BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Marc Masdeu (Universitat Autònoma de Barcelona)
DTSTART:20201203T143000Z
DTEND:20201203T145000Z
DTSTAMP:20260404T094319Z
UID:CompArithGroups/1
DESCRIPTION:Title: Quaternionic rigid meromorphic cocycles\nby Marc Masdeu
(Universitat Autònoma de Barcelona) as part of Computations with Arithme
tic Groups\n\n\nAbstract\nRigid meromorphic cocycles were introduced by Da
rmon and Vonk as a conjectural p-adic extension of the theory of singular
moduli to real quadratic base fields. They are certain cohomology classes
of $SL_2(\\mathbb{Z}[1/p])$ which can be evaluated at real quadratic irrat
ionalities and the values thus obtained are conjectured to lie in algebrai
c extensions of the base field.\n\nI will present joint work with X.Guitar
t and X.Xarles\, in which we generalize (and somewhat simplify) this const
ruction to the setting where $SL_2(\\mathbb{Z}[1/p])$ is replaced by an or
der in an indefinite quaternion algebra over a totally real number field $
F$. These quaternionic cohomology classes can be evaluated at elements in
almost totally complex extensions $K$ of $F$\, and we conjecture that the
corresponding values lie in algebraic extensions of $K$. I will show some
new numerical evidence for this conjecture\, along with some interesting q
uestions allowed by this flexibility.\n
LOCATION:https://stable.researchseminars.org/talk/CompArithGroups/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Graham Ellis (National University of Ireland\, Galway)
DTSTART:20201203T150000Z
DTEND:20201203T152000Z
DTSTAMP:20260404T094319Z
UID:CompArithGroups/2
DESCRIPTION:Title: An algorithm for computing Hecke operators\nby Graham E
llis (National University of Ireland\, Galway) as part of Computations wit
h Arithmetic Groups\n\n\nAbstract\nI will describe an approach to computin
g Hecke operators on the integral cuspidal cohomology of congruence subgro
ups of $SL_2(\\mathcal{O}_d)$ over various rings of quadratic integers $\\
mathcal{O}_d$. The approach makes use of an explicit contracting homotopy
on a classifying space for $SL_2(\\mathcal{O}_d)$. The approach\, which ha
s been partially implemented\, is also relevant for computations on congru
ence subgroups of $SL_m(\\mathbb{Z})$\, $m\\geq2$ (where it has been fully
implemented for $m=2$).\n
LOCATION:https://stable.researchseminars.org/talk/CompArithGroups/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angelica Babei (Centre de recherches mathématiques)
DTSTART:20201203T154500Z
DTEND:20201203T160500Z
DTSTAMP:20260404T094319Z
UID:CompArithGroups/3
DESCRIPTION:Title: Zeros of period polynomials for Hilbert modular forms\n
by Angelica Babei (Centre de recherches mathématiques) as part of Computa
tions with Arithmetic Groups\n\n\nAbstract\nThe study of period polynomial
s for classical modular forms has emerged due to their role in Eichler coh
omology. In particular\, the Eichler-Shimura isomorphism gives a correspon
dence between cusp eigenforms and their period polynomials. The coefficien
ts of period polynomials also encode critical L-values for the associated
modular form and thus contain rich arithmetic information. Recent works ha
ve considered the location of the zeros of period polynomials\, and it has
been shown that in various settings\, their zeros lie on a circle centere
d at the origin. \n\nIn this talk\, I will describe joint work with Larry
Rolen and Ian Wagner\, where we introduce period polynomials for Hilbert m
odular forms of level one and prove that their zeros lie on the unit circl
e. In particular\, I will detail some of the computational tools we used i
n our proof.\n
LOCATION:https://stable.researchseminars.org/talk/CompArithGroups/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Breen (Clemson University)
DTSTART:20201203T161500Z
DTEND:20201203T163500Z
DTSTAMP:20260404T094319Z
UID:CompArithGroups/4
DESCRIPTION:Title: A trace formula for Hilbert modular forms\nby Benjamin
Breen (Clemson University) as part of Computations with Arithmetic Groups\
n\n\nAbstract\nWe present an explicit trace formula for Hilbert modular fo
rms. The Jacquet-Langlands correspondence relates spaces of Hilbert modula
r forms to spaces of quaternionic modular forms\; the latter being far mor
e amenable to computations. We discuss how to compute traces of Hecke oper
ators on spaces of quaternionic modular forms and provide explicit example
s for some definite quaternion algebras.\n
LOCATION:https://stable.researchseminars.org/talk/CompArithGroups/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Avner Ash (Boston College)
DTSTART:20201203T170000Z
DTEND:20201203T172000Z
DTSTAMP:20260404T094319Z
UID:CompArithGroups/5
DESCRIPTION:Title: Cohomology of congruence subgroups of $SL_3(\\mathbb{Z})$ a
nd real quadratic fields\nby Avner Ash (Boston College) as part of Com
putations with Arithmetic Groups\n\n\nAbstract\nGiven the congruence subgr
oup $\\Gamma=\\Gamma_0(N)$ of $SL_3(\\mathbb{Z})$ and the real quadratic f
ield $E=\\mathbb{Q}(\\sqrt{d})$\, we compare the homology of $\\Gamma$ wit
h coefficients in the Steinberg modules of $E$ and $\\mathbb{Q}$. This lea
ds to a connecting homomorphism whose image H is a "natural" (in particula
r Hecke-stable) subspace of $H^3(\\Gamma\,\\mathbb{Q})$. The units $O^\\ti
mes_E$ are the main ingredient in the construction of elements of $H$. We
performed computations to determine $H$ for a variety of levels $N≤169$
and all $d≤10$. On the basis of the results we conjecture exactly what t
he image should be in general. This is joint work with Dan Yasaki.\n
LOCATION:https://stable.researchseminars.org/talk/CompArithGroups/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cecile Armana (Universite de Franche-Comte)
DTSTART:20201208T143000Z
DTEND:20201208T145000Z
DTSTAMP:20260404T094319Z
UID:CompArithGroups/6
DESCRIPTION:Title: Sturm bounds for Drinfeld-type automorphic forms over funct
ion fields\nby Cecile Armana (Universite de Franche-Comte) as part of
Computations with Arithmetic Groups\n\n\nAbstract\nSturm bounds say how ma
ny successive Fourier coefficients suffice to determine a modular form. Fo
r classical modular forms\, they also provide bounds for the number of Hec
ke operators generating the Hecke algebra. I will present Sturm bounds for
Drinfeld-type automorphic forms over the function field $\\mathbb{F}_q(t)
$. Their proof involve refinements of a fundamental domain for a correspon
ding Bruhat-Tits tree under the action of a congruence subgroup. This is a
joint work with Fu-Tsun Wei.\n
LOCATION:https://stable.researchseminars.org/talk/CompArithGroups/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Neil Dummigan (University of Sheffield)
DTSTART:20201208T150000Z
DTEND:20201208T152000Z
DTSTAMP:20260404T094319Z
UID:CompArithGroups/7
DESCRIPTION:Title: Congruences involving non-parallel weight Hilbert modular f
orms\nby Neil Dummigan (University of Sheffield) as part of Computatio
ns with Arithmetic Groups\n\n\nAbstract\nWhen newforms are congruent\, the
modulus appears in a near-central adjoint $L$-value. When those newforms
are complex conjugates\, it actually appears in the other critical values
too. The Bloch-Kato conjecture then demands non-zero elements of that orde
r in the associated Selmer groups. These are provided by conjectural congr
uences involving non-parallel weight Hilbert modular forms. An experimenta
l example of such a congruence showed up following computations of algebra
ic modular forms for a definite orthogonal group\, for the genus of even u
nimodular lattices of rank $12$ over the golden ring.\n
LOCATION:https://stable.researchseminars.org/talk/CompArithGroups/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fang-Ting Tu (Louisiana State University)
DTSTART:20201208T154500Z
DTEND:20201208T160500Z
DTSTAMP:20260404T094319Z
UID:CompArithGroups/8
DESCRIPTION:Title: A Geometric Interpretation of a Whipple's ${}_7F_6$ Formula
\nby Fang-Ting Tu (Louisiana State University) as part of Computations
with Arithmetic Groups\n\n\nAbstract\nThis talk is based on a joint work
with Wen-Ching Winnie Li and Ling Long. We consider hypergeometric motives
corresponding to a formula due to Whipple which relates certain hypergeom
etric values ${}_7F_6(1)$ and ${}_4F_3(1)$. From identities of hypergeomet
ric character sums\, we explain a special structure of the Galois represen
tation behind Whipple's formula leading to a decomposition that can be des
cribed by Hecke eigenforms. In this talk\, I will use an example to demons
trate our approach and relate the hypergeometric values to periods of modu
lar forms.\n
LOCATION:https://stable.researchseminars.org/talk/CompArithGroups/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark McConnell (Princeton University)
DTSTART:20201208T161500Z
DTEND:20201208T163500Z
DTSTAMP:20260404T094319Z
UID:CompArithGroups/9
DESCRIPTION:Title: Computing Hecke Operators for Arithmetic Subgroups of the S
ymplectic Group\nby Mark McConnell (Princeton University) as part of C
omputations with Arithmetic Groups\n\n\nAbstract\nLet $\\Gamma$ be an arit
hmetic subgroup of $G = Sp(4\,\\mathbb{R})$. We will describe a new algor
ithm for computing the cohomology $H^i$ of the locally symmetric space $\\
Gamma\\backslash G/K$\, and the Hecke operators on this cohomology\, in al
l degrees $i$. This builds on recent work of Bob MacPherson and the autho
r on computing the cohomology and Hecke operators on locally symmetric spa
ces for $SL(n\,\\mathbb{R})$. The computations for $SL$ use the well-temp
ered complex\, a contractible regular cell complex W on which arithmetic s
ubgroups of $SL$ act with only finitely many orbits of cells. For $Sp(4\,
\\mathbb{R})$\, we define a certain subcomplex V of the first barycentric
subdivision of W. This V is a contractible regular cell complex on which
$\\Gamma$ acts with only finitely many stabilizers of cells\, and it allow
s us to compute the Hecke operators. As a subcomplex\, V contains the sym
plectic well-rounded retract of MacPherson and the author (1993). The rec
ent work for $Sp(4\,\\mathbb{R})$ is joint with Dylan Galt.\n
LOCATION:https://stable.researchseminars.org/talk/CompArithGroups/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathilde Gerbelli-Gauthier (Centre de Recherches Mathématiques)
DTSTART:20201208T170000Z
DTEND:20201208T172000Z
DTSTAMP:20260404T094319Z
UID:CompArithGroups/10
DESCRIPTION:Title: Limit multiplicity of non-tempered representations and end
oscopy\nby Mathilde Gerbelli-Gauthier (Centre de Recherches Mathémati
ques) as part of Computations with Arithmetic Groups\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CompArithGroups/10/
END:VEVENT
END:VCALENDAR