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BEGIN:VEVENT
SUMMARY:Eva Bayer (EPF Lausanne)
DTSTART:20210621T130000Z
DTEND:20210621T134500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/1
DESCRIPTION:Title: Isometries of lattices\, knot theory and K3 surfaces\nby
Eva Bayer (EPF Lausanne) as part of Cogent Seminar\n\n\nAbstract\nWe give
necessary and sufficient conditions for an integral polynomial to be the
characteristic polynomial of an isometry of some even\, unimodular lattic
e of given signature. This result has applications in knot theory (existen
ce of knots with given Alexander polynomial and Milnor signatures) as well
as to K3 surfaces (existence of K3 surfaces having an automorphism with g
iven dynamical degree and determinant).\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Kontorovich (Rutgers University)
DTSTART:20210621T140000Z
DTEND:20210621T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/2
DESCRIPTION:Title: Hyperbolic arithmetic groups and sphere packings\nby Alex
Kontorovich (Rutgers University) as part of Cogent Seminar\n\n\nAbstract\
nWe will discuss the interactions of the two fields in the title\, with a
focus on algorithmic elements.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jennifer Wilson (University of Michigan-Ann Arbor)
DTSTART:20210705T140000Z
DTEND:20210705T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/3
DESCRIPTION:Title: The high-degree cohomology of the special linear group\nb
y Jennifer Wilson (University of Michigan-Ann Arbor) as part of Cogent Sem
inar\n\n\nAbstract\nIn this talk I will describe some current efforts to u
nderstand the high-degree rational cohomology of $SL_n(Z)$\, or more gener
ally the cohomology of $SL_n(O)$ when $O$ is a number ring. Although the g
roups $SL_n(O)$ do not satisfy Poincare duality\, they do satisfy a twiste
d form of duality\, called Bieri--Eckmann duality. Consequently\, their hi
gh-degree rational cohomology groups are governed by an $SL_n(O)$-represen
tation called the Steinberg module. I will overview some results\, conject
ures\, and ongoing work concerning these representations.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bettina Eick (TU Braunschweig)
DTSTART:20210913T130000Z
DTEND:20210913T134500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/4
DESCRIPTION:Title: The conjugacy problem in $GL(n\,\\mathbb{Z})$\nby Bettina
Eick (TU Braunschweig) as part of Cogent Seminar\n\n\nAbstract\nWe can de
cide whether two elements T and S of $GL(n\,\\mathbb{Z})$ are conjugate un
der $GL(n\,\\mathbb{Q})$ by computing their rational canonical forms. Howe
ver\, the problem of whether they are conjugate under $GL(n\,\\mathbb{Z})$
is much harder. In 1980 it was shown by Fritz Grunewald\, that the conjug
acy problem in $GL(n\,\\mathbb{Z})$ is decidable. More recently\, in a joi
nt work with Tommy Hofmann and Eamonn O'Brien\, we developed a first pract
ical method to solve this problem. This talk reports on this algorithm and
its applications.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Deraux (University of Grenoble Alpes)
DTSTART:20211025T130000Z
DTEND:20211025T134500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/5
DESCRIPTION:Title: Non-arithmetic lattices in PU(2\,1)\nby Martin Deraux (Un
iversity of Grenoble Alpes) as part of Cogent Seminar\n\n\nAbstract\nIn jo
int work with Parker and Paupert\, we gave a construction of several non-a
rithmetic lattices in the isometry group of the complex hyperbolic plane\,
that produces all examples known to this day. Our original proof\, which
is based on the construction of explicit fundamental domains\, relies hea
vily on computational tools. If time allows\, I will sketch methods to get
alternative proofs that no longer rely on the computer.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruth Kellerhals (University of Fribourg)
DTSTART:20211025T140000Z
DTEND:20211025T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/6
DESCRIPTION:Title: The non-arithmetic cusped hyperbolic 3-orbifold of minimal vo
lume\nby Ruth Kellerhals (University of Fribourg) as part of Cogent Se
minar\n\n\nAbstract\nTogether with Simon Drewitz\, we showed recently that
the 1-cusped quotient of the (real) hyperbolic 3-space by the tetrahedral
Coxeter group $\\Gamma = [5\, 3\, 6]$ has minimal volume among all non-ar
ithmetic cusped hyperbolic 3-orbifolds\, and as such it is uniquely determ
ined.\n\nFurthermore\, the lattice Γ is incommensurable to any Gromov-Pia
tetski-Shapiro type lattice.\nOur methods have their origin in the work of
Colin Adams. We extend considerably this approach via the geometry of the
underlying horoball configuration induced by a cusp. I shall present and
provide a borad outline of the proof.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asbjørn Nordentoft (University of Bonn)
DTSTART:20210830T130000Z
DTEND:20210830T134500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/7
DESCRIPTION:Title: On the distribution of modular symbols and beyond\nby Asb
jørn Nordentoft (University of Bonn) as part of Cogent Seminar\n\n\nAbstr
act\nIn 2016\, Mazur and Rubin conjectured that modular symbols should be
normally distributed. This conjecture was resolved (on average) independen
tly\, by Petridis--Risager and Lee--Sun using two completely different app
roaches (resp. spectral and dynamical methods). \n\nIn this talk\, I will
give an introduction to the conjectures of Mazur and Rubin and talk about
a number of different generalizations of the modular symbols conjecture (
including higher weight holomorphic forms\, Maass forms\, groups different
from GL2\, and residual distribution) and how they can be tackled. With t
he topic of the seminar in mind\, I will put special emphasis on the cohom
ological perspective.\n\nThe talk will feature joint work with Petru Const
antinescu and Sary Drappeau (in progress).\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eran Assaf (Dartmouth College)
DTSTART:20210830T140000Z
DTEND:20210830T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/8
DESCRIPTION:Title: Decomposition of Jacobians of Modular Curves\nby Eran Ass
af (Dartmouth College) as part of Cogent Seminar\n\n\nAbstract\nIn the tal
k\, I will present an efficient algorithm to compute the decomposition of
the Jacobians of modular curves\, using modular symbols. This is obtained
by working intrinsically with the curve\, unlike previous methods. I will
also discuss the possible consequences for deriving equations of modular c
urves.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaëtan Chenevier (CNRS\, ENS-PSL)
DTSTART:20210705T130000Z
DTEND:20210705T134500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/9
DESCRIPTION:Title: Unimodular hunting\nby Gaëtan Chenevier (CNRS\, ENS-PSL)
as part of Cogent Seminar\n\n\nAbstract\nIn this talk\, I will explain ho
w to classify the isometry classes of unimodular integral euclidean lattic
es in rank up to 28. In particular\, there are respectively 2566\, 17059 a
nd 374062 such lattices in rank 26\, 27 and 28 (this last and most difficu
lt computation is a\njoint work with Bill Allombert). As a general new ing
redient\, for any two lattices L and L' in a same (and arbitrary) genus\,
we prove an asymptotic formula for the proportion of Kneser p-neighbors of
L which are isometric to L'\, when the prime p goes to infinity.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen Miller (Rutgers University)
DTSTART:20210719T140000Z
DTEND:20210719T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/10
DESCRIPTION:Title: Automorphic realizations of Arthur packets and unitarity
\nby Stephen Miller (Rutgers University) as part of Cogent Seminar\n\n\nAb
stract\nJim Arthur's conjectures from the 1980s predict a fascinating fami
ly of automorphic forms\, connected to exotic unitary representations. I'l
l describe some recent examples from work with Joseph Hundley\, as well as
more recent results on the real group aspects with Jeffrey\nAdams\, Marc
van Leeuwen\, and David Vogan. Together this proves the unitary aspect of
Arthur's conjectures for all real forms of exceptional groups. The talk
will include a discussion of parallel computing techniques (such as SLURM)
which were used to speed up some computational parts of the proof.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Günter Harder (MPIM)
DTSTART:20210913T140000Z
DTEND:20210913T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/11
DESCRIPTION:Title: Mixed motives\, L-values\, denominators and congruences\
nby Günter Harder (MPIM) as part of Cogent Seminar\n\n\nAbstract\nI will
discuss briefly the concept of denominators of Eisenstein classes and the
resulting\ncongruences. I will speak in very general terms about the conje
ctural relationship between\nthe denominators and special values of L-func
tions. I will also mention the experimental aspects. If time permits I wil
l discuss in a special example the influence of the denominator (or the sp
ecial value of the L-function) on the structure of the Galois group.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claire Burrin (ETH Zurich)
DTSTART:20210802T130000Z
DTEND:20210802T134500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/12
DESCRIPTION:Title: Rademacher symbols for Fuchsian groups\nby Claire Burrin
(ETH Zurich) as part of Cogent Seminar\n\n\nAbstract\nThe Rademacher symb
ol is algebraically expressed as a conjugacy class invariant quasimorphism
$PSL(2\,\\Z)\\to \\Z$ yielding the bounded Euler class. I will explain (1
) how\, using continued fractions\, it is realized as the winding number f
or closed curves on the modular surface around the cusp\; (2) how\, using
Eisenstein series\, one can naturally construct a Rademacher symbol for an
y cusp of a general noncocompact Fuchsian group\; (3) and discuss some con
nections to arithmetic geometry.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonas Bergström (University of Stockholm)
DTSTART:20210927T130000Z
DTEND:20210927T134500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/13
DESCRIPTION:Title: Cohomology of a Picard modular surface\nby Jonas Bergstr
öm (University of Stockholm) as part of Cogent Seminar\n\n\nAbstract\nIn
joint work with Gerard van der Geer we have studied the cohomology of loca
l systems on the Picard modular surface of Eisenstein type and the related
modular forms. Our main technique is to use computer counts of the points
over finite fields of small cardinality. This is done via the interpretat
ion of this surface as a moduli space of degree three covers of the projec
tive line.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Garcia (University College London)
DTSTART:20210719T130000Z
DTEND:20210719T134500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/14
DESCRIPTION:Title: Eisenstein cocycles and values of L-functions\nby Luis G
arcia (University College London) as part of Cogent Seminar\n\n\nAbstract\
nThere are several recent constructions by many authors of Eisenstein cocy
cles of arithmetic groups. I will discuss a point of view on these constru
ctions using equivariant cohomology and differential forms. The resulting
objects behave like theta kernels relating the homology of arithmetic grou
ps to algebraic objects. I will also discuss an application to conjectures
of Sczech and Colmez on critical values of Hecke L-functions. The talk is
based on work-in-progress with Nicolas Bergeron\, Pierre Charollois and A
kshay Venkatesh.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Yasaki (University of North Carolina Greensboro)
DTSTART:20210802T140000Z
DTEND:20210802T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/15
DESCRIPTION:Title: Cohomology of Congruence Subgroups\, Steinberg Modules\, and
Real Quadratic Fields\nby Dan Yasaki (University of North Carolina Gr
eensboro) as part of Cogent Seminar\n\n\nAbstract\nGiven a real quadratic
field\, there is a naturally defined Hecke-stable subspace of the cohomolo
gy of a congruence subgroup of $SL_3(Z)$. We investigate this subspace an
d make conjectures about its dependence on the real quadratic field and t
he relationship to boundary cohomology. This is joint work with Avner Ash
.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kathryn Hess (EPF Lausanne)
DTSTART:20211122T140000Z
DTEND:20211122T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/16
DESCRIPTION:Title: On neurons and symmetric groups\nby Kathryn Hess (EPF La
usanne) as part of Cogent Seminar\n\n\nAbstract\nMotivated by the desire t
o automate classification of neuron morphologies\, we designed a topologic
al signature\, the Topological Morphology Descriptor (TMD)\, that assigns
a topological signature\, called a barcode\, to any geometric tree (i.e\,
any finite binary tree embedded in R^3). We showed that the TMD effective
ly determines the reliability of clusterings of random and neuronal trees.
Moreover\, using the TMD we performed an objective\, stable classificatio
n of pyramidal cells in the rat neocortex\, based only on the shape of the
ir dendrites.\n\nWe have also reverse-engineered the TMD\, in order to dig
itally synthesize dendrites\, to compensate for the dearth of available bi
ological reconstructions. The algorithm we developed\, called Topological
Neuron Synthesis (TNS)\, stochastically generates a geometric tree from a
barcode\, in a biologically grounded manner. The synthesized neurons are s
tatistically indistinguishable from real neurons of the same type. \n\nIn
this talk I will provide an overview of the TMD and the TNS and then descr
ibe the results of our theoretical and computational analysis of their beh
avior and properties\, in which symmetric groups and Coxeter complexes pla
y a key role.\n\nThis talk is based on joint work with Adélie Garin and L
ida Kanari\, as well as with Justin Curry\, Jordan Desha\, and Brendan Mal
lery\, and on work of Adélie Garin and Benjamin Brück\, building on earl
ier collaborations led by Lida Kanari.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yang-Hui He (City University of London)
DTSTART:20211122T150000Z
DTEND:20211122T154500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/17
DESCRIPTION:Title: Universes as Bigdata\, or\, Machine-Learning Mathematical St
ructures\nby Yang-Hui He (City University of London) as part of Cogent
Seminar\n\n\nAbstract\nWe review how historically the problem of string p
henomenology lead theoretical physics first to algebraic/differential geom
etry\, and then to computational geometry\, and now to data science and AI
.\n\nWith the concrete playground of the Calabi-Yau landscape\, accumulate
d by the collaboration of physicists\, mathematicians and computer scienti
sts over the last 4 decades\, we show how the latest techniques in machine
-learning can help explore problems of physical and mathematical interest\
, from geometry\, to group theory\, to combinatorics and number theory.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Alvarenga (University of São Paulo)
DTSTART:20210927T140000Z
DTEND:20210927T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/18
DESCRIPTION:Title: Automorphic forms and Hecke operators for $\\mathrm{GL}_n$ o
ver global function fields\nby Roberto Alvarenga (University of São P
aulo) as part of Cogent Seminar\n\n\nAbstract\nIn this talk\, we investiga
te the action of Hecke operators on automorphic forms through some graphs\
, known as graphs of Hecke operators. Geometric tools are raised to connec
t the problem of describe these graphs to calculate some products in the a
ssociated Hall algebra. In the case of elliptic function fields\, we prese
nt an algorithm which describes the graphs.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sander Dahmen (VU Amsterdam)
DTSTART:20220110T140000Z
DTEND:20220110T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/19
DESCRIPTION:Title: Formalization in number theory\nby Sander Dahmen (VU Ams
terdam) as part of Cogent Seminar\n\n\nAbstract\nProof assistants\, such a
s Coq\, Isabelle\, or Lean\, are software\ntools which assist in rigorousl
y expressing mathematical statements and\ntheir proofs in a formal logical
language. The mathematics that has been\nformalized this way\, ranges thr
ough many different fields. In this talk\,\nafter some general introductio
n\, we will take a pragmatic "working\nnumber theorist" point of view and
discuss some past\, present\, and\npotential future formalization work\, f
ocusing mostly (but not\nexclusively) on the Lean proof assistant.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Assia Mahboubi (Inria - VU Amsterdam)
DTSTART:20220110T150000Z
DTEND:20220110T154500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/20
DESCRIPTION:Title: Mathematics and formal proofs\nby Assia Mahboubi (Inria
- VU Amsterdam) as part of Cogent Seminar\n\n\nAbstract\nMathematical logi
c studies proofs as mathematical objects: existence\,\nshape\, classificat
ion\, etc. Yet these formal proofs are very far from\nthe demonstrations t
hat constitute the contemporary mathematical\nwriting\, as rigorous as the
y might be. On the other hand\, formal\nproofs provide data structures tha
t can be processed by computers\, so\nthat they can be constructed\, obser
ved\, verified\, by mechanical\nmeans. Proof assistants are pieces of soft
ware designed for performing\nthis nature of operations\, in practice and
in the large. In this talk\nwe will try to provide some hints of the mathe
matics that can be done\nwith the help of a proof assistant\, and of the b
enefits one can expect\nfrom this activity.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabor Wiese (University of Luxembourg)
DTSTART:20220124T140000Z
DTEND:20220124T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/21
DESCRIPTION:Title: Unlikely Revelations? -- The Hidden Lattice Problem\nby
Gabor Wiese (University of Luxembourg) as part of Cogent Seminar\n\n\nAbst
ract\nIn this talk\, which is based on joint work with Luca Notarnicola\,
I will present the Hidden Lattice Problem (HLP)\, which is the task of rec
overing a "small" lattice from the knowledge of only one or a few of its v
ectors. This problem can be traced back at least to the work on the Hidden
Subset Sum Problem by Nguyen and Stern\, who also came up with the "ortho
gonal lattice attack" for solving this kind of problem. The main novelty t
hat I am going to discuss and illustrate is an alternative algorithm for t
he HLP.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fredrik Strömberg (University of Nottingham)
DTSTART:20220124T150000Z
DTEND:20220124T154500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/22
DESCRIPTION:Title: A reduction algorithm for Hilbert modular groups\nby Fre
drik Strömberg (University of Nottingham) as part of Cogent Seminar\n\n\n
Abstract\nGiven a group acting on a topological space it often useful to h
ave a “nice” set of representatives\, a so-called fundamental domain\,
for this action. In practice it is also useful to not only know that such
a domain exists\, but also to know exactly how to reduce a given point to
its representative.\n\nFor the modular group\, $PSL(2\,\\Z)$\, a number o
f fundamental domains and associated reduction algorithms have been known
for a long time and are relatively simple to describe.\nIn the case of th
e Hilbert modular group $PSL(2\,O)$\, where $O$ is the ring of integers of
a totally real number field\, the fundamental domain is harder to describ
e geometrically but an algorithmic description has been known in principle
since works of Blumenthal\, Maass and others. Until recently\, however\,
no explicit (finite-time) reduction algorithm has been known in the case o
f class number greater than one. \n \n\nThe aim of this talk is to present
some of the motivations and the recent development and implementation of
a new reduction algorithm for Hilbert modular groups\, valid for any class
number and degree.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Daw (University of Reading)
DTSTART:20220307T150000Z
DTEND:20220307T154500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/23
DESCRIPTION:Title: Unlikely intersections in the moduli space of abelian variet
ies\nby Christopher Daw (University of Reading) as part of Cogent Semi
nar\n\n\nAbstract\nLet S be a Shimura variety (e.g. the moduli space $A_g$
of\nprincipally polarized abelian varieties of dimension g) and let $V$ b
e an\nirreducible algebraic subvariety of $S$ contained in no proper Shimu
ra\nsubvariety. The Zilber-Pink conjecture predicts that the intersection
$Y$ of\n$V$ with the Shimura subvarieties (e.g. the loci of abelian variet
ies with\nadditional endomorphisms) of codimension less than dim $V$ is co
ntained in a\nproper subvariety of $V$ (in other words\, it is non-Zariski
dense in $V$) — it\nis known as a problem in unlikely intersections.\n\
nThe Zilber-Pink conjecture is\, so to speak\, wide open. Primarily\, this
is\nbecause of its arithmetic complexity — in some sense\, the geometri
c aspect\nof the problem is now resolved. Indeed\, when $V$ is a curve\, t
he conjecture\nfollows from two arithmetic hypotheses: (1) the large Galoi
s orbits\nconjecture\, and (2) the parametrization problem. The large Galo
is orbits\nconjecture calls for a lower bound on the Galois orbits of the
points in $Y$.\nThe parametrization problem calls for an upper bound on th
e complexity of\ndata parametrizing Shimura subvarieties.\n\nIn this talk\
, I will survey ongoing programmes with Martin Orr (University\nof Manches
ter) aimed at problems (1) and (2)\, respectively\, which have\nyielded un
conditional cases of the Zilber-Pink conjecture in $A_g$.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kartik Prasanna (University of Michigan)
DTSTART:20220502T140000Z
DTEND:20220502T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/24
DESCRIPTION:Title: Modular forms of weight one\, motivic cohomology and the Jac
quet-Langlands correspondence\nby Kartik Prasanna (University of Michi
gan) as part of Cogent Seminar\n\n\nAbstract\nIn a previous paper with Ich
ino\, we showed that the Jacquet-Langlands correspondence for Hilbert modu
lar forms\, all of whose weights are at least two\, preserves rational Hod
ge structures. In this talk\, I will discuss some work in progress (with I
chino) on the case of weight one forms. Since weight one forms are not coh
omological\, it is not clear how to formulate an analogous result. I will
explain the formulation\, which is suggested by another recent development
\, namely the conjectural connection between the motivic cohomology of adj
oint motives and the cohomology of locally symmetric spaces.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Neil Dummigan (University of Sheffield)
DTSTART:20220307T140000Z
DTEND:20220307T154500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/25
DESCRIPTION:Title: Proving congruences for paramodular forms using quinary form
\nby Neil Dummigan (University of Sheffield) as part of Cogent Seminar
\n\n\nAbstract\nI will explain how it is possible to prove various congrue
nces of Hecke eigenvalues\, between Siegel cusp forms of genus 2 and param
odular level\, and genus 1 cusp forms\, including some of a type conjectur
ed by Harder\, for which Fretwell obtained computational evidence\, and so
me of a type discovered by Buzzard and Golyshev. Exploiting the recent pro
of by Roesner and Weissauer of Ibukiyama's genus 2 Jacquet-Langlands corre
spondence\, and my joint work with Pacetti\, Rama and Tornaria\, relating
algebraic modular forms for GU2 of a definite quaternion algebra and for O
(5)\, we can prove several examples using linear algebra computations.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melody Chan (Brown University)
DTSTART:20220404T130000Z
DTEND:20220404T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/26
DESCRIPTION:Title: The $S_n$-equivariant top-weight Euler characteristic of $M_
{g\,n}$\nby Melody Chan (Brown University) as part of Cogent Seminar\n
\n\nAbstract\nI will discuss joint work with Carel Faber\, Soren Galatius\
, and Sam Payne in which we prove a formula\, conjectured by Zagier in 200
8\, for the $S_n$-equivariant top-weight Euler characteristics of the modu
li spaces of n-marked\, genus g algebraic curves. Our techniques involve t
ropical geometry and graph complexes.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juliette Bruce (University of California Berkeley)
DTSTART:20220321T150000Z
DTEND:20220321T154500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/27
DESCRIPTION:Title: Syzygies in higher dimensions\nby Juliette Bruce (Univer
sity of California Berkeley) as part of Cogent Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Cadoret (Sorbonne Université)
DTSTART:20220516T140000Z
DTEND:20220516T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/28
DESCRIPTION:Title: Degeneration loci of $\\ell$-adic local systems\nby Anna
Cadoret (Sorbonne Université) as part of Cogent Seminar\n\n\nAbstract\nI
will make a partial survey of what is expected and known about the degene
ration loci of $\\ell$-adic local systems over varieties over number field
s. For $\\ell$-adic local systems arising from geometry\, understanding t
hese degeneration loci is closely related to describing the variation of
certain algebraic-geometric invariants (those encapsulated in $\\ell$-adic
cohomology) in algebraic families of smooth proper varieties.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Hutchinson (University College Dublin)
DTSTART:20220221T140000Z
DTEND:20220221T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/29
DESCRIPTION:Title: The third homology of $SL_2(\\Q)$\nby Kevin Hutchinson (
University College Dublin) as part of Cogent Seminar\n\n\nAbstract\nFor a
commutative ring $R$\, the integral homology groups of $SL_2(R)$ are natur
ally\nmodules over the group ring of the group of units modulo squares. We
will explain how this action can be understood and exploited to calculate
the third homology of $SL_2(\\Q)$ with half-integer coefficients. We will
discuss connections with K-theory\, scissors congruence groups and homolo
gy stability questions.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Cowan (Harvard University)
DTSTART:20220207T140000Z
DTEND:20220207T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/30
DESCRIPTION:Title: Computing modular forms using supersingular isogeny graphs\nby Alex Cowan (Harvard University) as part of Cogent Seminar\n\n\nAbst
ract\nWe describe an algorithm that we used to compute the q-expansions of
all weight 2 cusp forms of prime level at most 2\,000\,000 and dimension
at most 6\, and to verify that these are all but one form per Atkin-Lehner
eigenspace. Our algorithm is based on Mestre's Méthode des Graphes\, and
involves supersingular isogeny graphs and Wiedemann's algorithm for findi
ng the minimal polynomial of sparse matrices over finite fields.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weibo Fu (Princeton University)
DTSTART:20220207T150000Z
DTEND:20220207T154500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/31
DESCRIPTION:Title: Growth of Bianchi modular forms\nby Weibo Fu (Princeton
University) as part of Cogent Seminar\n\n\nAbstract\nIn this talk\, I will
establish a sharp bound on the growth of cuspidal Bianchi modular forms.
By the Eichler-Shimura isomorphism\, we actually give a sharp bound of the
second cohomology of a hyperbolic three manifold (Bianchi manifold) with
local system rising from the representation $Sym^k \\otimes \\overline{Sym
^k}$ of $SL_2(\\C)$. I will explain how a $p$-adic algebraic method is use
d for deriving our result.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Herbert Gangl (Durham University)
DTSTART:20220221T150000Z
DTEND:20220221T154500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/32
DESCRIPTION:Title: Multiple polylogarithms\, and Zagier's Conjecture revisited<
/a>\nby Herbert Gangl (Durham University) as part of Cogent Seminar\n\n\nA
bstract\nInstigated by work of Borel and Bloch\, Zagier formulated his Pol
ylogarithm Conjecture in the late eighties and proved it for weight 2. Aft
er a flurry of activity and advances at the time\, notably by Goncharov wh
o provided not only a proof for weight 3 but set out a vast program with a
plethora of conjectural statements for attacking it\, progress seemed to
be stalled for a number of years. More recently\, a solution to one of Gon
charov's central conjectures in weight 4 has been found. Moreover\, by ado
pting a new point of view\, work by Goncharov and Rudenko gave a proof of
the original conjecture in weight 4.\n\nIn this impressionist talk I inten
d to give a rough idea of the developments from the early days on\, avoidi
ng most of the technical bits\, and\, time permitting\, also hint at a num
ber of recent results for higher weight with new formulas for Grassmannian
and Aomoto polylogarithms in terms of iterated integrals (joint with S.Ch
arlton and D.Radchenko).\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mike Lipnowski (McGill University)
DTSTART:20220627T140000Z
DTEND:20220627T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/33
DESCRIPTION:Title: Rigid meromorphic cocycles for orthogonal groups\nby Mik
e Lipnowski (McGill University) as part of Cogent Seminar\n\n\nAbstract\nI
n the early 2000s\, Darmon initiated a fruitful study of analogies between
Hilbert modular surfaces and quotients $Y := SL_2(ZZ[1/p]) \\ H x H_p$\,
where $H$ is the complex upper half plane and $H_p$ is Drinfeld's p-adic u
pper half plane. As $Y$ mixes complex and $p$-adic topologies\, making di
rect sense of $Y$ as an analytic space seems difficult. Nonetheless\, $Y$
supports a large collection of exotic special points - corresponding to t
he units of real quadratic fields which are inert at $p$ - and Darmon-Vonk
have described an incarnation of meromorphic functions on $Y$\, so called
rigid meromorphic cocycles.\n\nThis talk describes joint work with Henri
Darmon and Lennart Gehrmann\, in which we study generalizations $Y'$ of th
e space $Y$ to orthogonal groups $G$ for quadratic spaces over $\\Q$ of ar
bitrary real signature. The spaces $Y'$ support large collections of exot
ic special points - corresponding to subtori of G of maximal real rank - a
nd we define explicit rigid meromorphic cocycles on $Y'$\; these RMCs are
analogous to meromorphic functions on orthogonal Shimura varieties with pr
escribed special divisors first studied by Borcherds\, and they generalize
the RMCs constructed by Darmon-Vonk. We will also discuss some computati
ons suggesting that values of our RMCs at special points might realize new
instances of explicit class field theory.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Funar (CNRS\, Université Grenoble Alpes)
DTSTART:20220321T140000Z
DTEND:20220321T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/34
DESCRIPTION:Title: Finite quotients of mapping class groups and central extensi
ons\nby Louis Funar (CNRS\, Université Grenoble Alpes) as part of Cog
ent Seminar\n\n\nAbstract\nA classical result of Deligne shows that nontri
vial central extensions of integral symplectic groups are not residually f
inite. We explore the case of mapping class groups and compute the Schur m
ultiplier of finite symplectic groups.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tommy Hofmann (Universität Siegen)
DTSTART:20220404T140000Z
DTEND:20220404T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/35
DESCRIPTION:Title: Lattice isomorphism and the integral matrix similarity probl
em\nby Tommy Hofmann (Universität Siegen) as part of Cogent Seminar\n
\n\nAbstract\nDeciding whether two lattices over orders of finite-dimensio
nal algebras over number fields is a classical problem in algorithmic numb
er theory. We present a new algorithm for this problem\, assuming that the
Wedderburn decomposition of the algebra is "nice". As an application we d
iscuss the connection to the similarity problem for integral matrices (the
conjugacy problem in GL(n\,Z)).\n\nThe resulting algorithm for the latter
problem is the first with proven complexity and performs very well in pra
ctice. This is joint work with Werner Bley and Henri Johnston.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oscar Randal-Williams (University of Cambridge)
DTSTART:20220516T130000Z
DTEND:20220516T134500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/36
DESCRIPTION:Title: Stable cohomology of congruence subgroups\nby Oscar Rand
al-Williams (University of Cambridge) as part of Cogent Seminar\n\n\nAbstr
act\nI will explain how to complete and extend an argument proposed by F.\
nCalegari for determining the $F_p$-cohomology of $SL_n(\\Z\, p^m)$ in a\n
certain range (namely in cohomological degrees $* < p$ and for all large\n
enough $n$). The result has a uniform description at regular primes\, but\
nat irregular primes has interesting correction terms\, controlled by\ntor
sion in $K_*(\\Z)$ and by special values of the $p$-adic L-function. The\n
argument for $m>1$ turns out to be almost trivial\, but for $m=1$ it\ninvo
lves a delicate analysis of the cohomology of the finite groups\n$SL_n(\\Z
/p)$ with coefficients in certain modular representations. The\ntalk is ba
sed on the preprint arXiv:2203.01697.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shayan Gholami (Université Sorbonne Paris Nord)
DTSTART:20220502T130000Z
DTEND:20220502T134500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/37
DESCRIPTION:Title: Vanishing of non-Eisenstein cohomology of locally symmetric
spaces for $GL_2$ over a CM field\nby Shayan Gholami (Université Sorb
onne Paris Nord) as part of Cogent Seminar\n\n\nAbstract\nLocally symmetri
c spaces are generalizations of modular curves\, and their cohomology play
s an important role in the Langlands program. In this talk\, I will first
speak about vanishing conjectures and known results about the cohomology o
f locally symmetric spaces of a reductive group $G$ with mod $p$ coefficie
nt after localizing at a maximal ideal of spherical Hecke algebra of $G$ a
nd after that\, I will explain a sketch of my proof for the case $G = GL_2
(F)$\, where $F$ is a CM field.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amina Abdurrahman (Princeton University)
DTSTART:20220530T130000Z
DTEND:20220530T134500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/38
DESCRIPTION:Title: Square roots of symplectic L-functions and Reidemeister tors
ion\nby Amina Abdurrahman (Princeton University) as part of Cogent Sem
inar\n\n\nAbstract\nIn the 70s Deligne gave a topological formula for the
local epsilon factors attached to an orthogonal representation. We conside
r the case of a symplectic representation and present a conjecture giving
a topological formula for a finer invariant\, the square class of its cent
ral value. We also formulate a topological analogue of the statement\, in
which the central value of the L-function is replaced by Reidemeister tors
ion of 3-manifolds\, and give a sketch of the proofs. This is joint work w
ith Akshay Venkatesh.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aurel Page (INRIA\, Université de Bordeaux)
DTSTART:20220530T140000Z
DTEND:20220530T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/39
DESCRIPTION:Title: Algorithms for the cohomology of compact arithmetic manifold
s\nby Aurel Page (INRIA\, Université de Bordeaux) as part of Cogent S
eminar\n\n\nAbstract\nIn this joint work with Michael Lipnowski\, we descr
ibe an algorithm that computes the cohomology of a given compact arithmeti
c manifold together with the action of Hecke operators.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Hill (University College London)
DTSTART:20220627T130000Z
DTEND:20220627T134500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/40
DESCRIPTION:Title: Fractional weight modular forms\nby Richard Hill (Univer
sity College London) as part of Cogent Seminar\n\n\nAbstract\nIt has been
known since the 1930s that for all positive rational numbers $p/q$\, there
exist holomorphic modular forms on $SL(2\,R)$ with weight $p/q$. This con
trasts with the situation for $Sp(2n\,R)$ with $n >1$\, where one has only
integral and half-integral weight forms. Until recently\, it was an open
question whether there is any other Lie group (other than $SL_2(R)$) with
holomorphic modular forms whose weight is neither integral nor half-integr
al. In this talk I will describe how we recently found examples of holomor
phic modular forms of weight $1/3$ on the group $SU(2\,1)$.\n\nThis is joi
nt work with Eberhard Freitag.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Horozov (City University of New York)
DTSTART:20221205T140000Z
DTEND:20221205T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/41
DESCRIPTION:Title: Cohomology of $GL(3\,\\Z)$ and $GL(4\,\\Z)$ with coefficient
s in irreducible highest weight representations\nby Ivan Horozov (City
University of New York) as part of Cogent Seminar\n\n\nAbstract\nFirst\,
we will introduce cohomology of $GL(2\,\\Z)$ and its relations to modular
forms of the group $SL(2\,\\Z)$.\n\nThen\, we will present explicit result
of our computations of the (Eisenstein) cohomology of the $GL(3\,\\Z)$ wi
th coefficients in any irreducible finite dimensional highest weight repre
sentation. When the presentation is not self dual\, this is the entire gro
up cohomology. It is a joint result with Harder\, Bajpai and Moya Guisti.
It is based on the Borel-Serre compactification\, Kostant formula\, Euler
characteristics of arithmetic groups and Poincare duality. We have applied
similar techniques for the computation for the cohomology of $Sp(4\,\\Z)$
with coefficients in irreducible highest weight representations (a joint
result with Bajpai and Moya Giusti). I will mention it briefly.\n\nAfter t
hat\, I will present an older result of mine on cohomology of $GL(4\,\\Z)
$ with coefficients in the standard representation twisted by the determin
ant\, based on the same ideas. It has a current continuation that has surp
rising consequences for the cohomology of $GL(3\,\\Z)$. From the current c
omputations\, it follows that there is a ghost class in $H^2(GL(3\,\\Z)\,
M)$$ where $M$ is the dual of the standard representation of $GL(3\,\\Z)$.
Having a ghost class means that the cohomological class in $GL(3\,\\Z)$ i
s not generated by a maximal parabolic subgroup. In this case\, it is gene
rated by a minimal parabolic subgroup - the Borel subgroup.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harald Grobner (University of Vienna)
DTSTART:20221107T140000Z
DTEND:20221107T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/42
DESCRIPTION:Title: A description of automorphic cohomology in low degrees\n
by Harald Grobner (University of Vienna) as part of Cogent Seminar\n\n\nAb
stract\nAs it is well-known by epoch-making work of Franke\, the cohomolog
y of arithmetic (congruence) subgroups of a reductive group $G$ can be exp
ressed as the relative Lie algebra cohomology of a space of automorphic fo
rms $\\mathcal{A}(G)$. In this talk we will show how to use Franke’s fil
tration of $\\mathcal{A}(G)$ in order to provide a description of automorp
hic cohomology in low degrees. These results of ours improve certain bound
s of vanishing\, established by Borel and also by Zucker\, and strengthen
a non-vanishing result of Rohlfs-Speh.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean Raimbault (Aix-Marseille Université)
DTSTART:20221107T150000Z
DTEND:20221107T154500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/43
DESCRIPTION:Title: Around the Bergeron-Venkatesh conjectures on torsion homolog
y of arithmetic lattices\nby Jean Raimbault (Aix-Marseille Université
) as part of Cogent Seminar\n\n\nAbstract\nThe following phenomena have be
en observed for hyperbolic 3-manifolds M: in the first homology group $H_1
(M\, \\Z)$\, the free part tends to have a small rank while the torsion su
bgroup tends to be quite large. In arithmetic setting Bergeron and Venkate
sh give a precise quantitative statement about the asymptotic size of the
torsion part in terms of the hyperbolic volume of the manifold\, as well a
s some more tentative heuristics for its finer structure. In fact they pro
vide such statements for arithmetic lattices in all symmetric spaces. Proo
fs remain elusive but there have been a number of efforts to numerically v
erify the first conjecture\, in particular in the setting of arithmetic la
ttices in hyperbolic 3-space (by Şengün\, Calegari-Dunfield and others).
I will spend most of the talk giving details for all the above\, and i wi
ll finish by reporting on difficulties arising when numerically testing th
e conjecture for higher-dimensional hyperbolic spaces.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolaos Diamantis (University of Nottingham)
DTSTART:20221121T140000Z
DTEND:20221121T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/44
DESCRIPTION:Title: Eichler cocycles and polynomials attached to derivatives of
$L$-functions\nby Nikolaos Diamantis (University of Nottingham) as par
t of Cogent Seminar\n\n\nAbstract\nWe discuss an analogue of the period po
lynomial we have associated with values of derivatives of $L$-functions. W
e state a conjecture for the location of its zeros and provide evidence fo
r its validity\, including some proved special cases. This is joint work w
ith L. Rolen.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Newton (University of Oxford)
DTSTART:20221121T150000Z
DTEND:20221121T154500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/45
DESCRIPTION:Title: Modularity of elliptic curves over imaginary quadratic field
s\nby James Newton (University of Oxford) as part of Cogent Seminar\n\
n\nAbstract\nI will discuss recent progress towards establishing modularit
y of elliptic curves over CM number fields\, particularly imaginary quadra
tic fields. One way of phrasing "modularity" in this context is that the $
L$-function of the elliptic curve can be described in terms of eigenvalues
of Hecke operators on the cohomology of arithmetic subgroups of $SL(2\,\\
C)$. The new results I will talk about are joint work with Ana Caraiani.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frédéric Rochon (Université du Québec à Montréal)
DTSTART:20221205T150000Z
DTEND:20221205T154500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/46
DESCRIPTION:Title: Torsion on some fibered cusp manifolds\nby Frédéric Ro
chon (Université du Québec à Montréal) as part of Cogent Seminar\n\n\n
Abstract\nGiven a number field $F$ with ring of integers $O_F$\, one can a
ssociate to any torsion free subgroup $\\Gamma$ of $SL(2\,O_F)$ of finite
index a complete Riemannian manifold of finite volume with fibered cusp en
ds. For natural choices of flat vector bundles on such a manifold\, we wi
ll explain how analytic torsion can be related to Reidemeister torsion. A
s an application\, we will indicate how\, in some arithmetic settings\, th
is relation can be used to derive exponential growth of torsion in cohomol
ogy for various sequences of congruence subgroups. This is an ongoing joi
nt work with Werner Mueller.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Studenmund (Binghamton University)
DTSTART:20221219T140000Z
DTEND:20221219T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/47
DESCRIPTION:Title: Counting flat cycles in the homology of certain locally symm
etric spaces\nby Daniel Studenmund (Binghamton University) as part of
Cogent Seminar\n\n\nAbstract\nFor $n \\geq 2$\, congruence covers $X(m)$ o
f the locally symmetric space $SL(n\,\\Z) \\backslash SL(n\,\\R) / SO(n)$
encode the information of all finite covering spaces. We will use geometri
c and arithmetic methods to determine lower bounds on the growth\, as a fu
nction of $m$\, of the dimension of a subspace rational homology groups $H
_n(X(m)\; \\Q)$ spanned by cycles represented by flat submanifolds. This b
uilds on work of\, and addresses a question of\, Avramidi and Nguyen-Phan\
, who showed that the homology of such covers arising from flat cycles gro
ws arbitrarily large. The proof of our result combines their techniques wi
th perspective of Millson--Raghunathan and a topological argument of Xue\,
along with concrete number theoretic constructions. We will also mention
similar results about orthogonal groups and Hilbert modular groups\, follo
wing work of Tshishiku and Zschumme. This work is joint with Bena Tshishik
u.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robin Sroka (McMaster University)
DTSTART:20221219T150000Z
DTEND:20221219T154500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/48
DESCRIPTION:Title: On the high-dimensional rational cohomology of arithmetic Ch
evalley groups\nby Robin Sroka (McMaster University) as part of Cogent
Seminar\n\n\nAbstract\nWhile the rational cohomology of arithmetic groups
such as $\\operatorname{SL}_n(\\mathbb{Z})$ and $\\operatorname{Sp}_{2n}(
\\mathbb{Z})$ can often be completely computed if the cohomological degree
is small compared to $n$\, little is known about it in high cohomological
degrees. In this talk\, I will discuss vanishing results that have recent
ly been obtained for the high-dimensional rational cohomology of $\\operat
orname{SL}_n(\\mathbb{Z})$\, $\\operatorname{Sp}_{2n}(\\mathbb{Z})$ and ot
her arithmetic Chevalley groups. This is related to a conjecture of Church
--Farb--Putman and based on joint works with Brück--Miller--Patzt--Wilson
\, Brück--Patzt and Brück--Santos Rego.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathilde Gerbelli-Gauthier (McGill University)
DTSTART:20230213T140000Z
DTEND:20230213T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/49
DESCRIPTION:Title: Growth of cohomology of arithmetic groups and endoscopy\
nby Mathilde Gerbelli-Gauthier (McGill University) as part of Cogent Semin
ar\n\n\nAbstract\nHow fast do Betti numbers grow in a congruence tower of
compact arithmetic manifolds? The dimension of the middle degree of cohomo
logy is proportional to the volume of the manifold\, but away from the mid
dle the growth is known to be sub-linear in the volume. I will explain how
automorphic representations and the phenomenon of endoscopy provide a fra
mework to understand and quantify this slow growth. Specifically\, I will
discuss how to obtain both general upper (and in a few cases\, show that t
hey are sharp) for lattices in unitary groups using Arthur’s stable trac
e formula. This is joint work with Rahul Dalal.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. Raghuram (Fordham University)
DTSTART:20230213T150000Z
DTEND:20230213T154500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/50
DESCRIPTION:Title: Special values of Rankin-Selberg L-functions over a totally
imaginary base field.\nby A. Raghuram (Fordham University) as part of
Cogent Seminar\n\n\nAbstract\nI will report on rationality results on the
ratios of critical values for Rankin-Selberg $L$-functions for $GL(n)\\tim
es GL(m)$ over a totally imaginary base field. In contrast to a totally re
al base field\, when the base field is totally imaginary\, some delicate s
ignatures enter the reciprocity laws for these special values. These signa
tures depend on whether or not the totally imaginary base field contains a
CM subfield. The proof depends on a generalization of my work with Günte
r Harder on rank-one Eisenstein cohomology for $GL(N)$ where $N = n+m$. Th
e rationality result comes from interpreting Langlands’s constant term t
heorem in terms of an arithmetically defined intertwining operator between
Hecke summands in the cohomology of the Borel-Serre boundary of a locally
symmetric space for $GL(N)$. The signatures arise from Galois action on c
ertain local systems that intervene in boundary cohomology.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandra Iozzi (ETH Zurich)
DTSTART:20230227T150000Z
DTEND:20230227T154500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/51
DESCRIPTION:Title: Irreducible lattices and bounded cohomology\nby Alessand
ra Iozzi (ETH Zurich) as part of Cogent Seminar\n\n\nAbstract\nWe show som
e of the similarities and some of the differences between irreducible latt
ices in product of semisimple Lie groups and their siblings in product of
locally compact groups. In the case of product of trees\, we give a concr
ete example with interesting properties\, among which some in terms of bou
nded cohomology and quasimorphisms.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Satoshi Kondo (Middle East Technical University Northern Cyprus)
DTSTART:20230313T140000Z
DTEND:20230313T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/52
DESCRIPTION:Title: Automorphic forms over function fields with Steinberg at inf
inity and modular symbols\nby Satoshi Kondo (Middle East Technical Uni
versity Northern Cyprus) as part of Cogent Seminar\n\n\nAbstract\nJoint wo
rk with Yasuda (Hokkaido U). Let $F$ be a global field of positive charac
teristic and $\\infty$ a place of $F$. We study automorphic forms for $\\m
athrm{GL}_d$ over $F$\nsuch that ``the $\\infty$-component of the associat
ed automorphic representation is isomorphic to the Steinberg representatio
n".\nWe introduce modular symbols in this context and show that the modula
r symbols generate the space of such automorphic forms with $\\mathbb{Q}$-
coefficients. We also have some results with $\\mathbb{Z}$-coefficients.
\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Logan (Tutte Institute for Mathematics and Computing)
DTSTART:20230313T150000Z
DTEND:20230313T154500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/53
DESCRIPTION:Title: Higher modularity of elliptic curves over function fields\nby Adam Logan (Tutte Institute for Mathematics and Computing) as part o
f Cogent Seminar\n\n\nAbstract\n(joint with Jared Weinstein) The ideas of
Wiles on the modularity of elliptic curves over Q\, and subsequent extensi
ons and adaptations\, have had a great influence on the study of Diophanti
ne equations through the modular method. There is an analogous concept fo
r elliptic curves over function fields over finite fields\, known as Drinf
eld modularity: an elliptic curve over ${\\mathbb F}_q(t)$ with split mult
iplicative reduction at infinity is covered by a Drinfeld modular curve\,
which parametrizes Drinfeld modules of rank $2$ with a suitable level stru
cture. More generally\, let $E$ be an elliptic curve over ${\\mathbb F}_q
(t)$\, and let $E_i$ be the elliptic curve over ${\\mathbb F}_q(t_1\,\\dot
s\,t_n)$ obtained by replacing $t$ by $t_i$. Then there is an $n$-dimensi
onal moduli space of "shtukas" over ${\\mathbb F}_q(t_1\,\\dots\,t_n)$ tha
t is conjectured to be in correspondence with $E_1 \\times \\dots E_n$. W
e describe how to construct these moduli spaces concretely as the sets of
$2 \\times 2$ matrices of polynomials satisfying certain specialization co
nditions and prove the conjecture in a few special cases by means of compu
tations on K3 surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Fabrizio Di Cerbo (University of Florida at Gainsville)
DTSTART:20230327T130000Z
DTEND:20230327T134500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/54
DESCRIPTION:Title: POSTPONED!\nby Luca Fabrizio Di Cerbo (University of Flo
rida at Gainsville) as part of Cogent Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alice Pozzi (Imperial College London)
DTSTART:20230424T130000Z
DTEND:20230424T134500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/55
DESCRIPTION:Title: Rigid meromorphic cocycles and $p$-adic variations of modula
r forms\nby Alice Pozzi (Imperial College London) as part of Cogent Se
minar\n\n\nAbstract\nA rigid meromorphic cocycle is a class in the first c
ohomology of the group ${\\rm SL}_2(\\Z[1/p])$ acting on the non-zero rigi
d meromorphic functions on the Drinfeld $p$-adic upper half plane by M\\"o
bius transformation. Rigid meromorphic cocycles can be evaluated at points
of "real multiplication''\, and their values conjecturally lie in composi
ta of abelian extensions of real quadratic fields\, suggesting striking an
alogies with the classical theory of complex multiplication.\n\nIn this ta
lk\, we discuss the proof of this conjecture for a special class of rigid
meromorphic cocycles. Our proof connects the values of rigid meromorphic c
ocycles to the study of certain $p$-adic variations of Hilbert modular for
ms. This is joint work with Henri Darmon and Jan Vonk.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jitendra Bajpai (Georg-August-Universität Göttingen)
DTSTART:20230424T140000Z
DTEND:20230424T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/56
DESCRIPTION:Title: Arithmeticity and thinness of hypergeometric groups\nby
Jitendra Bajpai (Georg-August-Universität Göttingen) as part of Cogent S
eminar\n\n\nAbstract\nThe monodromy groups of hypergeometric differential
equations of type ${}_nF_{n-1}$ are often called hypergeometric groups. Th
ese are subgroups of $GL(n)$. Recently\, the arithmeticity and thinness of
these groups have caught a lot of attention. In the talk\, a gentle intro
duction and recent progress in the theory of hypergeometric groups will be
presented.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Kupers (University of Toronto Scarborough)
DTSTART:20230508T140000Z
DTEND:20230508T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/57
DESCRIPTION:Title: Cohomology of arithmetic groups and high-dimensional manifol
ds\nby Alexander Kupers (University of Toronto Scarborough) as part of
Cogent Seminar\n\n\nAbstract\nI will discuss several older and more recen
t results about relationships between arithmetic groups and diffeomorphism
groups of high-dimensional manifolds\, which in turn relate their cohomol
ogy groups. This includes joint work with Oscar Randal-Williams\, Mauricio
Bustamente\, and Manuel Krannich.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Caraiani (Imperial College London / University of Bonn)
DTSTART:20230522T130000Z
DTEND:20230522T134500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/58
DESCRIPTION:Title: On Ihara's lemma for Hilbert modular varieties\nby Ana C
araiani (Imperial College London / University of Bonn) as part of Cogent S
eminar\n\n\nAbstract\nHilbert modular varieties are Shimura varieties atta
ched to $GL_2$\nover a totally real field\, generalizing modular curves. I
will discuss\non-going work with Matteo Tamiozzo\, whose aim is to unders
tand the\ncohomology of Hilbert modular varieties with torsion coefficient
s. I will\nfocus on a result known as Ihara's lemma\, which leads to a\nre
presentation-theoretic description of the cohomology. I will explain a\nph
enomenon known as geometric Jacquet-Langlands which plays a key role in\no
ur proof.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lenny Fukshansky (Claremont McKenna College)
DTSTART:20230605T130000Z
DTEND:20230605T134500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/59
DESCRIPTION:Title: Sparsity\, virtually rectangular lattices and elliptic curve
s\nby Lenny Fukshansky (Claremont McKenna College) as part of Cogent S
eminar\n\n\nAbstract\nA lattice is called virtually rectangular if it cont
ains an orthogonal sublattice of finite index. We establish necessary and
sufficient conditions for a lattice to be virtually rectangular and determ
ine the smallest index of an orthogonal sublattice. This investigation is
closely connected to the study of sparsity and a certain sparse analogue o
f Minkowski’s successive minima theorem. In the 2-dimensional case\, our
results imply certain isogeny properties of elliptic curves.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamara Kohler (Universidad Complutense Madrid)
DTSTART:20230605T140000Z
DTEND:20230605T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/60
DESCRIPTION:Title: Clique homology is QMA1 hard\nby Tamara Kohler (Universi
dad Complutense Madrid) as part of Cogent Seminar\n\n\nAbstract\nIn this s
eminar I will discuss recent work studying the computational complexity of
determining homology groups of simplicial complexes\, a fundamental task
in computational topology. We show that the decision version of this probl
em is QMA1-hard - where QMA1 is a quantum version of the classical complex
ity class NP. Moreover\, we show that a version of the problem satisfying
a suitable promise and certain constraints is contained in QMA (a slightly
different quantum analogue of NP). This suggests that the seemingly class
ical problem may in fact be quantum mechanical. In fact\, we are able to s
ignificantly strengthen this by showing that the problem remains QMA1-hard
in the case of clique complexes\, a family of simplicial complexes specif
ied by a graph which is relevant to the problem of topological data analys
is. The proof combines a number of techniques from Hamiltonian complexity
and homological algebra. I will discuss potential implications for the pro
blem of quantum advantage in topological data analysis.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victoria Cantoral Farfan (Leibniz Universität\, Hannover)
DTSTART:20230703T130000Z
DTEND:20230703T134500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/62
DESCRIPTION:Title: Monodromy groups of Jacobians with definite quaternionic mul
tiplication\nby Victoria Cantoral Farfan (Leibniz Universität\, Hanno
ver) as part of Cogent Seminar\n\n\nAbstract\nLet $A$ be an abelian variet
y over a number field. The connected monodromy field of $A$ is the minimal
field over which the images of all the $\\ell$-adic torsion representatio
ns have connected Zariski closure. During this talk\, we will show that fo
r all even $g\\geq4$\, there exist infinitely many geometrically nonisogen
ous abelian varieties $A$ over $\\mathbb Q$ of dimension $g$ where the con
nected monodromy field is strictly larger than the field of definition of
the endomorphisms of $A$. Our construction arises from explicit families o
f hyperelliptic Jacobians with definite quaternionic multiplication. This
is a joint work with Lombardo and Voight.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romain Branchereau (University of Manitoba)
DTSTART:20230703T140000Z
DTEND:20230703T144500Z
DTSTAMP:20260404T111416Z
UID:cogentseminar/63
DESCRIPTION:Title: Upper bound on the denominators of Eisenstein classes in Bia
nchi manifolds\nby Romain Branchereau (University of Manitoba) as part
of Cogent Seminar\n\n\nAbstract\nA general conjecture of Harder relates t
he denominator of the Eisenstein cohomology of certain locally symmetric s
paces to special values of L-functions. In this talk\, we consider the loc
ally symmetric space associated with SL(2\,K) where K is an imaginary quad
ratic field. I will explain how results of Ito and Sczech can be used to p
rove an upper bound on the denominator in terms of a special value of a He
cke L-function. When the class number of K is one\, we can combine this re
sult with a lower bound obtained by Berger to get the exact denominator.\n
LOCATION:https://stable.researchseminars.org/talk/cogentseminar/63/
END:VEVENT
END:VCALENDAR