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BEGIN:VEVENT
SUMMARY:Eva Bayer (EPF Lausanne)
DTSTART;VALUE=DATE-TIME:20210621T130000Z
DTEND;VALUE=DATE-TIME:20210621T134500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/1
DESCRIPTION:Title: Isometries of lattices\, knot theory and K3 surfaces\nby Eva Bay
er (EPF Lausanne) as part of Cogent Seminar\n\n\nAbstract\nWe give necessa
ry and sufficient conditions for an integral polynomial to be the charact
eristic polynomial of an isometry of some even\, unimodular lattice of gi
ven signature. This result has applications in knot theory (existence of k
nots with given Alexander polynomial and Milnor signatures) as well as to
K3 surfaces (existence of K3 surfaces having an automorphism with given dy
namical degree and determinant).\n
LOCATION:https://researchseminars.org/talk/cogentseminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Kontorovich (Rutgers University)
DTSTART;VALUE=DATE-TIME:20210621T140000Z
DTEND;VALUE=DATE-TIME:20210621T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/2
DESCRIPTION:Title: Hyperbolic arithmetic groups and sphere packings\nby Alex Kontor
ovich (Rutgers University) as part of Cogent Seminar\n\n\nAbstract\nWe wil
l discuss the interactions of the two fields in the title\, with a focus o
n algorithmic elements.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jennifer Wilson (University of Michigan-Ann Arbor)
DTSTART;VALUE=DATE-TIME:20210705T140000Z
DTEND;VALUE=DATE-TIME:20210705T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/3
DESCRIPTION:Title: The high-degree cohomology of the special linear group\nby Jenni
fer Wilson (University of Michigan-Ann Arbor) as part of Cogent Seminar\n\
n\nAbstract\nIn this talk I will describe some current efforts to understa
nd the high-degree rational cohomology of $SL_n(Z)$\, or more generally th
e cohomology of $SL_n(O)$ when $O$ is a number ring. Although the groups $
SL_n(O)$ do not satisfy Poincare duality\, they do satisfy a twisted form
of duality\, called Bieri--Eckmann duality. Consequently\, their high-degr
ee rational cohomology groups are governed by an $SL_n(O)$-representation
called the Steinberg module. I will overview some results\, conjectures\,
and ongoing work concerning these representations.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bettina Eick (TU Braunschweig)
DTSTART;VALUE=DATE-TIME:20210913T130000Z
DTEND;VALUE=DATE-TIME:20210913T134500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
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 decide wh
ether two elements T and S of $GL(n\,\\mathbb{Z})$ are conjugate under $GL
(n\,\\mathbb{Q})$ by computing their rational canonical forms. However\, t
he problem of whether they are conjugate under $GL(n\,\\mathbb{Z})$ is muc
h harder. In 1980 it was shown by Fritz Grunewald\, that the conjugacy pro
blem in $GL(n\,\\mathbb{Z})$ is decidable. More recently\, in a joint work
with Tommy Hofmann and Eamonn O'Brien\, we developed a first practical me
thod to solve this problem. This talk reports on this algorithm and its ap
plications.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Deraux (University of Grenoble Alpes)
DTSTART;VALUE=DATE-TIME:20211025T130000Z
DTEND;VALUE=DATE-TIME:20211025T134500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/5
DESCRIPTION:Title: Non-arithmetic lattices in PU(2\,1)\nby Martin Deraux (Universit
y of Grenoble Alpes) as part of Cogent Seminar\n\n\nAbstract\nIn joint wor
k with Parker and Paupert\, we gave a construction of several non-arithmet
ic lattices in the isometry group of the complex hyperbolic plane\, that p
roduces all examples known to this day. Our original proof\, which is bas
ed on the construction of explicit fundamental domains\, relies heavily on
computational tools. If time allows\, I will sketch methods to get altern
ative proofs that no longer rely on the computer.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruth Kellerhals (University of Fribourg)
DTSTART;VALUE=DATE-TIME:20211025T140000Z
DTEND;VALUE=DATE-TIME:20211025T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/6
DESCRIPTION:Title: The non-arithmetic cusped hyperbolic 3-orbifold of minimal volume\nby Ruth Kellerhals (University of Fribourg) as part of Cogent Seminar\n
\n\nAbstract\nTogether with Simon Drewitz\, we showed recently that the 1-
cusped quotient of the (real) hyperbolic 3-space by the tetrahedral Coxete
r group $\\Gamma = [5\, 3\, 6]$ has minimal volume among all non-arithmeti
c cusped hyperbolic 3-orbifolds\, and as such it is uniquely determined.\n
\nFurthermore\, the lattice Γ is incommensurable to any Gromov-Piatetski-
Shapiro type lattice.\nOur methods have their origin in the work of Colin
Adams. We extend considerably this approach via the geometry of the underl
ying horoball configuration induced by a cusp. I shall present and provide
a borad outline of the proof.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asbjørn Nordentoft (University of Bonn)
DTSTART;VALUE=DATE-TIME:20210830T130000Z
DTEND;VALUE=DATE-TIME:20210830T134500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/7
DESCRIPTION:Title: On the distribution of modular symbols and beyond\nby Asbjørn N
ordentoft (University of Bonn) as part of Cogent Seminar\n\n\nAbstract\nIn
2016\, Mazur and Rubin conjectured that modular symbols should be normall
y distributed. This conjecture was resolved (on average) independently\, b
y Petridis--Risager and Lee--Sun using two completely different approaches
(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 numbe
r of different generalizations of the modular symbols conjecture (includi
ng higher weight holomorphic forms\, Maass forms\, groups different from G
L2\, and residual distribution) and how they can be tackled. With the topi
c of the seminar in mind\, I will put special emphasis on the cohomologica
l perspective.\n\nThe talk will feature joint work with Petru Constantines
cu and Sary Drappeau (in progress).\n
LOCATION:https://researchseminars.org/talk/cogentseminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eran Assaf (Dartmouth College)
DTSTART;VALUE=DATE-TIME:20210830T140000Z
DTEND;VALUE=DATE-TIME:20210830T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/8
DESCRIPTION:Title: Decomposition of Jacobians of Modular Curves\nby Eran Assaf (Dar
tmouth College) as part of Cogent Seminar\n\n\nAbstract\nIn the talk\, I w
ill present an efficient algorithm to compute the decomposition of the Jac
obians of modular curves\, using modular symbols. This is obtained by work
ing intrinsically with the curve\, unlike previous methods. I will also di
scuss the possible consequences for deriving equations of modular curves.\
n
LOCATION:https://researchseminars.org/talk/cogentseminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaëtan Chenevier (CNRS\, ENS-PSL)
DTSTART;VALUE=DATE-TIME:20210705T130000Z
DTEND;VALUE=DATE-TIME:20210705T134500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/9
DESCRIPTION:Title: Unimodular hunting\nby Gaëtan Chenevier (CNRS\, ENS-PSL) as par
t of Cogent Seminar\n\n\nAbstract\nIn this talk\, I will explain how to cl
assify the isometry classes of unimodular integral euclidean lattices in r
ank up to 28. In particular\, there are respectively 2566\, 17059 and 3740
62 such lattices in rank 26\, 27 and 28 (this last and most difficult comp
utation is a\njoint work with Bill Allombert). As a general new ingredient
\, for any two lattices L and L' in a same (and arbitrary) genus\, we prov
e an asymptotic formula for the proportion of Kneser p-neighbors of L whic
h are isometric to L'\, when the prime p goes to infinity.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen Miller (Rutgers University)
DTSTART;VALUE=DATE-TIME:20210719T140000Z
DTEND;VALUE=DATE-TIME:20210719T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/10
DESCRIPTION:Title: Automorphic realizations of Arthur packets and unitarity\nby St
ephen Miller (Rutgers University) as part of Cogent Seminar\n\n\nAbstract\
nJim Arthur's conjectures from the 1980s predict a fascinating family of a
utomorphic forms\, connected to exotic unitary representations. I'll descr
ibe some recent examples from work with Joseph Hundley\, as well as more r
ecent results on the real group aspects with Jeffrey\nAdams\, Marc van Lee
uwen\, and David Vogan. Together this proves the unitary aspect of Arthur
's conjectures for all real forms of exceptional groups. The talk will in
clude a discussion of parallel computing techniques (such as SLURM) which
were used to speed up some computational parts of the proof.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Günter Harder (MPIM)
DTSTART;VALUE=DATE-TIME:20210913T140000Z
DTEND;VALUE=DATE-TIME:20210913T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/11
DESCRIPTION:Title: Mixed motives\, L-values\, denominators and congruences\nby Gü
nter Harder (MPIM) as part of Cogent Seminar\n\n\nAbstract\nI will discuss
briefly the concept of denominators of Eisenstein classes and the resulti
ng\ncongruences. I will speak in very general terms about the conjectural
relationship between\nthe denominators and special values of L-functions.
I will also mention the experimental aspects. If time permits I will discu
ss in a special example the influence of the denominator (or the special v
alue of the L-function) on the structure of the Galois group.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claire Burrin (ETH Zurich)
DTSTART;VALUE=DATE-TIME:20210802T130000Z
DTEND;VALUE=DATE-TIME:20210802T134500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/12
DESCRIPTION:Title: Rademacher symbols for Fuchsian groups\nby Claire Burrin (ETH Z
urich) as part of Cogent Seminar\n\n\nAbstract\nThe Rademacher symbol is a
lgebraically 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 for clos
ed curves on the modular surface around the cusp\; (2) how\, using Eisenst
ein series\, one can naturally construct a Rademacher symbol for any cusp
of a general noncocompact Fuchsian group\; (3) and discuss some connection
s to arithmetic geometry.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonas Bergström (University of Stockholm)
DTSTART;VALUE=DATE-TIME:20210927T130000Z
DTEND;VALUE=DATE-TIME:20210927T134500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/13
DESCRIPTION:Title: Cohomology of a Picard modular surface\nby Jonas Bergström (Un
iversity of Stockholm) as part of Cogent Seminar\n\n\nAbstract\nIn joint w
ork with Gerard van der Geer we have studied the cohomology of local syste
ms on the Picard modular surface of Eisenstein type and the related modula
r forms. Our main technique is to use computer counts of the points over f
inite fields of small cardinality. This is done via the interpretation of
this surface as a moduli space of degree three covers of the projective li
ne.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Garcia (University College London)
DTSTART;VALUE=DATE-TIME:20210719T130000Z
DTEND;VALUE=DATE-TIME:20210719T134500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/14
DESCRIPTION:Title: Eisenstein cocycles and values of L-functions\nby Luis Garcia (
University College London) as part of Cogent Seminar\n\n\nAbstract\nThere
are several recent constructions by many authors of Eisenstein cocycles of
arithmetic groups. I will discuss a point of view on these constructions
using equivariant cohomology and differential forms. The resulting objects
behave like theta kernels relating the homology of arithmetic groups to a
lgebraic objects. I will also discuss an application to conjectures of Scz
ech and Colmez on critical values of Hecke L-functions. The talk is based
on work-in-progress with Nicolas Bergeron\, Pierre Charollois and Akshay V
enkatesh.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Yasaki (University of North Carolina Greensboro)
DTSTART;VALUE=DATE-TIME:20210802T140000Z
DTEND;VALUE=DATE-TIME:20210802T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/15
DESCRIPTION:Title: Cohomology of Congruence Subgroups\, Steinberg Modules\, and Real Q
uadratic Fields\nby Dan Yasaki (University of North Carolina Greensbor
o) as part of Cogent Seminar\n\n\nAbstract\nGiven a real quadratic field\,
there is a naturally defined Hecke-stable subspace of the cohomology of a
congruence subgroup of $SL_3(Z)$. We investigate this subspace and make
conjectures about its dependence on the real quadratic field and the rela
tionship to boundary cohomology. This is joint work with Avner Ash.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kathryn Hess (EPF Lausanne)
DTSTART;VALUE=DATE-TIME:20211122T140000Z
DTEND;VALUE=DATE-TIME:20211122T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/16
DESCRIPTION:Title: On neurons and symmetric groups\nby Kathryn Hess (EPF Lausanne)
as part of Cogent Seminar\n\n\nAbstract\nMotivated by the desire to autom
ate classification of neuron morphologies\, we designed a topological sign
ature\, the Topological Morphology Descriptor (TMD)\, that assigns a topo
logical signature\, called a barcode\, to any geometric tree (i.e\, any fi
nite binary tree embedded in R^3). We showed that the TMD effectively dete
rmines the reliability of clusterings of random and neuronal trees. Moreov
er\, using the TMD we performed an objective\, stable classification of py
ramidal cells in the rat neocortex\, based only on the shape of their dend
rites.\n\nWe have also reverse-engineered the TMD\, in order to digitally
synthesize dendrites\, to compensate for the dearth of available biologica
l 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 statisti
cally indistinguishable from real neurons of the same type. \n\nIn this ta
lk I will provide an overview of the TMD and the TNS and then describe the
results of our theoretical and computational analysis of their behavior a
nd properties\, in which symmetric groups and Coxeter complexes play a key
role.\n\nThis talk is based on joint work with Adélie Garin and Lida Kan
ari\, as well as with Justin Curry\, Jordan Desha\, and Brendan Mallery\,
and on work of Adélie Garin and Benjamin Brück\, building on earlier col
laborations led by Lida Kanari.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yang-Hui He (City University of London)
DTSTART;VALUE=DATE-TIME:20211122T150000Z
DTEND;VALUE=DATE-TIME:20211122T154500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/17
DESCRIPTION:Title: Universes as Bigdata\, or\, Machine-Learning Mathematical Structure
s\nby Yang-Hui He (City University of London) as part of Cogent Semina
r\n\n\nAbstract\nWe review how historically the problem of string phenomen
ology lead theoretical physics first to algebraic/differential geometry\,
and then to computational geometry\, and now to data science and AI.\n\nWi
th the concrete playground of the Calabi-Yau landscape\, accumulated by th
e collaboration of physicists\, mathematicians and computer scientists ove
r the last 4 decades\, we show how the latest techniques in machine-learni
ng can help explore problems of physical and mathematical interest\, from
geometry\, to group theory\, to combinatorics and number theory.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Alvarenga (University of São Paulo)
DTSTART;VALUE=DATE-TIME:20210927T140000Z
DTEND;VALUE=DATE-TIME:20210927T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/18
DESCRIPTION:Title: Automorphic forms and Hecke operators for $\\mathrm{GL}_n$ over glo
bal function fields\nby Roberto Alvarenga (University of São Paulo) a
s part of Cogent Seminar\n\n\nAbstract\nIn this talk\, we investigate the
action of Hecke operators on automorphic forms through some graphs\, known
as graphs of Hecke operators. Geometric tools are raised to connect the p
roblem of describe these graphs to calculate some products in the associat
ed Hall algebra. In the case of elliptic function fields\, we present an a
lgorithm which describes the graphs.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sander Dahmen (VU Amsterdam)
DTSTART;VALUE=DATE-TIME:20220110T140000Z
DTEND;VALUE=DATE-TIME:20220110T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/19
DESCRIPTION:Title: Formalization in number theory\nby Sander Dahmen (VU Amsterdam)
as part of Cogent Seminar\n\n\nAbstract\nProof assistants\, such as Coq\,
Isabelle\, or Lean\, are software\ntools which assist in rigorously expre
ssing mathematical statements and\ntheir proofs in a formal logical langua
ge. The mathematics that has been\nformalized this way\, ranges through ma
ny different fields. In this talk\,\nafter some general introduction\, we
will take a pragmatic "working\nnumber theorist" point of view and discuss
some past\, present\, and\npotential future formalization work\, focusing
mostly (but not\nexclusively) on the Lean proof assistant.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Assia Mahboubi (Inria - VU Amsterdam)
DTSTART;VALUE=DATE-TIME:20220110T150000Z
DTEND;VALUE=DATE-TIME:20220110T154500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/20
DESCRIPTION:Title: Mathematics and formal proofs\nby Assia Mahboubi (Inria - VU Am
sterdam) as part of Cogent Seminar\n\n\nAbstract\nMathematical logic studi
es proofs as mathematical objects: existence\,\nshape\, classification\, e
tc. Yet these formal proofs are very far from\nthe demonstrations that con
stitute the contemporary mathematical\nwriting\, as rigorous as they might
be. On the other hand\, formal\nproofs provide data structures that can b
e processed by computers\, so\nthat they can be constructed\, observed\, v
erified\, by mechanical\nmeans. Proof assistants are pieces of software de
signed for performing\nthis nature of operations\, in practice and in the
large. In this talk\nwe will try to provide some hints of the mathematics
that can be done\nwith the help of a proof assistant\, and of the benefits
one can expect\nfrom this activity.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabor Wiese (University of Luxembourg)
DTSTART;VALUE=DATE-TIME:20220124T140000Z
DTEND;VALUE=DATE-TIME:20220124T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/21
DESCRIPTION:Title: Unlikely Revelations? -- The Hidden Lattice Problem\nby Gabor W
iese (University of Luxembourg) as part of Cogent Seminar\n\n\nAbstract\nI
n this talk\, which is based on joint work with Luca Notarnicola\, I will
present the Hidden Lattice Problem (HLP)\, which is the task of recovering
a "small" lattice from the knowledge of only one or a few of its vectors.
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 "orthogonal l
attice attack" for solving this kind of problem. The main novelty that I a
m going to discuss and illustrate is an alternative algorithm for the HLP.
\n
LOCATION:https://researchseminars.org/talk/cogentseminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fredrik Strömberg (University of Nottingham)
DTSTART;VALUE=DATE-TIME:20220124T150000Z
DTEND;VALUE=DATE-TIME:20220124T154500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/22
DESCRIPTION:Title: A reduction algorithm for Hilbert modular groups\nby Fredrik St
römberg (University of Nottingham) as part of Cogent Seminar\n\n\nAbstrac
t\nGiven a group acting on a topological space it often useful to have a
“nice” set of representatives\, a so-called fundamental domain\, for t
his action. In practice it is also useful to not only know that such a dom
ain exists\, but also to know exactly how to reduce a given point to its r
epresentative.\n\nFor the modular group\, $PSL(2\,\\Z)$\, a number of fun
damental domains and associated reduction algorithms have been known for a
long time and are relatively simple to describe.\nIn the case of the Hilb
ert modular group $PSL(2\,O)$\, where $O$ is the ring of integers of a tot
ally real number field\, the fundamental domain is harder to describe geom
etrically but an algorithmic description has been known in principle since
works of Blumenthal\, Maass and others. Until recently\, however\, no exp
licit (finite-time) reduction algorithm has been known in the case of clas
s 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 numbe
r and degree.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Daw (University of Reading)
DTSTART;VALUE=DATE-TIME:20220307T150000Z
DTEND;VALUE=DATE-TIME:20220307T154500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/23
DESCRIPTION:Title: Unlikely intersections in the moduli space of abelian varieties
\nby Christopher Daw (University of Reading) as part of Cogent Seminar\n\n
\nAbstract\nLet S be a Shimura variety (e.g. the moduli space $A_g$ of\npr
incipally polarized abelian varieties of dimension g) and let $V$ be an\ni
rreducible algebraic subvariety of $S$ contained in no proper Shimura\nsub
variety. The Zilber-Pink conjecture predicts that the intersection $Y$ of\
n$V$ with the Shimura subvarieties (e.g. the loci of abelian varieties wit
h\nadditional endomorphisms) of codimension less than dim $V$ is contained
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 Zi
lber-Pink conjecture is\, so to speak\, wide open. Primarily\, this is\nbe
cause of its arithmetic complexity — in some sense\, the geometric aspec
t\nof the problem is now resolved. Indeed\, when $V$ is a curve\, the conj
ecture\nfollows from two arithmetic hypotheses: (1) the large Galois orbit
s\nconjecture\, and (2) the parametrization problem. The large Galois orbi
ts\nconjecture calls for a lower bound on the Galois orbits of the points
in $Y$.\nThe parametrization problem calls for an upper bound on the compl
exity of\ndata parametrizing Shimura subvarieties.\n\nIn this talk\, I wil
l survey ongoing programmes with Martin Orr (University\nof Manchester) ai
med at problems (1) and (2)\, respectively\, which have\nyielded unconditi
onal cases of the Zilber-Pink conjecture in $A_g$.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kartik Prasanna (University of Michigan)
DTSTART;VALUE=DATE-TIME:20220502T140000Z
DTEND;VALUE=DATE-TIME:20220502T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/24
DESCRIPTION:Title: Modular forms of weight one\, motivic cohomology and the Jacquet-La
nglands correspondence\nby Kartik Prasanna (University of Michigan) as
part of Cogent Seminar\n\n\nAbstract\nIn a previous paper with Ichino\, w
e showed that the Jacquet-Langlands correspondence for Hilbert modular for
ms\, all of whose weights are at least two\, preserves rational Hodge stru
ctures. In this talk\, I will discuss some work in progress (with Ichino)
on the case of weight one forms. Since weight one forms are not cohomologi
cal\, it is not clear how to formulate an analogous result. I will explain
the formulation\, which is suggested by another recent development\, name
ly the conjectural connection between the motivic cohomology of adjoint mo
tives and the cohomology of locally symmetric spaces.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Neil Dummigan (University of Sheffield)
DTSTART;VALUE=DATE-TIME:20220307T140000Z
DTEND;VALUE=DATE-TIME:20220307T154500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/25
DESCRIPTION:Title: Proving congruences for paramodular forms using quinary form\nb
y Neil Dummigan (University of Sheffield) as part of Cogent Seminar\n\n\nA
bstract\nI will explain how it is possible to prove various congruences of
Hecke eigenvalues\, between Siegel cusp forms of genus 2 and paramodular
level\, and genus 1 cusp forms\, including some of a type conjectured by H
arder\, for which Fretwell obtained computational evidence\, and some of a
type discovered by Buzzard and Golyshev. Exploiting the recent proof by R
oesner and Weissauer of Ibukiyama's genus 2 Jacquet-Langlands corresponden
ce\, and my joint work with Pacetti\, Rama and Tornaria\, relating algebra
ic modular forms for GU2 of a definite quaternion algebra and for O(5)\, w
e can prove several examples using linear algebra computations.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melody Chan (Brown University)
DTSTART;VALUE=DATE-TIME:20220404T130000Z
DTEND;VALUE=DATE-TIME:20220404T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
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\nAbs
tract\nI will discuss joint work with Carel Faber\, Soren Galatius\, and S
am Payne in which we prove a formula\, conjectured by Zagier in 2008\, for
the $S_n$-equivariant top-weight Euler characteristics of the moduli spac
es of n-marked\, genus g algebraic curves. Our techniques involve tropical
geometry and graph complexes.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juliette Bruce (University of California Berkeley)
DTSTART;VALUE=DATE-TIME:20220321T150000Z
DTEND;VALUE=DATE-TIME:20220321T154500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/27
DESCRIPTION:Title: Syzygies in higher dimensions\nby Juliette Bruce (University of
California Berkeley) as part of Cogent Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/cogentseminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Cadoret (Sorbonne Université)
DTSTART;VALUE=DATE-TIME:20220516T140000Z
DTEND;VALUE=DATE-TIME:20220516T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/28
DESCRIPTION:Title: Degeneration loci of $\\ell$-adic local systems\nby Anna Cadore
t (Sorbonne Université) as part of Cogent Seminar\n\n\nAbstract\nI will m
ake a partial survey of what is expected and known about the degeneration
loci of $\\ell$-adic local systems over varieties over number fields. For
$\\ell$-adic local systems arising from geometry\, understanding these de
generation loci is closely related to describing the variation of certain
algebraic-geometric invariants (those encapsulated in $\\ell$-adic cohomo
logy) in algebraic families of smooth proper varieties.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Hutchinson (University College Dublin)
DTSTART;VALUE=DATE-TIME:20220221T140000Z
DTEND;VALUE=DATE-TIME:20220221T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/29
DESCRIPTION:Title: The third homology of $SL_2(\\Q)$\nby Kevin Hutchinson (Univers
ity College Dublin) as part of Cogent Seminar\n\n\nAbstract\nFor a commuta
tive ring $R$\, the integral homology groups of $SL_2(R)$ are naturally\nm
odules over the group ring of the group of units modulo squares. We will e
xplain how this action can be understood and exploited to calculate the th
ird homology of $SL_2(\\Q)$ with half-integer coefficients. We will discus
s connections with K-theory\, scissors congruence groups and homology stab
ility questions.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Cowan (Harvard University)
DTSTART;VALUE=DATE-TIME:20220207T140000Z
DTEND;VALUE=DATE-TIME:20220207T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/30
DESCRIPTION:Title: Computing modular forms using supersingular isogeny graphs\nby
Alex Cowan (Harvard University) as part of Cogent Seminar\n\n\nAbstract\nW
e describe an algorithm that we used to compute the q-expansions of all we
ight 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 eigens
pace. Our algorithm is based on Mestre's Méthode des Graphes\, and involv
es supersingular isogeny graphs and Wiedemann's algorithm for finding the
minimal polynomial of sparse matrices over finite fields.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weibo Fu (Princeton University)
DTSTART;VALUE=DATE-TIME:20220207T150000Z
DTEND;VALUE=DATE-TIME:20220207T154500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/31
DESCRIPTION:Title: Growth of Bianchi modular forms\nby Weibo Fu (Princeton Univers
ity) as part of Cogent Seminar\n\n\nAbstract\nIn this talk\, I will establ
ish 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 s
ystem rising from the representation $Sym^k \\otimes \\overline{Sym^k}$ of
$SL_2(\\C)$. I will explain how a $p$-adic algebraic method is used for d
eriving our result.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Herbert Gangl (Durham University)
DTSTART;VALUE=DATE-TIME:20220221T150000Z
DTEND;VALUE=DATE-TIME:20220221T154500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/32
DESCRIPTION:Title: Multiple polylogarithms\, and Zagier's Conjecture revisited\nby
Herbert Gangl (Durham University) as part of Cogent Seminar\n\n\nAbstract
\nInstigated by work of Borel and Bloch\, Zagier formulated his Polylogari
thm Conjecture in the late eighties and proved it for weight 2. After a fl
urry of activity and advances at the time\, notably by Goncharov who provi
ded not only a proof for weight 3 but set out a vast program with a pletho
ra of conjectural statements for attacking it\, progress seemed to be stal
led for a number of years. More recently\, a solution to one of Goncharov'
s central conjectures in weight 4 has been found. Moreover\, by adopting a
new point of view\, work by Goncharov and Rudenko gave a proof of the ori
ginal conjecture in weight 4.\n\nIn this impressionist talk I intend to gi
ve a rough idea of the developments from the early days on\, avoiding most
of the technical bits\, and\, time permitting\, also hint at a number of
recent results for higher weight with new formulas for Grassmannian and Ao
moto polylogarithms in terms of iterated integrals (joint with S.Charlton
and D.Radchenko).\n
LOCATION:https://researchseminars.org/talk/cogentseminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mike Lipnowski (McGill University)
DTSTART;VALUE=DATE-TIME:20220627T140000Z
DTEND;VALUE=DATE-TIME:20220627T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/33
DESCRIPTION:Title: Rigid meromorphic cocycles for orthogonal groups\nby Mike Lipno
wski (McGill University) as part of Cogent Seminar\n\n\nAbstract\nIn the e
arly 2000s\, Darmon initiated a fruitful study of analogies between Hilber
t 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 upper ha
lf plane. As $Y$ mixes complex and $p$-adic topologies\, making direct se
nse of $Y$ as an analytic space seems difficult. Nonetheless\, $Y$ suppor
ts a large collection of exotic special points - corresponding to the unit
s of real quadratic fields which are inert at $p$ - and Darmon-Vonk have d
escribed 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 the space
$Y$ to orthogonal groups $G$ for quadratic spaces over $\\Q$ of arbitrary
real signature. The spaces $Y'$ support large collections of exotic spec
ial points - corresponding to subtori of G of maximal real rank - and we d
efine explicit rigid meromorphic cocycles on $Y'$\; these RMCs are analogo
us to meromorphic functions on orthogonal Shimura varieties with prescribe
d special divisors first studied by Borcherds\, and they generalize the RM
Cs constructed by Darmon-Vonk. We will also discuss some computations sug
gesting that values of our RMCs at special points might realize new instan
ces of explicit class field theory.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Funar (CNRS\, Université Grenoble Alpes)
DTSTART;VALUE=DATE-TIME:20220321T140000Z
DTEND;VALUE=DATE-TIME:20220321T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/34
DESCRIPTION:Title: Finite quotients of mapping class groups and central extensions
\nby Louis Funar (CNRS\, Université Grenoble Alpes) as part of Cogent Sem
inar\n\n\nAbstract\nA classical result of Deligne shows that nontrivial ce
ntral extensions of integral symplectic groups are not residually finite.
We explore the case of mapping class groups and compute the Schur multipli
er of finite symplectic groups.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tommy Hofmann (Universität Siegen)
DTSTART;VALUE=DATE-TIME:20220404T140000Z
DTEND;VALUE=DATE-TIME:20220404T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/35
DESCRIPTION:Title: Lattice isomorphism and the integral matrix similarity problem\
nby Tommy Hofmann (Universität Siegen) as part of Cogent Seminar\n\n\nAbs
tract\nDeciding whether two lattices over orders of finite-dimensional alg
ebras over number fields is a classical problem in algorithmic number theo
ry. We present a new algorithm for this problem\, assuming that the Wedder
burn decomposition of the algebra is "nice". As an application we discuss
the connection to the similarity problem for integral matrices (the conjug
acy problem in GL(n\,Z)).\n\nThe resulting algorithm for the latter proble
m is the first with proven complexity and performs very well in practice.
This is joint work with Werner Bley and Henri Johnston.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oscar Randal-Williams (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20220516T130000Z
DTEND;VALUE=DATE-TIME:20220516T134500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/36
DESCRIPTION:Title: Stable cohomology of congruence subgroups\nby Oscar Randal-Will
iams (University of Cambridge) as part of Cogent Seminar\n\n\nAbstract\nI
will explain how to complete and extend an argument proposed by F.\nCalega
ri for determining the $F_p$-cohomology of $SL_n(\\Z\, p^m)$ in a\ncertain
range (namely in cohomological degrees $* < p$ and for all large\nenough
$n$). The result has a uniform description at regular primes\, but\nat irr
egular primes has interesting correction terms\, controlled by\ntorsion in
$K_*(\\Z)$ and by special values of the $p$-adic L-function. The\nargumen
t for $m>1$ turns out to be almost trivial\, but for $m=1$ it\ninvolves a
delicate analysis of the cohomology of the finite groups\n$SL_n(\\Z/p)$ wi
th coefficients in certain modular representations. The\ntalk is based on
the preprint arXiv:2203.01697.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shayan Gholami (Université Sorbonne Paris Nord)
DTSTART;VALUE=DATE-TIME:20220502T130000Z
DTEND;VALUE=DATE-TIME:20220502T134500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
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 Sorbonne Pa
ris Nord) as part of Cogent Seminar\n\n\nAbstract\nLocally symmetric space
s are generalizations of modular curves\, and their cohomology plays an im
portant role in the Langlands program. In this talk\, I will first speak a
bout vanishing conjectures and known results about the cohomology of local
ly symmetric spaces of a reductive group $G$ with mod $p$ coefficient afte
r localizing at a maximal ideal of spherical Hecke algebra of $G$ and afte
r 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://researchseminars.org/talk/cogentseminar/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amina Abdurrahman (Princeton University)
DTSTART;VALUE=DATE-TIME:20220530T130000Z
DTEND;VALUE=DATE-TIME:20220530T134500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/38
DESCRIPTION:Title: Square roots of symplectic L-functions and Reidemeister torsion
\nby Amina Abdurrahman (Princeton University) as part of Cogent Seminar\n\
n\nAbstract\nIn the 70s Deligne gave a topological formula for the local e
psilon factors attached to an orthogonal representation. We consider the c
ase of a symplectic representation and present a conjecture giving a topol
ogical formula for a finer invariant\, the square class of its central val
ue. We also formulate a topological analogue of the statement\, in which t
he central value of the L-function is replaced by Reidemeister torsion of
3-manifolds\, and give a sketch of the proofs. This is joint work with Aks
hay Venkatesh.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aurel Page (INRIA\, Université de Bordeaux)
DTSTART;VALUE=DATE-TIME:20220530T140000Z
DTEND;VALUE=DATE-TIME:20220530T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/39
DESCRIPTION:Title: Algorithms for the cohomology of compact arithmetic manifolds\n
by Aurel Page (INRIA\, Université de Bordeaux) as part of Cogent Seminar\
n\n\nAbstract\nIn this joint work with Michael Lipnowski\, we describe an
algorithm that computes the cohomology of a given compact arithmetic manif
old together with the action of Hecke operators.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Hill (University College London)
DTSTART;VALUE=DATE-TIME:20220627T130000Z
DTEND;VALUE=DATE-TIME:20220627T134500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/40
DESCRIPTION:Title: Fractional weight modular forms\nby Richard Hill (University Co
llege London) as part of Cogent Seminar\n\n\nAbstract\nIt has been known s
ince the 1930s that for all positive rational numbers $p/q$\, there exist
holomorphic modular forms on $SL(2\,R)$ with weight $p/q$. This contrasts
with the situation for $Sp(2n\,R)$ with $n >1$\, where one has only integr
al and half-integral weight forms. Until recently\, it was an open questio
n whether there is any other Lie group (other than $SL_2(R)$) with holomor
phic modular forms whose weight is neither integral nor half-integral. In
this talk I will describe how we recently found examples of holomorphic mo
dular forms of weight $1/3$ on the group $SU(2\,1)$.\n\nThis is joint work
with Eberhard Freitag.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Horozov (City University of New York)
DTSTART;VALUE=DATE-TIME:20221205T140000Z
DTEND;VALUE=DATE-TIME:20221205T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/41
DESCRIPTION:Title: Cohomology of $GL(3\,\\Z)$ and $GL(4\,\\Z)$ with coefficients in ir
reducible highest weight representations\nby Ivan Horozov (City Univer
sity 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 o
f the group $SL(2\,\\Z)$.\n\nThen\, we will present explicit result of our
computations of the (Eisenstein) cohomology of the $GL(3\,\\Z)$ with coef
ficients in any irreducible finite dimensional highest weight representati
on. When the presentation is not self dual\, this is the entire group coho
mology. It is a joint result with Harder\, Bajpai and Moya Guisti. It is b
ased on the Borel-Serre compactification\, Kostant formula\, Euler charact
eristics of arithmetic groups and Poincare duality. We have applied simila
r techniques for the computation for the cohomology of $Sp(4\,\\Z)$ with c
oefficients in irreducible highest weight representations (a joint result
with Bajpai and Moya Giusti). I will mention it briefly.\n\nAfter that\, I
will present an older result of mine on cohomology of $GL(4\,\\Z)$ with
coefficients in the standard representation twisted by the determinant\, b
ased on the same ideas. It has a current continuation that has surprising
consequences for the cohomology of $GL(3\,\\Z)$. From the current computat
ions\, it follows that there is a ghost class in $H^2(GL(3\,\\Z)\, M)$$ wh
ere $M$ is the dual of the standard representation of $GL(3\,\\Z)$. Having
a ghost class means that the cohomological class in $GL(3\,\\Z)$ is not g
enerated by a maximal parabolic subgroup. In this case\, it is generated b
y a minimal parabolic subgroup - the Borel subgroup.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harald Grobner (University of Vienna)
DTSTART;VALUE=DATE-TIME:20221107T140000Z
DTEND;VALUE=DATE-TIME:20221107T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/42
DESCRIPTION:Title: A description of automorphic cohomology in low degrees\nby Hara
ld Grobner (University of Vienna) as part of Cogent Seminar\n\n\nAbstract\
nAs it is well-known by epoch-making work of Franke\, the cohomology of ar
ithmetic (congruence) subgroups of a reductive group $G$ can be expressed
as the relative Lie algebra cohomology of a space of automorphic forms $\\
mathcal{A}(G)$. In this talk we will show how to use Franke’s filtration
of $\\mathcal{A}(G)$ in order to provide a description of automorphic coh
omology in low degrees. These results of ours improve certain bounds of va
nishing\, established by Borel and also by Zucker\, and strengthen a non-v
anishing result of Rohlfs-Speh.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean Raimbault (Aix-Marseille Université)
DTSTART;VALUE=DATE-TIME:20221107T150000Z
DTEND;VALUE=DATE-TIME:20221107T154500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/43
DESCRIPTION:Title: Around the Bergeron-Venkatesh conjectures on torsion homology of ar
ithmetic lattices\nby Jean Raimbault (Aix-Marseille Université) as pa
rt of Cogent Seminar\n\n\nAbstract\nThe following phenomena have been obse
rved 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 subgroup
tends to be quite large. In arithmetic setting Bergeron and Venkatesh give
a precise quantitative statement about the asymptotic size of the torsion
part in terms of the hyperbolic volume of the manifold\, as well as some
more tentative heuristics for its finer structure. In fact they provide su
ch statements for arithmetic lattices in all symmetric spaces. Proofs rema
in elusive but there have been a number of efforts to numerically verify t
he first conjecture\, in particular in the setting of arithmetic lattices
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 will fini
sh by reporting on difficulties arising when numerically testing the conje
cture for higher-dimensional hyperbolic spaces.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolaos Diamantis (University of Nottingham)
DTSTART;VALUE=DATE-TIME:20221121T140000Z
DTEND;VALUE=DATE-TIME:20221121T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/44
DESCRIPTION:Title: Eichler cocycles and polynomials attached to derivatives of $L$-fun
ctions\nby Nikolaos Diamantis (University of Nottingham) as part of Co
gent Seminar\n\n\nAbstract\nWe discuss an analogue of the period polynomia
l we have associated with values of derivatives of $L$-functions. We state
a conjecture for the location of its zeros and provide evidence for its v
alidity\, including some proved special cases. This is joint work with L.
Rolen.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Newton (University of Oxford)
DTSTART;VALUE=DATE-TIME:20221121T150000Z
DTEND;VALUE=DATE-TIME:20221121T154500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/45
DESCRIPTION:Title: Modularity of elliptic curves over imaginary quadratic fields\n
by James Newton (University of Oxford) as part of Cogent Seminar\n\n\nAbst
ract\nI will discuss recent progress towards establishing modularity of el
liptic curves over CM number fields\, particularly imaginary quadratic fie
lds. One way of phrasing "modularity" in this context is that the $L$-func
tion of the elliptic curve can be described in terms of eigenvalues of Hec
ke operators on the cohomology of arithmetic subgroups of $SL(2\,\\C)$. Th
e new results I will talk about are joint work with Ana Caraiani.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frédéric Rochon (Université du Québec à Montréal)
DTSTART;VALUE=DATE-TIME:20221205T150000Z
DTEND;VALUE=DATE-TIME:20221205T154500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/46
DESCRIPTION:Title: Torsion on some fibered cusp manifolds\nby Frédéric Rochon (U
niversité du Québec à Montréal) as part of Cogent Seminar\n\n\nAbstrac
t\nGiven a number field $F$ with ring of integers $O_F$\, one can associat
e to any torsion free subgroup $\\Gamma$ of $SL(2\,O_F)$ of finite index a
complete Riemannian manifold of finite volume with fibered cusp ends. Fo
r natural choices of flat vector bundles on such a manifold\, we will expl
ain how analytic torsion can be related to Reidemeister torsion. As an ap
plication\, we will indicate how\, in some arithmetic settings\, this rela
tion can be used to derive exponential growth of torsion in cohomology for
various sequences of congruence subgroups. This is an ongoing joint work
with Werner Mueller.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Studenmund (Binghamton University)
DTSTART;VALUE=DATE-TIME:20221219T140000Z
DTEND;VALUE=DATE-TIME:20221219T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/47
DESCRIPTION:Title: Counting flat cycles in the homology of certain locally symmetric s
paces\nby Daniel Studenmund (Binghamton University) as part of Cogent
Seminar\n\n\nAbstract\nFor $n \\geq 2$\, congruence covers $X(m)$ of the l
ocally symmetric space $SL(n\,\\Z) \\backslash SL(n\,\\R) / SO(n)$ encode
the information of all finite covering spaces. We will use geometric and a
rithmetic methods to determine lower bounds on the growth\, as a function
of $m$\, of the dimension of a subspace rational homology groups $H_n(X(m)
\; \\Q)$ spanned by cycles represented by flat submanifolds. This builds o
n work of\, and addresses a question of\, Avramidi and Nguyen-Phan\, who s
howed that the homology of such covers arising from flat cycles grows arbi
trarily large. The proof of our result combines their techniques with pers
pective 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\, following wo
rk of Tshishiku and Zschumme. This work is joint with Bena Tshishiku.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robin Sroka (McMaster University)
DTSTART;VALUE=DATE-TIME:20221219T150000Z
DTEND;VALUE=DATE-TIME:20221219T154500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/48
DESCRIPTION:Title: On the high-dimensional rational cohomology of arithmetic Chevalley
groups\nby Robin Sroka (McMaster University) as part of Cogent Semina
r\n\n\nAbstract\nWhile the rational cohomology of arithmetic groups such a
s $\\operatorname{SL}_n(\\mathbb{Z})$ and $\\operatorname{Sp}_{2n}(\\mathb
b{Z})$ can often be completely computed if the cohomological degree is sma
ll compared to $n$\, little is known about it in high cohomological degree
s. In this talk\, I will discuss vanishing results that have recently been
obtained for the high-dimensional rational cohomology of $\\operatorname{
SL}_n(\\mathbb{Z})$\, $\\operatorname{Sp}_{2n}(\\mathbb{Z})$ and other ari
thmetic Chevalley groups. This is related to a conjecture of Church--Farb-
-Putman and based on joint works with Brück--Miller--Patzt--Wilson\, Brü
ck--Patzt and Brück--Santos Rego.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathilde Gerbelli-Gauthier (McGill University)
DTSTART;VALUE=DATE-TIME:20230213T140000Z
DTEND;VALUE=DATE-TIME:20230213T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/49
DESCRIPTION:Title: Growth of cohomology of arithmetic groups and endoscopy\nby Mat
hilde Gerbelli-Gauthier (McGill University) as part of Cogent Seminar\n\n\
nAbstract\nHow fast do Betti numbers grow in a congruence tower of compact
arithmetic manifolds? The dimension of the middle degree of cohomology is
proportional to the volume of the manifold\, but away from the middle the
growth is known to be sub-linear in the volume. I will explain how automo
rphic representations and the phenomenon of endoscopy provide a framework
to understand and quantify this slow growth. Specifically\, I will discuss
how to obtain both general upper (and in a few cases\, show that they are
sharp) for lattices in unitary groups using Arthur’s stable trace formu
la. This is joint work with Rahul Dalal.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. Raghuram (Fordham University)
DTSTART;VALUE=DATE-TIME:20230213T150000Z
DTEND;VALUE=DATE-TIME:20230213T154500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/50
DESCRIPTION:Title: Special values of Rankin-Selberg L-functions over a totally imagina
ry 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 $GL(n)\\times GL(m
)$ over a totally imaginary base field. In contrast to a totally real base
field\, when the base field is totally imaginary\, some delicate signatur
es enter the reciprocity laws for these special values. These signatures d
epend on whether or not the totally imaginary base field contains a CM sub
field. The proof depends on a generalization of my work with Günter Harde
r on rank-one Eisenstein cohomology for $GL(N)$ where $N = n+m$. The ratio
nality result comes from interpreting Langlands’s constant term theorem
in terms of an arithmetically defined intertwining operator between Hecke
summands in the cohomology of the Borel-Serre boundary of a locally symmet
ric space for $GL(N)$. The signatures arise from Galois action on certain
local systems that intervene in boundary cohomology.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandra Iozzi (ETH Zurich)
DTSTART;VALUE=DATE-TIME:20230227T150000Z
DTEND;VALUE=DATE-TIME:20230227T154500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/51
DESCRIPTION:Title: Irreducible lattices and bounded cohomology\nby Alessandra Iozz
i (ETH Zurich) as part of Cogent Seminar\n\n\nAbstract\nWe show some of th
e similarities and some of the differences between irreducible lattices 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 concrete exa
mple with interesting properties\, among which some in terms of bounded co
homology and quasimorphisms.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Satoshi Kondo (Middle East Technical University Northern Cyprus)
DTSTART;VALUE=DATE-TIME:20230313T140000Z
DTEND;VALUE=DATE-TIME:20230313T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/52
DESCRIPTION:Title: Automorphic forms over function fields with Steinberg at infinity a
nd modular symbols\nby Satoshi Kondo (Middle East Technical University
Northern Cyprus) as part of Cogent Seminar\n\n\nAbstract\nJoint work with
Yasuda (Hokkaido U). Let $F$ be a global field of positive characteristi
c and $\\infty$ a place of $F$. We study automorphic forms for $\\mathrm{G
L}_d$ over $F$\nsuch that ``the $\\infty$-component of the associated auto
morphic representation is isomorphic to the Steinberg representation".\nWe
introduce modular symbols in this context and show that the modular symbo
ls generate the space of such automorphic forms with $\\mathbb{Q}$-coeffic
ients. We also have some results with $\\mathbb{Z}$-coefficients.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Logan (Tutte Institute for Mathematics and Computing)
DTSTART;VALUE=DATE-TIME:20230313T150000Z
DTEND;VALUE=DATE-TIME:20230313T154500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/53
DESCRIPTION:Title: Higher modularity of elliptic curves over function fields\nby A
dam Logan (Tutte Institute for Mathematics and Computing) as part of Cogen
t Seminar\n\n\nAbstract\n(joint with Jared Weinstein) The ideas of Wiles o
n the modularity of elliptic curves over Q\, and subsequent extensions and
adaptations\, have had a great influence on the study of Diophantine equa
tions through the modular method. There is an analogous concept for ellip
tic curves over function fields over finite fields\, known as Drinfeld mod
ularity: an elliptic curve over ${\\mathbb F}_q(t)$ with split multiplicat
ive reduction at infinity is covered by a Drinfeld modular curve\, which p
arametrizes Drinfeld modules of rank $2$ with a suitable level structure.
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\,\\dots\,t_n)
$ obtained by replacing $t$ by $t_i$. Then there is an $n$-dimensional mo
duli space of "shtukas" over ${\\mathbb F}_q(t_1\,\\dots\,t_n)$ that is co
njectured to be in correspondence with $E_1 \\times \\dots E_n$. We descr
ibe how to construct these moduli spaces concretely as the sets of $2 \\ti
mes 2$ matrices of polynomials satisfying certain specialization condition
s and prove the conjecture in a few special cases by means of computations
on K3 surfaces.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Fabrizio Di Cerbo (University of Florida at Gainsville)
DTSTART;VALUE=DATE-TIME:20230327T130000Z
DTEND;VALUE=DATE-TIME:20230327T134500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/54
DESCRIPTION:Title: POSTPONED!\nby Luca Fabrizio Di Cerbo (University of Florida at
Gainsville) as part of Cogent Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/cogentseminar/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alice Pozzi (Imperial College London)
DTSTART;VALUE=DATE-TIME:20230424T130000Z
DTEND;VALUE=DATE-TIME:20230424T134500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/55
DESCRIPTION:Title: Rigid meromorphic cocycles and $p$-adic variations of modular forms
\nby Alice Pozzi (Imperial College London) as part of Cogent Seminar\n
\n\nAbstract\nA rigid meromorphic cocycle is a class in the first cohomolo
gy of the group ${\\rm SL}_2(\\Z[1/p])$ acting on the non-zero rigid merom
orphic functions on the Drinfeld $p$-adic upper half plane by M\\"obius tr
ansformation. Rigid meromorphic cocycles can be evaluated at points of "re
al multiplication''\, and their values conjecturally lie in composita of a
belian extensions of real quadratic fields\, suggesting striking analogies
with the classical theory of complex multiplication.\n\nIn this talk\, we
discuss the proof of this conjecture for a special class of rigid meromor
phic cocycles. Our proof connects the values of rigid meromorphic cocycles
to the study of certain $p$-adic variations of Hilbert modular forms. Thi
s is joint work with Henri Darmon and Jan Vonk.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jitendra Bajpai (Georg-August-Universität Göttingen)
DTSTART;VALUE=DATE-TIME:20230424T140000Z
DTEND;VALUE=DATE-TIME:20230424T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/56
DESCRIPTION:Title: Arithmeticity and thinness of hypergeometric groups\nby Jitendr
a Bajpai (Georg-August-Universität Göttingen) as part of Cogent Seminar\
n\n\nAbstract\nThe monodromy groups of hypergeometric differential equatio
ns of type ${}_nF_{n-1}$ are often called hypergeometric groups. These are
subgroups of $GL(n)$. Recently\, the arithmeticity and thinness of these
groups have caught a lot of attention. In the talk\, a gentle introduction
and recent progress in the theory of hypergeometric groups will be presen
ted.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Kupers (University of Toronto Scarborough)
DTSTART;VALUE=DATE-TIME:20230508T140000Z
DTEND;VALUE=DATE-TIME:20230508T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/57
DESCRIPTION:Title: Cohomology of arithmetic groups and high-dimensional manifolds\
nby Alexander Kupers (University of Toronto Scarborough) as part of Cogent
Seminar\n\n\nAbstract\nI will discuss several older and more recent resul
ts about relationships between arithmetic groups and diffeomorphism groups
of high-dimensional manifolds\, which in turn relate their cohomology gro
ups. This includes joint work with Oscar Randal-Williams\, Mauricio Bustam
ente\, and Manuel Krannich.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Caraiani (Imperial College London / University of Bonn)
DTSTART;VALUE=DATE-TIME:20230522T130000Z
DTEND;VALUE=DATE-TIME:20230522T134500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/58
DESCRIPTION:Title: On Ihara's lemma for Hilbert modular varieties\nby Ana Caraiani
(Imperial College London / University of Bonn) as part of Cogent Seminar\
n\n\nAbstract\nHilbert modular varieties are Shimura varieties attached to
$GL_2$\nover a totally real field\, generalizing modular curves. I will d
iscuss\non-going work with Matteo Tamiozzo\, whose aim is to understand th
e\ncohomology of Hilbert modular varieties with torsion coefficients. I wi
ll\nfocus on a result known as Ihara's lemma\, which leads to a\nrepresent
ation-theoretic description of the cohomology. I will explain a\nphenomeno
n known as geometric Jacquet-Langlands which plays a key role in\nour proo
f.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lenny Fukshansky (Claremont McKenna College)
DTSTART;VALUE=DATE-TIME:20230605T130000Z
DTEND;VALUE=DATE-TIME:20230605T134500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/59
DESCRIPTION:Title: Sparsity\, virtually rectangular lattices and elliptic curves\n
by Lenny Fukshansky (Claremont McKenna College) as part of Cogent Seminar\
n\n\nAbstract\nA lattice is called virtually rectangular if it contains an
orthogonal sublattice of finite index. We establish necessary and suffici
ent conditions for a lattice to be virtually rectangular and determine the
smallest index of an orthogonal sublattice. This investigation is closely
connected to the study of sparsity and a certain sparse analogue of Minko
wski’s successive minima theorem. In the 2-dimensional case\, our result
s imply certain isogeny properties of elliptic curves.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamara Kohler (Universidad Complutense Madrid)
DTSTART;VALUE=DATE-TIME:20230605T140000Z
DTEND;VALUE=DATE-TIME:20230605T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/60
DESCRIPTION:Title: Clique homology is QMA1 hard\nby Tamara Kohler (Universidad Com
plutense Madrid) as part of Cogent Seminar\n\n\nAbstract\nIn this seminar
I will discuss recent work studying the computational complexity of determ
ining homology groups of simplicial complexes\, a fundamental task in comp
utational topology. We show that the decision version of this problem is Q
MA1-hard - where QMA1 is a quantum version of the classical complexity cla
ss NP. Moreover\, we show that a version of the problem satisfying a suita
ble promise and certain constraints is contained in QMA (a slightly differ
ent quantum analogue of NP). This suggests that the seemingly classical pr
oblem may in fact be quantum mechanical. In fact\, we are able to signific
antly strengthen this by showing that the problem remains QMA1-hard in the
case of clique complexes\, a family of simplicial complexes specified by
a graph which is relevant to the problem of topological data analysis. The
proof combines a number of techniques from Hamiltonian complexity and hom
ological algebra. I will discuss potential implications for the problem of
quantum advantage in topological data analysis.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victoria Cantoral Farfan (Leibniz Universität\, Hannover)
DTSTART;VALUE=DATE-TIME:20230703T130000Z
DTEND;VALUE=DATE-TIME:20230703T134500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/62
DESCRIPTION:Title: Monodromy groups of Jacobians with definite quaternionic multiplica
tion\nby Victoria Cantoral Farfan (Leibniz Universität\, Hannover) as
part of Cogent Seminar\n\n\nAbstract\nLet $A$ be an abelian variety over
a number field. The connected monodromy field of $A$ is the minimal field
over which the images of all the $\\ell$-adic torsion representations have
connected Zariski closure. During this talk\, we will show that for all e
ven $g\\geq4$\, there exist infinitely many geometrically nonisogenous abe
lian varieties $A$ over $\\mathbb Q$ of dimension $g$ where the connected
monodromy field is strictly larger than the field of definition of the end
omorphisms of $A$. Our construction arises from explicit families of hyper
elliptic Jacobians with definite quaternionic multiplication. This is a jo
int work with Lombardo and Voight.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romain Branchereau (University of Manitoba)
DTSTART;VALUE=DATE-TIME:20230703T140000Z
DTEND;VALUE=DATE-TIME:20230703T144500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115113Z
UID:cogentseminar/63
DESCRIPTION:Title: Upper bound on the denominators of Eisenstein classes in Bianchi ma
nifolds\nby Romain Branchereau (University of Manitoba) as part of Cog
ent Seminar\n\n\nAbstract\nA general conjecture of Harder relates the deno
minator of the Eisenstein cohomology of certain locally symmetric spaces t
o special values of L-functions. In this talk\, we consider the locally sy
mmetric space associated with SL(2\,K) where K is an imaginary quadratic f
ield. I will explain how results of Ito and Sczech can be used to prove an
upper bound on the denominator in terms of a special value of a Hecke L-f
unction. When the class number of K is one\, we can combine this result wi
th a lower bound obtained by Berger to get the exact denominator.\n
LOCATION:https://researchseminars.org/talk/cogentseminar/63/
END:VEVENT
END:VCALENDAR