTSTART:20230131T150000Z
DTEND:20230131T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/73
DESCRIPTION:Title: Continuity and value distribution of quantum modular forms<
/a>\nby Sandro Bettin (University of Genova) as part of International semi
nar on automorphic forms\n\n\nAbstract\nQuantum modular forms are function
s f defined 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 case of k=0\, f can be interpreted as a Birkhoff sums associated with
the Gauss map. In particular\, under mild hypotheses on G\, one can show c
onvergence to a stable law. If k is non-zero\, the situation is rather dif
ferent and we can show that mild conditions on psi imply that f itself has
to exhibit some continuity property. Finally\, we discuss the convergence
in distribution also in this case. This is a joint work with Sary Drappea
u.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulia Cesana (University of Cologne)
DTSTART:20230207T150000Z
DTEND:20230207T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/74
DESCRIPTION:Title: Asymptotic equidistribution for partition statistics and to
pological invariants\nby Giulia Cesana (University of Cologne) as part
of International seminar on automorphic forms\n\n\nAbstract\nThroughout m
athematics\, the equidistribution properties of certain objects are a cent
ral theme studied by many authors. In my talk I am going to speak about a
joint project with William Craig and Joshua Males\, where we provide a gen
eral framework for proving asymptotic equidistribution\, convexity\, and l
og-concavity of coefficients of generating functions on arithmetic progres
sions.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abhishek Saha (Queen Mary University (London))
DTSTART:20230502T140000Z
DTEND:20230502T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/75
DESCRIPTION:Title: Mass equidistribution for Saito-Kurokawa lifts\nby Abhi
shek Saha (Queen Mary University (London)) as part of International semina
r on automorphic forms\n\n\nAbstract\nThe Quantum Unique Ergodicity (QUE)
conjecture was proved in the classical case for Maass forms of full level
in the eigenvalue aspect by Lindenstrauss and Soundararajan\, and for holo
morphic forms in the weight aspect by Holowinsky and Soundararajan. In th
is talk\, I will discuss some joint work with Jesse Jaasaari and Steve Les
ter on the analogue of the QUE conjecture in the weight aspect for holomor
phic Siegel cusp forms of degree 2 and full level. Assuming the Generalize
d Riemann Hypothesis (GRH) we establish QUE for Saito–Kurokawa lifts as
the weight tends to infinity. As an application\, we prove the equidistrib
ution of zero divisors of Saito-Kurokawa lifts.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabrizio Andreatta (University of Milan)
DTSTART:20230516T140000Z
DTEND:20230516T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/76
DESCRIPTION:Title: Endoscopy for GSp(4) and rational points on elliptic curves
\nby Fabrizio Andreatta (University of Milan) as part of International
seminar on automorphic forms\n\n\nAbstract\nI report on a joint project w
ith M. Bertolini \, M.A. Seveso and R. Venerucci\, aimed at studying the e
quivariant BSD conjecture for rational elliptic curves twisted by certain
self-dual 4-dimensional Artin representations in situations of odd analyti
c rank. We use the endoscopy for GSp(4) to construct Selmer classes relate
d to the relevant (complex and p-adic) L-values via explicit reciprocity l
aws.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oguz Gezmis (Heidelberg University)
DTSTART:20230425T140000Z
DTEND:20230425T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/77
DESCRIPTION:Title: Almost holomorphic Drinfeld modular forms\nby Oguz Gezm
is (Heidelberg University) as part of International seminar on automorphic
forms\n\n\nAbstract\nIn his series of papers from 1970s\, Shimura analyze
d a non-holomorphic operator\, nowadays called the Maass-Shimura operator\
, and later extensively studied almost holomorphic modular forms. He also
discovered their role on constructing class fields as well as the connecti
on with periods of CM elliptic curves. In this talk\, our first goal is to
introduce their positive characteristic counterpart\, almost holomorphic
Drinfeld modular forms. We further relate them to Drinfeld quasi-modular f
orms which leads us to generalize the work of Bosser and Pellarin to a cer
tain extend. Moreover\, we introduce the Maass-Shimura operator $\\delta_k
$ in our setting for any nonnegative integer k and investigate the relatio
n between the periods of CM Drinfeld modules and the values at CM points o
f arithmetic Drinfeld modular forms under the image of $\\delta_k$. If t
ime permits\, we also reveal how to construct class fields by using such v
alues. This is a joint work with Yen-Tsung Chen.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sachi Hashimoto (MPI Leipzig)
DTSTART:20230509T140000Z
DTEND:20230509T150000Z
DTSTAMP:20260404T110644Z
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 a
utomorphic forms\n\n\nAbstract\nFaltings' theorem states that there are fi
nitely many rational points on a nice projective curve defined over the ra
tionals of genus at least 2. The quadratic Chabauty method makes explicit
some cases of Faltings' theorem. Quadratic Chabauty has recent notable suc
cess in determining the rational points of some modular curves. In this ta
lk\, I will explain how we can leverage information from p-adic Gross-Zagi
er formulas to give a new quadratic Chabauty method for certain modular cu
rves. Gross-Zagier formulas relate analytic quantities (special values of
p-adic L-functions) to invariants of algebraic cycles (the p-adic height a
nd logarithm of Heegner points). By using p-adic Gross-Zagier formulas\, t
his new quadratic Chabauty method makes essential use of modular forms to
determine rational points.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Salim Tayou (Harvard)
DTSTART:20230620T140000Z
DTEND:20230620T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/79
DESCRIPTION:Title: Mixed mock modularity of special divisors\nby Salim Tay
ou (Harvard) as part of International seminar on automorphic forms\n\n\nAb
stract\nKudla-Millson and Borcherds have proved some time ago that the gen
erating series of special divisors in orthogonal Shimura varieties are mod
ular forms. In this talk\, I will explain an extension of these results to
toroidal compactifications where we prove that the generating series is a
mixed mock modular form. More precisely\, we find an explicit completion
using theta series associated to rays in the cone decomposition. The proof
relies on intersection theory at the boundary of the Shimura variety. Thi
s recovers and refines recent results of Bruinier and Zemel. The result of
this talk are joint work with Philip Engel and François Greer.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toshiki Matsusaka (Kyushu)
DTSTART:20230530T070000Z
DTEND:20230530T080000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/80
DESCRIPTION:Title: Discontinuity property of a certain Habiro series at roots
of unity\nby Toshiki Matsusaka (Kyushu) as part of International semin
ar on automorphic forms\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ezra Waxman (Haifa)
DTSTART:20230606T140000Z
DTEND:20230606T150000Z
DTSTAMP:20260404T110644Z
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 automor
phic forms\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nina Zubrilina (Princeton)
DTSTART:20230627T140000Z
DTEND:20230627T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/82
DESCRIPTION:Title: Root Number Correlation Bias of Fourier Coefficients of Mod
ular Forms\nby Nina Zubrilina (Princeton) as part of International sem
inar on automorphic forms\n\n\nAbstract\nIn a recent machine learning base
d study\, He\, Lee\, Oliver\, and Pozdnyakov observed a striking\noscillat
ing pattern in the average value of the P-th Frobenius trace of elliptic c
urves of\nprescribed rank and conductor in an interval range. Sutherland d
iscovered that this bias\nextends to Dirichlet coefficients of a much broa
der class of arithmetic L-functions when\nsplit by root number. In my talk
\, I will discuss this root number correlation bias when\nthe average is t
aken over all weight 2 modular newforms. I will point to a source of this\
nphenomenon in this case and compute the correlation function exactly.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sander Zwegers (University of Cologne)
DTSTART:20230613T070000Z
DTEND:20230613T080000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/83
DESCRIPTION:Title: Indefinite Theta Functions: something old\, something new\nby Sander Zwegers (University of Cologne) as part of International sem
inar on automorphic forms\n\n\nAbstract\nIn this talk we give an overview
of the theory of indefinite theta functions and discuss some recent result
s.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan-Willem van Ittersum (MPIM Bonn)
DTSTART:20230418T140000Z
DTEND:20230418T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/84
DESCRIPTION:Title: On quasimodular forms associated to projective representati
ons of symmetric groups\nby Jan-Willem van Ittersum (MPIM Bonn) as par
t of International seminar on automorphic forms\n\n\nAbstract\nWe explain
how one can naturally associate a quasimodular form to a representation of
a symmetric group. We determine its growth and explain how this construct
ion is applied to several problems in enumerative geometry. Finally\, we d
iscuss the difference between linear and projective representations. This
is based on joint work with Adrien Sauvaget.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Annika Burmester (Bielefeld University)
DTSTART:20230704T140000Z
DTEND:20230704T150000Z
DTSTAMP:20260404T110644Z
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 o
f International seminar on automorphic forms\n\n\nAbstract\nMultiple zeta
values and modular forms have a deep\, partly \nmysterious\, connection. T
his can be seen in the Broadhurst-Kreimer \nconjecture\, which was made pa
rtly explicit by Gangl-Kaneko-Zagier in \n2006. Further\, multiple zeta va
lues occur in the Fourier expansion of \nmultiple Eisenstein series as com
puted by Bachmann. We will study this \nconnection in more details on a fo
rmal level. This means\, we review \nformal multiple zeta values and then
introduce the algebra G^f\, which \nshould be seen as a formal version of
multiple Eisenstein series\, and \nalso multiple q-zeta values and polynom
ial functions on partitions \nsimultaneously. We will give a surjective al
gebra morphism from G^f into \nthe algebra of formal multiple zeta values.
\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathilde Gerbelli-Gauthier (McGill University)
DTSTART:20230711T140000Z
DTEND:20230711T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/86
DESCRIPTION:Title: Counting non-tempered automorphic forms using endoscopy
\nby Mathilde Gerbelli-Gauthier (McGill University) as part of Internation
al seminar on automorphic forms\n\n\nAbstract\nHow many automorphic repres
entations of level n have a specified local factor at the infinite places?
When this local factor is a discrete series representation\, this questio
n is asymptotically well-undersertood as $n$ grows. Non-tempered local fac
tors\, on the other hand\, violate the Ramanujan conjecture and should be
very rare. We use the endoscopic classification for representations to qua
ntify this rarity in the case of cohomological representations of unitary
groups\, and discuss some applications to the growth of cohomology of Shim
ura varieties.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksander Horawa (University of Oxford)
DTSTART:20231024T140000Z
DTEND:20231024T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/87
DESCRIPTION:Title: Siegel modular forms and higher algebraic cycles\nby Al
eksander Horawa (University of Oxford) as part of International seminar on
automorphic forms\n\n\nAbstract\nIn recent work with Kartik Prasanna\, we
propose an explicit relationship between the cohomology of vector bundles
on Siegel modular threefolds and higher Chow groups (aka motivic cohomolo
gy groups). For Yoshida lifts of Hilbert modular forms\, we a result of Ra
makrishnan to prove our conjecture. For Yoshida lifts off Bianchi modular
forms\, we show that our conjecture implies the conjecture of Prasanna—V
enkatesh.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Pollack (UCSD)
DTSTART:20231031T150000Z
DTEND:20231031T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/88
DESCRIPTION:Title: Arithmeticity of modular forms on $G_2$\nby Aaron Polla
ck (UCSD) as part of International seminar on automorphic forms\n\n\nAbstr
act\nHolomorphic modular forms on Hermitian tube domains have a good notio
n of Fourier expansion and Fourier coefficients. These Fourier coefficien
ts give the holomorphic modular forms an arithmetic structure: there is a
basis of the space of holomorphic modular forms for which all Fourier coef
ficients of all elements of the basis are algebraic numbers. The group $G
_2$ does not have an associated Shimura variety\, but nevertheless there i
s a class of automorphic functions on $G_2$ which possess a semi-classical
Fourier expansion\, called the quaternionic modular forms. I will explai
n the proof that (in even weight at least 6) the cuspidal quaternionic mod
ular forms possess an arithmetic structure\, defined in terms of Fourier c
oefficients.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaoyu Zhang (University Duisburg-Essen)
DTSTART:20231107T150000Z
DTEND:20231107T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/89
DESCRIPTION:Title: Global theta correspondence mod p for unitary groups\nb
y Xiaoyu Zhang (University Duisburg-Essen) as part of International semina
r on automorphic forms\n\n\nAbstract\nTheta correspondence is a very impor
tant tool in Langlands program. A fundamental problem in theta corresponde
nce is the non-vanishing of the theta lifting of an automorphic representa
tion. In this talk\, we would like to consider a mod p version of the non-
vanishing problem for global theta correspondence for certain reductive du
al pairs of unitary groups. We approach this by looking at the Fourier coe
fficients of the theta lifting and reduce the problem to the equidistribut
ion of unipotent orbits.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robin Zhang (MIT)
DTSTART:20231114T150000Z
DTEND:20231114T160000Z
DTSTAMP:20260404T110644Z
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 clas
s number formula describes the behavior of the Dedekind zeta function at $
s = 0$ and $s = 1$. The Stark and Gross conjectures extend the class numbe
r formula\, describing the behavior of Artin $L$-functions and $p$-adic $L
$-functions at $s = 0$ and $s = 1$ in terms of units. The Harris–Venkate
sh conjecture describes the residue of Stark units modulo $p$\, giving a m
odular analogue to the Stark and Gross conjectures while also serving as t
he first verifiable part of the broader conjectures of Venkatesh\, Prasann
a\, and Galatius. In this talk\, I will draw an introductory picture\, for
mulate a unified conjecture combining Harris–Venkatesh and Stark for wei
ght one modular forms\, and describe the proof of this in the imaginary di
hedral case.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steve Lester (King's College London)
DTSTART:20231121T150000Z
DTEND:20231121T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/91
DESCRIPTION:Title: Around the Gauss circle problem\nby Steve Lester (King'
s College London) as part of International seminar on automorphic forms\n\
n\nAbstract\nHardy conjectured that the error term arising from approximat
ing 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
heuristic that uses i.i.d. random variables to model the lattice points ly
ing near the boundary and square-root cancellation of sums of these random
variables. In this talk I will examine this heuristic and discuss how lat
tice points near the circle interact with one another. This is joint work
with Igor Wigman.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Humphries (University of Virginia)
DTSTART:20231128T150000Z
DTEND:20231128T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/92
DESCRIPTION:Title: Restricted Arithmetic Quantum Unique Ergodicity\nby Pet
er Humphries (University of Virginia) as part of International seminar on
automorphic forms\n\n\nAbstract\nThe quantum unique ergodicity conjecture
of Rudnick and Sarnak concerns the mass equidistribution in the large eige
nvalue limit of Laplacian eigenfunctions on negatively curved manifolds. T
his conjecture has been resolved by Lindenstrauss when this manifold is th
e modular surface assuming these eigenfunctions are additionally Hecke eig
enfunctions\, namely Hecke-Maass cusp forms. I will discuss a variant of t
his problem in this arithmetic setting concerning the mass equidistributio
n of Hecke-Maass cusp forms on submanifolds of the modular surface.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Min Lee (University of Bristol)
DTSTART:20231205T150000Z
DTEND:20231205T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/93
DESCRIPTION:Title: Murmurations of holomorphic modular forms in the weight asp
ect\nby Min Lee (University of Bristol) as part of International semin
ar on automorphic forms\n\n\nAbstract\nIn April 2022\, He\, Lee\, Oliver\,
and Pozdnyakov made an interesting discovery using machine learning – a
surprising correlation between the root numbers of elliptic curves and th
e coefficients of their L-functions. They coined this correlation 'murmura
tions of elliptic curves.' Naturally\, one might wonder whether we can ide
ntify 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. Booker and David Lowry-Duda\, demonstrating murmurations in holomorphic
modular forms.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anke Pohl (University of Bremen)
DTSTART:20231212T150000Z
DTEND:20231212T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/94
DESCRIPTION:Title: Resonances of Schottky surfaces\nby Anke Pohl (Universi
ty of Bremen) as part of International seminar on automorphic forms\n\n\nA
bstract\nThe investigation of $L^2$-Laplace eigenvalues and eigenfunctions
for hyperbolic 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 surface
s of infinite area\, the discrete $L^2$-spectrum is finite. A natural repl
acement are the resonances of the considered hyperbolic surface\, which ar
e the poles of the meromorphically continued resolvent of the Laplacian.\n
These spectral entities also play an important role in number theory and v
arious other fields\, and many fascinating results about them have already
been found\; the generalization of Selberg's $3/16$-theorem by Bourgain\,
Gamburd 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\,
Borthwick noticed for some classes of Schottky surfaces (hyperbolic surfa
ces of infinite area without cusps and conical singularities) that their s
ets 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 discuss an alternative numerical method\, combining tools from dynami
cs\, zeta functions\, transfer operators and thermodynamic formalism\, fun
ctional analysis and approximation theory. The emphasis of the presentatio
n will be on motivation\, heuristics and pictures. This is joint work with
Oscar Bandtlow\, Torben Schick and Alex Weisse.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pietro Mercuri (University of Rome - La Sapienza)
DTSTART:20240116T150000Z
DTEND:20240116T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/95
DESCRIPTION:Title: Automorphism group of Cartan modular curves\nby Pietro
Mercuri (University of Rome - La Sapienza) as part of International semina
r on automorphic forms\n\n\nAbstract\nWe consider the modular curves assoc
iated to a Cartan subgroup of $GL(2\,\\mathbb{Z}/n\\mathbb{Z})$ or to a pa
rticular class of subgroups of $GL(2\,\\mathbb{Z}/n\\mathbb{Z})$ containin
g the Cartan subgroup as a normal subgroup. We describe the automorphism g
roup of these curves when the level is large enough. If time permits\, we
give a sketch of the proof.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wee Teck Gan (National University of Singapore)
DTSTART:20240123T080000Z
DTEND:20240123T090000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/96
DESCRIPTION:Title: The BZSV duality and the relative Langlands program\nby
Wee Teck Gan (National University of Singapore) as part of International
seminar on automorphic forms\n\n\nAbstract\nI will discuss a duality of Ha
miltonian group varieties proposed in a recent preprint of Ben-Zvi\, Sakel
laridis and Venkatesh\, which gives a new paradigm for the relative Langla
nds program.\nI will then discuss a joint work with Bryan Wang on instance
s of this duality for certain Hamiltonian varieties which quantize to gene
ralized Whittaker models.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew de Courcy-Ireland (Stockholm University)
DTSTART:20240130T150000Z
DTEND:20240130T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/97
DESCRIPTION:Title: Six-dimensional sphere packing and linear programming\n
by Matthew de Courcy-Ireland (Stockholm University) as part of Internation
al seminar on automorphic forms\n\n\nAbstract\nThis talk is based on joint
work with Maria Dostert and Maryna Viazovska. We prove that the Cohn--Elk
ies linear programming bound is not sharp for sphere packing in dimension
6. This is in contrast to Viazovska's sharp bound in dimension 8\, even th
ough it is believed that closely related lattices achieve the optimal dens
ities in both dimensions. The proof uses modular forms to construct feasib
le points in a dual program\, generalizing a construction of Cohn and Tria
ntafillou to the case of odd weight and non-trivial Dirichlet character. N
on-sharpness of linear programming is demonstrated by comparing this dual
bound to a stronger upper bound obtained from semidefinite programming by
Cohn\, de Laat\, and Salmon. Our construction has vanishing Fourier coeffi
cients along an arithmetic progression\, which can be explained using skew
self-adjointness of Hecke operators.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Newton (King’s College London)
DTSTART:20240206T150000Z
DTEND:20240206T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/98
DESCRIPTION:Title: Evaluating the wild Brauer group\nby Rachel Newton (Kin
g’s College London) as part of International seminar on automorphic form
s\n\n\nAbstract\nThe local-global approach to the study of rational points
on varieties over number fields begins by embedding the set of rational p
oints on 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\, that contains the rational points. If the set of adelic points is no
n-empty but the Brauer--Manin set is empty then we say there's a Brauer--M
anin obstruction to the existence of rational points on X. Computing the B
rauer--Manin pairing involves evaluating elements of the Brauer group of X
at local 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 poin
t modulo p. For p-torsion elements this is no longer the case: in order to
compute the evaluation map one must know the point to a higher p-adic pre
cision. Classifying Brauer group elements according to the precision requi
red 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
Swinnerton-Dyer's question about which places can play a role in the Brau
er--Manin obstruction. This is joint work with Martin Bright.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elisa Lorenzo Garcia (Université de Neuchâtel)
DTSTART:20240213T150000Z
DTEND:20240213T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/99
DESCRIPTION:Title: On the conductor of Ciani plane quartics\nby Elisa Lore
nzo Garcia (Université de Neuchâtel) as part of International seminar on
automorphic forms\n\n\nAbstract\nIn this talk we will discuss the determi
nation of the conductor exponent of non-special Ciani quartics at primes o
f potentially good reduction in terms of their Ciani invariants. As an int
ermediate step\, we will provide a reconstruction algorithm to construct C
iani quartics with given invariants. During the talk we will consider many
particular examples and extensions of the presented results. (j.w.w. I. B
ouw\, N. Coppola and A. Somoza)\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesse Thorner (UIUC)
DTSTART:20240430T140000Z
DTEND:20240430T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/100
DESCRIPTION:Title: A new zero-free region for Rankin-Selberg L-functions\
nby Jesse Thorner (UIUC) as part of International seminar on automorphic f
orms\n\n\nAbstract\nI will present a new zero-free region for GL(m) x GL(n
) Rankin--Selberg L-functions in the GL(1) twist aspect. The proof is insp
ired by Siegel's lower bound for Dirichlet L-functions at s = 1. This is j
oint work with Gergely Harcos.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Duke (UCLA)
DTSTART:20240507T140000Z
DTEND:20240507T150000Z
DTSTAMP:20260404T110644Z
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\nAb
stract\nI will give a characterization of when a kind of quadratic recipr
ocity holds for irreducible polynomials whose coefficients are in a number
field.\nThe method is based on Gauss’s second proof of classical quadra
tic reciprocity using binary quadratic forms.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Disegni (Aix-Marseille University)
DTSTART:20240514T140000Z
DTEND:20240514T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/102
DESCRIPTION:Title: Gan-Gross-Prasad cycles and derivatives of p-adic L-functi
ons\nby Daniel Disegni (Aix-Marseille University) as part of Internati
onal seminar on automorphic forms\n\n\nAbstract\nCertain Rankin-Selberg mo
tives of rank n(n+1) are endowed with algebraic cycles arising from maps o
f unitary Shimura varieties. Gan-Gross-Prasad conjectured that these cycle
s are analogous to Heegner points\, in the sense that their nontriviality
should be detected by derivatives of L-functions.\nI will propose another
nontriviality criterion\, based on p-adic L-functions. Under some local co
nditions\, this variant can be established in a refined quantitative form\
, via the construction and comparison two p-adic relative-trace formulas.
(Joint work with Wei Zhang.)\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fu-Tsun Wei (National Tsing Hua University)
DTSTART:20240521T140000Z
DTEND:20240521T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/103
DESCRIPTION:Title: Chowla-Selberg phenomenon over function fields\nby Fu-
Tsun Wei (National Tsing Hua University) as part of International seminar
on automorphic forms\n\n\nAbstract\nIn this talk\, I will first determine
the algebraic relations among various special gamma values over function f
ields. The result is based on the intrinsic relations between gamma values
\nin question and periods of CM dual t-motives\, which are interpreted in
terms of their “distributions”. This enables us to express every "abel
ian" CM period by a suitable product of special gamma values (up to an alg
ebraic multiple)\, and derive a Chowla–Selberg-type formula in the funct
ion field case.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hohto Bekki (MPIM Bonn)
DTSTART:20240611T140000Z
DTEND:20240611T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/104
DESCRIPTION:Title: On the denominators of the special values of the partial z
eta functions of real quadratic fields\nby Hohto Bekki (MPIM Bonn) as
part of International seminar on automorphic forms\n\n\nAbstract\nIt is cl
assically known that the special values of the partial zeta functions of r
eal quadratic fields\, or more generally\, of totally real fields at negat
ive integers are rational numbers. In this talk\, I would like to discuss
the denominators of these rational numbers in the case of real quadratic f
ields. \nMore precisely\, Duke recently presented a conjecture which gives
a universal upper bound for the denominators of these special values of t
he partial zeta functions of real quadratic fields. I would like to explai
n that by using Harder's theory on the denominator of the Eisenstein class
for $\\operatorname{SL}(2\,\\mathbb Z)$\, we can prove the conjecture of
Duke and moreover the sharpness of his upper bound. This is a joint work w
ith Ryotaro Sakamoto.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miao Gu (University of Michigan)
DTSTART:20240618T140000Z
DTEND:20240618T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/105
DESCRIPTION:Title: The fiber bundle method applied to triple product L-functi
ons\nby Miao Gu (University of Michigan) as part of International semi
nar on automorphic forms\n\n\nAbstract\nThe Poisson summation conjecture o
f Braverman-Kazhdan\, L. Lafforgue\, Ngô\, and Sakellaridis predicts that
spherical varieties (or Whittaker induction thereof) over a global field
admit a theory of Fourier analysis\, including a generalized Poisson summa
tion formula. The fiber bundle method is a technique for proving the Poiss
on summation conjecture for spherical varieties that can be written as a f
amily of simpler spherical varieties for which the Poisson summation conje
cture is known. In this talk\, I will first explain how to relate a genera
lized Whittaker induction to triple product L-functions. Then I will expla
in the fiber bundle method and describe an approach to applying it to prov
e the expected analytic properties of the triple product L-functions. This
is joint work with Jayce Getz\, Chun-Hsien Hsu\, and Spencer Leslie.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lola Thompson (Utrecht University)
DTSTART:20240625T140000Z
DTEND:20240625T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/106
DESCRIPTION:Title: Salem numbers and short geodesics\nby Lola Thompson (U
trecht University) as part of International seminar on automorphic forms\n
\n\nAbstract\nWe will discuss how Mahler measure and related concepts (e.g
.\, Salem numbers) are connected to problems about lengths of geodesics on
arithmetic hyperbolic manifolds. As a result\, by solving problems using
tools from number theory\, we are able to answer quantitative questions in
spectral geometry. This talk will build towards two goals: showing that s
hort geodesics on arithmetic hyperbolic surfaces are rare\, and showing th
at\, on average\, geodesic lengths of non-compact arithmetic hyperbolic or
bifolds appear with high multiplicity. This talk is based on joint work wi
th Mikhail Belolipetsky\, Matilde Lalín\, and Plinio G. P. Murillo\; and
with Benjamin Linowitz\, D. B. McReynolds\, and Paul Pollack.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Möller (Goethe University Frankfurt)
DTSTART:20240702T140000Z
DTEND:20240702T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/107
DESCRIPTION:Title: Spectral decomposition and Siegel-Veech transforms: The ca
se of marked tori\nby Martin Möller (Goethe University Frankfurt) as
part of International seminar on automorphic forms\n\n\nAbstract\nGenerali
zing the well-known construction of Eisenstein series on the modular curve
s\, Siegel-Veech transforms provide a natural construction of square-integ
rable functions on strata of differentials on Riemannian surfaces. Even th
e case of marked tori\, a homogeneous space but not for a reductive group
provides features that we highlight in this talk with an eye on the genera
l case.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hang Xue (University of Arizona)
DTSTART:20240709T150000Z
DTEND:20240709T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/108
DESCRIPTION:Title: Fourier-Jacobi periods on unitary groups\nby Hang Xue
(University of Arizona) as part of International seminar on automorphic fo
rms\n\n\nAbstract\nWe prove the Gan-Gross-Prasad conjecture for Fourier-Ja
cobi periods on unitary groups via relative trace formulae.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haluk Şengün (University of Sheffield)
DTSTART:20240716T140000Z
DTEND:20240716T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/109
DESCRIPTION:Title: Theta correspondence via C*-algebras\nby Haluk Şengü
n (University of Sheffield) as part of International seminar on automorphi
c forms\n\n\nAbstract\nThe local theta correspondence sets up a bijection
between certain subsets of admissible duals of suitable pairs of reductive
groups. There are two special cases in which the correspondence is known
to enjoy extra features\, the ‘equal rank’ case where temperedness is
preserved and the ‘stable range’ case where unitarity is preserved. In
joint work with Bram Mesland (Leiden)\, we show that in these special cas
es\, the local theta correspondence is actually given by a Morita equivale
nce of suitable \nC*\n-algebras. I will try to expose this result and\, ti
me permitting\, some applications.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harald Grobner (University of Vienna)
DTSTART:20241022T140000Z
DTEND:20241022T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/110
DESCRIPTION:Title: On the cohomology of $SL(n\,\\mathbb Z)$ beyond the "stabl
e range"\nby Harald Grobner (University of Vienna) as part of Internat
ional seminar on automorphic forms\n\n\nAbstract\nThe cohomology of the gr
oup $SL(n\,\\mathbb{Z})\, n>1$\, plays a fundamental role in geometry\, to
pology and representation theory\, while yielding many number theoretical
applications: For instance\, Borel used his description of $H^*(SL(n\,\\ma
thbb Z))$ to compute the algebraic K-theory of the integers\; whereas the
(non-)vanishing of $H^*(SL(n\,\\mathbb Z))$ tells a lot about the existenc
e of certain automorphic forms. In this talk we will study the cohomology
of $SL(n\,\\mathbb Z)$\, „right outside“ of what one calls the stable
range. More precisely\, we will show new non-vanishing results in degrees
n−1 and n. As a byproduct\, we will also answer a question\, recently as
ked by F. Brown for n=6 and explain a phenomenon for n=8\, which has been
considered by A. Ash. (This is joint work with N. Grbac.)\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qihang Sun (University of Lille)
DTSTART:20241029T150000Z
DTEND:20241029T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/111
DESCRIPTION:Title: Exact formulae for ranks of partitions\nby Qihang Sun
(University of Lille) as part of International seminar on automorphic form
s\n\n\nAbstract\nDyson's ranks provided a new understanding of the integer
partition function\, especially of its congruence properties. In 2009\, B
ringmann used the circle method to prove an asymptotic formula for the Fou
rier coefficients of rank generating functions. In this talk\, we will pro
ve that the asymptotic formula\, when summing up to infinity\, converges a
nd becomes a Rademacher-type exact formula for the rank of partitions.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Petrow (UCL)
DTSTART:20241105T150000Z
DTEND:20241105T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/112
DESCRIPTION:Title: Counting characters on algebraic tori according to their L
anglands L-functions\nby Ian Petrow (UCL) as part of International sem
inar on automorphic forms\n\n\nAbstract\nGiven a connected reductive group
G over a global field\, Langlands introduced the automorphic\nL-function
L(s\, π\, r) of a cuspidal automorphic representation π of G and a compl
ex representation r of the L-group of G. While in general very little is k
nown about Langlands L-functions\, if G = T is a torus the properties of t
hese L-functions can be obtained from class field theory and one can attem
pt to study analytic problems pertaining to them. In this talk I will desc
ribe some analytic results on automorphic characters of tori with respect
to the analytic conductor of L(s\, π\, r)\, attempting to focus on the in
terplay of analytic and\nalgebraic ideas that arise in the proofs.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leila Smajlovic (University of Sarajevo)
DTSTART:20241112T150000Z
DTEND:20241112T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/113
DESCRIPTION:Title: On an extension of the Rohrlich-Jensen formula\nby Lei
la Smajlovic (University of Sarajevo) as part of International seminar on
automorphic forms\n\n\nAbstract\nWe revisit the Rohrlich-Jensen formula an
d prove that\, in the case of any Fuchsian group of the first kind with on
e cusp it can be viewed as a regularized inner product of special values o
f two Poincar\\'e series\, one of which is the Niebur-Poincaré series and
the other is the resolvent kernel of the Laplacian. The regularized inner
product can be seen as a type of Maass-Selberg relation. In this form\, w
e develop a Rohrlich-Jensen formula associated to any Fuchsian group $\\Ga
mma$ of the first kind with one cusp by employing a type of Kronecker lim
it formula associated to the resolvent kernel. We present two examples of
our main result: First\, when $\\Gamma$ is the full modular group\; and s
econd when $\\Gamma$ is an Atkin-Lehner group $\\Gamma_{0}(N)^+$.\nThis wo
rk is joint with James Cogdell and Jay Jorgenson.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laure Flapan (Michigan State University)
DTSTART:20241119T150000Z
DTEND:20241119T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/114
DESCRIPTION:Title: Cones of Noether-Lefschetz divisors and moduli of hyperkä
hler manifolds\nby Laure Flapan (Michigan State University) as part of
International seminar on automorphic forms\n\n\nAbstract\nWe describe how
to compute cones of Noether-Lefschetz divisors on orthogonal modular vari
eties with a particular view towards moduli spaces of polarized K3 surface
s and hyperkähler manifolds. We then describe some geometric applications
of these cone computations for these moduli spaces. This is joint work wi
th I. Barros\, P. Beri\, and B. Williams.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthias Storzer (University College Dublin)
DTSTART:20241126T150000Z
DTEND:20241126T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/115
DESCRIPTION:Title: Knots\, q-series\, and modular forms\nby Matthias Stor
zer (University College Dublin) as part of International seminar on automo
rphic forms\n\n\nAbstract\nTo study knots\, we use knot invariants like th
e colored Jones polynomials (CJP). For alternating knots\, it is known tha
t the CJP converge to a well-defined q-series\, the tail of the CJP. For s
everal but not all knots with up to 10 crossings\, the tail of the CJP can
be written as a product of (partial) theta functions and thus has modular
properties. In this talk\, we present a general formula for a class of kn
ots.Moreover\, we argue that the tail of the CJP for some knots does not h
ave any modular properties. We also briefly discuss potential topological
interpretations of the (non-)modularity.\nThis is joint work with Robert O
sburn.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cormac O'Sullivan (CUNY)
DTSTART:20241203T150000Z
DTEND:20241203T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/116
DESCRIPTION:Title: Topographs and some infinite series\nby Cormac O'Sulli
van (CUNY) as part of International seminar on automorphic forms\n\n\nAbst
ract\nThe Fibonacci numbers are a familiar recursive sequence. Topographs
are a kind of two dimensional version conjured up by J.H. Conway in his st
udy of integral binary quadratic forms. These forms are ax^2 + bxy + cy^2
with integer coefficients\, and have a long history in number theory. We'l
l review Conway's classification of topographs into 4 types and look at so
me new discoveries. Applications are to new class number formulas and a si
mplification of a proof of Gauss related to sums of three squares. We'll a
lso see how several infinite series over all the numbers in a topograph ma
y be evaluated explicitly. This generalizes and extends results of Hurwitz
and more recent authors and requires a certain Poincare series.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yiannis Petridis (UCL)
DTSTART:20250114T150000Z
DTEND:20250114T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/118
DESCRIPTION:Title: Counting and equidistribution\nby Yiannis Petridis (UC
L) as part of International seminar on automorphic forms\n\n\nAbstract\nI
will discuss how counting orbits in hyperbolic spaces lead to interesting
number theoretic problems. The counting problems (and the associated equid
istribution) can be studied with various methods\, and I will emphasize au
tomorphic form techniques\, originating in the work of H. Huber and studie
d extensively by A. Good. My collaborators is various aspects of this proj
ect are Chatzakos\, Lekkas\, Risager\, and Voskou.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romain Branchereau (McGill University)
DTSTART:20250121T150000Z
DTEND:20250121T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/119
DESCRIPTION:Title: Kudla-Millson lift on the symmetric space of $SL_N$\nb
y Romain Branchereau (McGill University) as part of International seminar
on automorphic forms\n\n\nAbstract\nI will present a construction of a map
from the homology in degree N-1 of locally symmetric spaces associated to
$SL_N$\, to modular forms of weight N. The image of a cycle C by this map
is a modular form whose Fourier coefficients are intersection numbers bet
ween C and a family of generalized modular symbols on the locally symmetri
c space. This map can be seen as a Kudla-Millson theta lift for the dual p
air $(SL_N\, SL_2)$ and also resembles a construction of Bergeron-Charollo
is-Garcia.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liyang Yang (Princeton University)
DTSTART:20250128T150000Z
DTEND:20250128T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/120
DESCRIPTION:Title: Uniform Non-vanishing of Hilbert Modular $L$-values\nb
y Liyang Yang (Princeton University) as part of International seminar on a
utomorphic forms\n\n\nAbstract\nLet $\\mathcal{F}(\\mathbf{k}\, \\mathfrak
{q})$ be the set of normalized Hilbert newforms of weight $\\mathbf{k}$ an
d prime level $\\mathfrak{q}$. In this talk\, we will present a uniform po
sitive proportion of $ \\# \\{\\pi \\in \\mathcal{F}(\\mathbf{k}\, \\mathf
rak{q}) : L(1/2\, \\pi) \\neq 0\\}$ as $ \\# \\mathcal{F}(\\mathbf{k}\, \\
mathfrak{q}) \\to +\\infty$. This is joint work with Zhining Wei and Shifa
n Zhao.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hazem Hassan (McGill)
DTSTART:20241217T150000Z
DTEND:20241217T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/121
DESCRIPTION:Title: p-adic higher Green's functions for Stark-Heegner Cycles\nby Hazem Hassan (McGill) as part of International seminar on automorph
ic forms\n\n\nAbstract\nHeegner Cycles are higher weight generalizations o
f Heegner points on Modular curves. As such\, one expects them to capture
similar arithmetic and modular properties to Heegner points. The higher di
mensional nature of Heegner cycles makes them less amenable to algebro-geo
metric and deformation theoretic approaches. I will introduce Stark-Heegne
r Cycles\, which are a conjectural analogue to Heegner Cycles in the theor
y of Real Multiplication. They are defined through p-adic analytic means.
Then\, I will describe a p-adic pairing on these cycles which behaves as a
local height pairing. When one of the cycles is principal\, the pairing c
omputationally seems to produce algebraic integers living in class fields
of real quadratic fields.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ameya Pitale (University of Oklahoma)
DTSTART:20250204T150000Z
DTEND:20250204T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/122
DESCRIPTION:Title: Lifting of Maass forms to O(1\,8n+1) and applications to t
he sup-norm problem\nby Ameya Pitale (University of Oklahoma) as part
of International seminar on automorphic forms\n\n\nAbstract\nIn a joint pa
per with Yingkun Li and Hiroaki Narita\, we had constructed liftings from
Maass forms with respect to $\\mathrm{SL}_2(\\mathbb{Z})$ to Maass forms o
n $\\mathrm{O}(1\,8n+1)$\, which violated the Generalized Ramanujan conjec
ture. These were constructed via Borcherds theta lifts and we were able to
give explicit formulas for their Fourier coefficients. In a recent joint
work with Simon Marshall and Hiroaki Narita\, we first computed the Peters
son inner product of the lift using the Rallis inner product formula. This
essentially involves an archimedean integral computation. These are usual
ly very complicated and intractable\, but in this case we are able to get
an exact formula for the Petersson norm. Explicit formulas for the Fourier
coefficients and Petersson norm are the essential ingredients of one of t
he approaches to obtain sup-norm bounds on these Maass forms. Investigatio
ns regarding sup-norm bounds for modular forms in the $\\mathrm{GL}(2)$ ca
se has been recently a very active area of research. Using the method ment
ioned above\, as well as a pre-trace formula approach\, we obtain the firs
t sup-norm bounds results for these orthogonal groups.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mads Christensen (UCL)
DTSTART:20250211T150000Z
DTEND:20250211T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/123
DESCRIPTION:Title: Linking numbers and non-holomorphic Siegel modular forms\nby Mads Christensen (UCL) as part of International seminar on automorp
hic forms\n\n\nAbstract\nIn an arithmetic hyperbolic 3-manifold there is a
n abundance of naturally defined closed geodesics. I will present a result
which relates linking number invariants of these geodesics to the Fourier
coefficients of certain non-holomorphic Siegel modular forms of genus 2.\
n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seewoo Lee (UC Berkeley)
DTSTART:20250429T140000Z
DTEND:20250429T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/124
DESCRIPTION:Title: Algebraic proof of modular form inequalities for optimal s
phere packings\nby Seewoo Lee (UC Berkeley) as part of International s
eminar on automorphic forms\n\n\nAbstract\nWe give algebraic proofs of Via
zovska and Cohn-Kumar-Miller-Radchenko-Viazovska’s modular form inequali
ties for 8 and 24-dimensional optimal sphere packings. If time permits\, w
e also discuss follow-up in-progress works on other LP problems.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gene Kopp (Louisiana State University)
DTSTART:20250506T140000Z
DTEND:20250506T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/125
DESCRIPTION:Title: The Shintani–Faddeev modular cocycle: Stark units from q
-Pochhammer ratios\nby Gene Kopp (Louisiana State University) as part
of International seminar on automorphic forms\n\n\nAbstract\nWe give a new
interpretation of Stark units associated to real quadratic fields as spec
ial "real multiplication values" of a modular cocycle described by complex
meromorphic continuation of a simple infinite product. The cocycle encode
s the modular transformations of the infinite q-Pochhammer symbol and is r
elated to the Shintani–Barnes double sine funciton and the Faddeev quant
um dilogarithm. As a corollary\, we describe some intriguing features of t
he asymptotic behavior of the infinite q-Pochhammer symbol as the modular
parameter approaches a real quadratic number.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/125/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhiyuan Li (SCMS\, Fudan University)
DTSTART:20250513T080000Z
DTEND:20250513T090000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/126
DESCRIPTION:Title: Theta series and tautological cycles on orthogonal Shimura
varieties\nby Zhiyuan Li (SCMS\, Fudan University) as part of Interna
tional seminar on automorphic forms\n\n\nAbstract\nIn this talk\, I will e
xplore the fascinating interplay between lattice theory and vector- valued
modular forms via theta series\, presenting an elegant connection that br
idges these areas. I will discuss its applications in the study of cycle t
heory on orthogonal Shimura varieties. One of our findings reveal that the
Picard group of the Baily-Borel compactification of a broad class of Shim
ura varieties is isomorphic to ℤ. I will also explain the geometric moti
vation of this project. Most results are joint work with Huang\, Müller a
nd Ye.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naomi Sweeting (Princeton University)
DTSTART:20250610T140000Z
DTEND:20250610T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/127
DESCRIPTION:Title: The arithmetic of Fourier coefficients of Gan-Gurevich lif
ts on $G_2$\nby Naomi Sweeting (Princeton University) as part of Inter
national seminar on automorphic forms\n\n\nAbstract\nModular forms on exce
ptional groups carry a surprisingly rich arithmetic structure. For instanc
e\, modular forms on $G_2$ have a theory of Fourier expansions\, in which
the coefficients are indexed by cubic rings (e.g. rings of integers in cub
ic field extensions of $\\mathbb{Q}$). This talk is about the Gan-Gurevich
lifts\, which are modular forms on $G_2$ arising by Langlands functoriali
ty from classical modular forms on $PGL_2$. Gross conjectured in 2000 that
the norm squared of the Fourier coefficients of a Gan-Gurevich lift encod
e the cubic-twisted L values of the corresponding classical cusp form (ech
oing Waldspurger's work on Fourier coefficients of half-integral weight mo
dular forms). We prove this conjecture for a large class of Gan-Gurevich l
ifts coming from CM forms\, thus giving the first complete examples of Gro
ss's conjecture. Based on joint work in progress with Petar Bakic\, Alex H
orawa\, and Siyan Daniel Li-Huerta.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marti Roset Julia (McGill University)
DTSTART:20250527T140000Z
DTEND:20250527T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/128
DESCRIPTION:Title: Rigid cocycles for $SL_n$ and their values at special poin
ts\nby Marti Roset Julia (McGill University) as part of International
seminar on automorphic forms\n\n\nAbstract\nThe theory of complex multipli
cation implies that the values of modular functions at CM points belong to
abelian extensions of imaginary quadratic fields. In this talk\, we propo
se a conjectural extension of this phenomenon to the setting of totally re
al fields. Generalizing the work of Darmon\, Pozzi\, and Vonk\, we constru
ct rigid cocycles for $SL_n$\, which play the role of modular functions\,
and define their values at points associated with totally real fields. The
construction of these cocycles originates from a topological source: the
Eisenstein class of a torus bundle. This is ongoing joint work with Peter
Xu.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Mihatsch (Zhejiang University)
DTSTART:20250603T140000Z
DTEND:20250603T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/129
DESCRIPTION:Title: Construction of Gaussian test functions\nby Andreas Mi
hatsch (Zhejiang University) as part of International seminar on automorph
ic forms\n\n\nAbstract\nThe relative trace formula comparison of Jacquet--
Rallis relates two trace formulas: one for general linear groups and one f
or unitary groups. In this context\, one considers the transfer of test fu
nctions between the two sides. At the archimedean place\, the Gaussian for
the positive definite unitary group provides a distinguished test functio
n that often comes up in arithmetic settings. Accordingly\, it is of inter
est to understand its transfers to the general linear side. In my talk\, I
will explain a direct construction of such transfers which is based on Ku
dla--Millson theory. This is joint work with Siddarth Sankaran and Tonghai
Yang.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ziqi Guo (Peking Unviersity)
DTSTART:20251104T140000Z
DTEND:20251104T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/130
DESCRIPTION:Title: Modular Heights of Unitary Shimura Varieties\nby Ziqi
Guo (Peking Unviersity) as part of International seminar on automorphic fo
rms\n\n\nAbstract\nThe goal of our work is to prove a formula expressing t
he modular height of a unitary Shimura variety over a CM number field in t
erms of the logarithm derivative of the Hecke L-function associated with t
he CM extension. In a more specific term\, we will introduce a global cano
nical integral model of such a unitary Shimura variety\, and compute the a
rithmetic top self-intersection number of a canonical arithmetic line bund
le with Hermitian metric on such integral model. At the same time\, we als
o delve into a thorough investigation of the arithmetic generating series
of divisors on unitary Shimura varieties. Therefore\, we will also obtain
the so-called "arithmetic Siegel-Weil formula" in our setting.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhiyu Zhang (Stanford University)
DTSTART:20251111T150000Z
DTEND:20251111T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/131
DESCRIPTION:Title: Twisted period integrals and applications\nby Zhiyu Zh
ang (Stanford University) as part of International seminar on automorphic
forms\n\n\nAbstract\nThe Waldspurger formula reveals a striking relation b
etween twisted versions of Hecke periods and central L-values of modular f
orms. The use of quadratic twists is crucial in many applications\, includ
ing equidistribution of integer points on spheres and of Heegner points. \
n\nIn this talk\, I will present the twisted Gan-Gross-Prasad conjecture o
n twisted versions of tensor product L-functions. In particular\, it provi
des new information on twisted symmetric square L-functions of modular for
ms\, via the Langlands transfer of quadratic base change.\n\nI will outlin
e a proof of this conjecture under some local assumptions\, based on joint
work with Lu and Wang. There are some essential differences compared to u
ntwisted settings\, leading to new applications and new questions.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Phillips (College of Idaho)
DTSTART:20251118T140000Z
DTEND:20251118T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/132
DESCRIPTION:Title: The Gross-Zagier formula on singular moduli for Shimura cu
rves\nby Andrew Phillips (College of Idaho) as part of International s
eminar on automorphic forms\n\n\nAbstract\nThe Gross-Zagier formula on sin
gular moduli\, which gives a formula for the prime factorization of differ
ences of j-values\, can be seen as a calculation of the intersection multi
plicity of two CM divisors on the integral model of a modular curve. We wi
ll discuss a generalization of this result to a Shimura curve.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Radu Toma (IMJ-PRG)
DTSTART:20251125T140000Z
DTEND:20251125T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/133
DESCRIPTION:Title: Refined equidistribution of Hecke points and cryptography<
/a>\nby Radu Toma (IMJ-PRG) as part of International seminar on automorphi
c forms\n\n\nAbstract\nA classic theorem states that\, fixing a Euclidean
lattice L\, its sublattices of large index equidistribute in the space of
lattices. The literature leaves open the question: how does the rate of eq
uidistribution depend on L? In joint work with de Boer\, Page\, and Wesolo
wski\, we answer this using automorphic theory and geometry of numbers. Mo
tivated by lattice-based cryptography\, we apply the result to show that a
computational problem called SIVP is as hard for Haar random module latti
ces as it is in the worst case.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giada Grossi (Paris 13)
DTSTART:20251202T151500Z
DTEND:20251202T161500Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/134
DESCRIPTION:Title: From Asai to Triple Product: Euler Systems and p-adic L-fu
nctions\nby Giada Grossi (Paris 13) as part of International seminar o
n automorphic forms\n\n\nAbstract\nI will discuss recent work on Euler sys
tems and p-adic L-functions for Hilbert modular forms. In the case of Asai
motives attached to quadratic Hilbert modular forms\, a Rankin–Selberg-
type integral yields both the Asai–Flach Euler system and a p-adic L-fun
ction. I will outline how their relation\, proved in joint work with D. Lo
effler and S. Zerbes\, leads to new cases of the Bloch-–Kato conjecture.
I will also present ongoing work with A. Graham on the twisted triple pro
duct L-function. Ichino’s integral and higher Hida theory play a central
role in constructing a p-adic L-function in the “Hilbert dominant regio
n”\, with the goal of approaching higher-rank analogues of the Birch–S
winnerton-Dyer conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francois Greer (Michigan State University)
DTSTART:20251209T140000Z
DTEND:20251209T150000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/135
DESCRIPTION:Title: Kudla's conjecture in cohomology for unitary Shimura varie
ties\nby Francois Greer (Michigan State University) as part of Interna
tional seminar on automorphic forms\n\n\nAbstract\nThe generating series f
or special cycles in a unitary Shimura variety $X$ associated to a Hermiti
an lattice of signature $(1\,n)$ is a modular form. Such a Shimura variety
has a unique toroidal compactification\, and one can consider the closure
s of the special cycles there. We prove that for codimension up to the mid
dle\, the generating series for these closures is quasi-modular\, and expl
ain how to make boundary corrections to restore modularity\, answering a q
uestion of Kudla. This is based on joint work with Salim Tayou.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitrii Adler (MPIM Bonn)
DTSTART:20260113T150000Z
DTEND:20260113T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/136
DESCRIPTION:Title: Jacobi forms and modular differential equations\nby Di
mitrii Adler (MPIM Bonn) as part of International seminar on automorphic f
orms\n\n\nAbstract\nThe Serre derivative is a differential operator that r
aises the weight of a modular form by 2. One possible generalization of th
e Serre derivative to the setting of Jacobi forms is a modification of the
heat operator involving the quasi-modular Eisenstein series E_2. In this
talk\, I will present an approach to constructing modular differential equ
ations for Jacobi forms with respect to this operator. This method makes i
t possible to describe solutions of first- and second-order modular differ
ential equations (Kaneko–Zagier type equations)\, to construct higher-or
der differential equations\, and to obtain applications to the elliptic ge
nus of Calabi–Yau manifolds. This is joint work with Valery Gritsenko.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katy Woo (Stanford University)
DTSTART:20260120T160000Z
DTEND:20260120T170000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/137
DESCRIPTION:Title: Sums of Hecke eigenvalues along polynomials and arithmetic
applications\nby Katy Woo (Stanford University) as part of Internatio
nal seminar on automorphic forms\n\n\nAbstract\nWe study sums of absolute
values of Hecke eigenvalues of $\\textrm{GL}(2)$ representations that are
tempered at all finite places. We show that these sums exhibit logarithmic
savings over the trivial bound if and only if the representation is cuspi
dal. Further\, we connect the problem of studying the sums of Hecke eigenv
alues along polynomial values to the base change problem for $\\textrm{GL}
(2).$ Finally\, we will describe some arithmetic applications of bounds on
these sums for counting rational points on del Pezzo surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/137/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pan Yan (University of Arizona)
DTSTART:20260127T150000Z
DTEND:20260127T160000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/138
DESCRIPTION:Title: On the global Gan-Gross-Prasad conjecture for GSpin groups
\nby Pan Yan (University of Arizona) as part of International seminar
on automorphic forms\n\n\nAbstract\nWe prove one direction of the global G
an-Gross-Prasad conjecture for generic representations of GSpin groups\, n
amely the implication from the non-vanishing of the Bessel period to the n
on-vanishing of the central value of L-function. The proof is based on a n
ew Rankin-Selberg integral for GSpin groups using Bessel models.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/138/
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BEGIN:VEVENT
SUMMARY:Tariq Osman (University of Zurich)
DTSTART:20260203T160000Z
DTEND:20260203T170000Z
DTSTAMP:20260404T110644Z
UID:IntSemAutForms/139
DESCRIPTION:Title: Bounds for Theta Sums with Rational Parameters\nby Tar
iq Osman (University of Zurich) as part of International seminar on automo
rphic forms\n\n\nAbstract\nA theta sum is an exponential sum of the form $
S_N^f(t\, r\, s) := \\sum_{n \\in \\mathbb Z + s}f(n/N)e(1/2 (t n^2 + r n)
)$\, where $t\, r$ and $s$ are real numbers and $f$ is a sufficiently regu
lar cut-off function. Upper bounds for theta sums have been well studied\,
and in this generality\, estimates go back to work of J. Marklof\, L. Fla
minio and G. Forni\, among others. Through their work one has\, for instan
ce\, that for Lebesgue almost every $t$ the estimate $|S_N^f (t\,r\,s)| \\
ll_{f\,t} \\sqrt N \\log N$ holds\, for any pair $(r\,s)$. We contrast thi
s result by showing that there exist rational pairs $(r\,s)$ such that for
any Schwartz cut-off $f$\, there exists a constant $C$ independent of $t$
for which $|S_N^f| \\leq C \\sqrt N$. A key feature of the proof is to re
alise that $S_N^f$\, when normalised appropriately\, agrees with a theta
function $\\Theta_f$ along a special curve known as a horocycle lift\, whi
ch depends on the pair $(r\,s)$. The result follows from showing that for
certain rational pairs $(r\,s)$\, the horocycle lift avoids all regions wh
ere the modulus of $\\Theta_f$ can be large. Time permitting\, we will als
o discuss extensions of this result to theta sums in more than one variabl
e. This talk is based on joint work with Francesco Cellarosi as well as a
separate project with Michael Lu.\n
LOCATION:https://stable.researchseminars.org/talk/IntSemAutForms/139/
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