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BEGIN:VEVENT
SUMMARY:Mikhail Belolipetsky (IMPA)
DTSTART:20211004T130000Z
DTEND:20211004T134500Z
DTSTAMP:20260422T185352Z
UID:BIRS-21w5205/1
DESCRIPTION:Title: Subspace stabilisers in hyperbolic lattices\nby Mikhail Belolipet
sky (IMPA) as part of BIRS workshop: Lattices and Cohomology of Arithmetic
Groups\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5205/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Miller (Purdue University)
DTSTART:20211004T141000Z
DTEND:20211004T145500Z
DTSTAMP:20260422T185352Z
UID:BIRS-21w5205/2
DESCRIPTION:Title: Stability patterns in the cohomology of SLn(Z) and its congruence sub
groups\nby Jeremy Miller (Purdue University) as part of BIRS workshop:
Lattices and Cohomology of Arithmetic Groups\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5205/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Patzt (Copenhagen University/ University of Oklahoma)
DTSTART:20211004T160000Z
DTEND:20211004T164500Z
DTSTAMP:20260422T185352Z
UID:BIRS-21w5205/3
DESCRIPTION:Title: Top cohomology of congruence subgroups of SL_n(Z)\nby Peter Patzt
(Copenhagen University/ University of Oklahoma) as part of BIRS workshop:
Lattices and Cohomology of Arithmetic Groups\n\n\nAbstract\nThe principal
congruence subgroup of SL_n(Z) of prime level\np is the kernel of the mod
p map SL_n(Z) to SL_n(Z/pZ). Its cohomology\nvanishes in degrees above n(
n-1)/2. Lee and Szczarba gave a comparison\nmap of its cohomology in top d
egree n(n-1)/2 to the top homology of an\n"oriented" version of the Tits b
uilding of F_p. We prove this map is\nsurjective for all primes p and inje
ctive if and only if p=2\,3\,5. In\nparticular\, the case p=5 is a new and
complete computation of the top\ncohomology. This is joint work with Jere
my Miller and Andrew Putman.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5205/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jennifer Wilson (University of Michigan)
DTSTART:20211004T170000Z
DTEND:20211004T174500Z
DTSTAMP:20260422T185352Z
UID:BIRS-21w5205/4
DESCRIPTION:Title: The high-degree cohomology of the special linear group\nby Jennif
er Wilson (University of Michigan) as part of BIRS workshop: Lattices and
Cohomology of Arithmetic Groups\n\n\nAbstract\nIn this talk I will describ
e some current efforts to understand the\nhigh-degree rational cohomology
of SL_n(Z)\, or more generally the\ncohomology of SL_n(O) when O is a numb
er ring. I will survey some results\,\nconjectures\, and ongoing work towa
rd this goal. We will see that a key\napproach is to construct appropriate
ly "small" flat resolutions of an\nSL_n(O)-representation called the Stein
berg module\, and overview how we may\nhope to accomplish this by studying
the topology of certain associated\nsimplicial complexes. This talk inclu
des work joint with Brück\, Kupers\,\nMiller\, Patzt\, Sroka\, and Yasaki
.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5205/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haluk Sengun (University of Sheffield)
DTSTART:20211005T130000Z
DTEND:20211005T134500Z
DTSTAMP:20260422T185352Z
UID:BIRS-21w5205/5
DESCRIPTION:Title: Periods of mod p Bianchi modular forms and Selmer groups\nby Halu
k Sengun (University of Sheffield) as part of BIRS workshop: Lattices and
Cohomology of Arithmetic Groups\n\n\nAbstract\nThe relationship between sp
ecial values of L-functions modular\nforms and Selmer group of modular p-a
dic Galois representations is a\nmajor theme in number theory. Given the d
eveloping mod p Langlands\nprogram\, it is natural to ask whether there so
me kind of mod p analogue\nof the above theme. Notice that mod p modular f
orms do not have\nassociated L-functions! In this talk\, I will report on
ongoing work with\nLewis Combes in which we formulate\, and computationall
y test\, a\nconnection between Selmer groups of mod p Galois representatio
ns and mod\np Bianchi modular forms. This is inspired by a speculation of
Calegari\nand Venkatesh.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5205/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renaud Coulangeon (Institut de Mathematiques de Bordeaux)
DTSTART:20211005T140000Z
DTEND:20211005T144500Z
DTSTAMP:20260422T185352Z
UID:BIRS-21w5205/6
DESCRIPTION:Title: On Grayson-Stuhler filtration of Euclidean lattices\nby Renaud Co
ulangeon (Institut de Mathematiques de Bordeaux) as part of BIRS workshop:
Lattices and Cohomology of Arithmetic Groups\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5205/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Rickards (University of Colorado Boulder)
DTSTART:20211005T160000Z
DTEND:20211005T163000Z
DTSTAMP:20260422T185352Z
UID:BIRS-21w5205/7
DESCRIPTION:Title: Improved computation of fundamental domains for arithmetic Fuchsian g
roups\nby James Rickards (University of Colorado Boulder) as part of B
IRS workshop: Lattices and Cohomology of Arithmetic Groups\n\n\nAbstract\n
The fundamental domain of an arithmetic Fuchsian group $\\Gamma$ reveals a
lot of interesting information about the group. An algorithm to compute t
his fundamental domain in practice was given by Voight\, and it was later
expanded by Page to the case of arithmetic Kleinian groups. Page's version
features a probabilistic enumeration of group elements\, which performs s
ignificantly better in practice. In this talk\, we describe work to improv
e the geometric algorithms\, and specialize Page's enumeration down to Fuc
hsian groups\, to produce a final algorithm that is much more efficient. O
ptimal choices of constants in the enumeration are given by heuristics\, w
hich are supported by large amounts of data. This algorithm has been imple
mented in PARI/GP\, and we demonstrate its practicality by comparing runni
ng times versus the live Magma implementation of Voight's algorithm.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5205/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Yasaki (The University of North Carolina at Greensboro)
DTSTART:20211005T164500Z
DTEND:20211005T171500Z
DTSTAMP:20260422T185352Z
UID:BIRS-21w5205/8
DESCRIPTION:Title: Perfect Forms Over Imaginary Quadratic Fields\nby Dan Yasaki (The
University of North Carolina at Greensboro) as part of BIRS workshop: Lat
tices and Cohomology of Arithmetic Groups\n\n\nAbstract\nGiven an imaginar
y quadratic field\, there is a finite number of\nequivalence classes of pe
rfect forms over that field. We investigate these\nforms in the rank 2 ca
se using a Voronoi's reduction theory. We show that\nthe perfect forms ca
nnot get too complicated\, which allows us to give a\nlower bound on the n
umber such perfect forms in terms of the discriminant\nof the field and th
e value of the Dedekind zeta function at 2. This is\njoint work with Kris
ten Scheckelhoff and Kalani Thalagoda.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5205/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruth Kellerhals (University of Fribourg)
DTSTART:20211007T130000Z
DTEND:20211007T134500Z
DTSTAMP:20260422T185352Z
UID:BIRS-21w5205/13
DESCRIPTION:Title: A polyhedral approach to the arithmetic and geometry of hyperbolic l
ink complements\nby Ruth Kellerhals (University of Fribourg) as part o
f BIRS workshop: Lattices and Cohomology of Arithmetic Groups\n\n\nAbstrac
t\nMotivated by the work of Meyer\, Millichap and Trapp [MMT] and by Thurs
ton\, I shall present an elementary polyhedral approach to study and deduc
e results about the arithmeticity and commensurability of an infinite fami
ly of hyperbolic link complements M_n for n>2. The manifold M_n is the co
mplement of the 3-sphere by the (2n)-link chain. \nThe hyperbolic structur
e of M_n stems from an ideal right-angled polyhedron that can be cut into
four copies of an ideal right-angled n-gonal antiprism. \nEach of these po
lyhedra gives rise to a hyperbolic Coxeter orbifold that is commensurable
to a hyperbolic orbifold with a single cusp. Vinberg's arithmeticity crite
rion and certain cusp density and volume computations allow us to reproduc
e some of the main results in [MMT] about M_n in a comparatively elementar
y and direct way. This approach works in several other cases of link compl
ements as well.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5205/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean Raimbault ((Institut de Mathematiques de Toulouse)
DTSTART:20211007T140000Z
DTEND:20211007T144500Z
DTSTAMP:20260422T185352Z
UID:BIRS-21w5205/14
DESCRIPTION:Title: Asymptotic bounds for the homology of arithmetic lattices\nby Je
an Raimbault ((Institut de Mathematiques de Toulouse) as part of BIRS work
shop: Lattices and Cohomology of Arithmetic Groups\n\n\nAbstract\nI will d
iscuss work with M. Frączyk and S. Hurtado which implies the following st
atements: given a semisimple Lie group G there is a constant C such that f
or any (torsion-free) lattice Γ\\Gamma in G\, the size of the torsion sub
groups of all its homology groups is at most C^v where v is its covolume i
n G. We prove this by constructing a simplicial complex with O(v) vertices
and bounded degree which is a classifying space for Γ\\Gamma\, solving a
conjecture of T. Gelande\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5205/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ha Tran (Concordia University of Edmonton)
DTSTART:20211007T160000Z
DTEND:20211007T163000Z
DTSTAMP:20260422T185352Z
UID:BIRS-21w5205/15
DESCRIPTION:Title: The size function for imaginary sextic fields\nby Ha Tran (Conco
rdia University of Edmonton) as part of BIRS workshop: Lattices and Cohomo
logy of Arithmetic Groups\n\n\nAbstract\nLet $F$ be an imaginary cylic sex
tic field with discriminant $\\Delta$ and the ring of integers $O_F$. \n
The size function $h^0$ for $F$ is an analogue of the dime
nsion of the Riemann-Roch spaces of divisors on an algebraic curve. By Van
der Geer and Schoof's conjecture\, on the set of all (isometric) ideal la
ttices of covolume $\\sqrt{|\\Delta|}$ the function $h^0$ attains its max
imum at the trivial ideal lattice $O_F$. In this talk we will discuss the
main idea to prove that the conjecture holds for $F$.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5205/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamar Blanks (Rutgers University)
DTSTART:20211007T164500Z
DTEND:20211007T171500Z
DTSTAMP:20260422T185352Z
UID:BIRS-21w5205/16
DESCRIPTION:Title: Generating Cryptographically-Strong Random Lattice Bases and Recogni
zing Rotations of Z^n\nby Tamar Blanks (Rutgers University) as part of
BIRS workshop: Lattices and Cohomology of Arithmetic Groups\n\n\nAbstract
\nLattice-based cryptography relies on generating random bases which are d
ifficult to fully reduce. Given a lattice basis (such as the private basis
for a cryptosystem)\, all other bases are related by multiplication by ma
trices in GL(n\, Z). We compare the strengths of various methods to sample
random elements of SL(n\, Z)\, finding some are stronger than others with
respect to the problem of recognizing rotations of the Z^n lattice. In pa
rticular\, the standard algorithm of multiplying unipotent generators toge
ther (as implemented in Magma's RandomSLnZ command) generates instances of
this last problem which can be efficiently broken\, even in dimensions ne
aring 1\,500. We also can efficiently break the random basis generation me
thod in one of the NIST Post-Quantum Cryptography competition submissions
(DRS). Other random basis generation algorithms (some older\, some newer)
are described which appear to be much stronger.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5205/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tian An Wong (University of Michigan-Dearborn)
DTSTART:20211006T130000Z
DTEND:20211006T134500Z
DTSTAMP:20260422T185352Z
UID:BIRS-21w5205/17
DESCRIPTION:Title: On Eisenstein cocycles over imaginary quadratic fields\nby Tian
An Wong (University of Michigan-Dearborn) as part of BIRS workshop: Lattic
es and Cohomology of Arithmetic Groups\n\n\nAbstract\nEisenstein cocyles a
re elements in the group cohomology of\nGL(n) that parametrize special val
ues of L-functions. I will report on\njoint work with J. Flórez and C. Ka
rabulut on our construction of\nEisenstein cocyles over imaginary quadrati
c fields $K$\, proving the\nintegrality of Hecke L-functions attached to d
egree $n$ extensions of\n$K$. This gives a new proof of a result previousl
y obtained by P. Colmez\nand L. Schneps\, and most recently by N. Bergeron
\, P. Charollois\, and L.\nGarcia. Time permitting\, I will discuss work i
n progress on the\ninterpolation of these special values via a p-adic L-fu
nction.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5205/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ling Long (Louisiana State University)
DTSTART:20211006T140000Z
DTEND:20211006T144500Z
DTSTAMP:20260422T185352Z
UID:BIRS-21w5205/18
DESCRIPTION:Title: From hypergeometric functions to lattices of generalized Legendre cu
rves and beyond\nby Ling Long (Louisiana State University) as part of
BIRS workshop: Lattices and Cohomology of Arithmetic Groups\n\n\nAbstract\
nIn this talk\, we will explain how to use hypergeometric functions to com
pute period lattices of generalized Legendre curves based on the work of A
rchinard and Wolfart and automorphic forms on arithmetic triangle groups b
ased on the work of Yang. From which we will see how some recent developme
nts on hypergeometric functions over finite fields can be used to compute
the action of Hecke operators on automorphic forms on arithmetic triangle
groups.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5205/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Espitau (NTT Secure Platform Laboratories)
DTSTART:20211008T121500Z
DTEND:20211008T124500Z
DTSTAMP:20260422T185352Z
UID:BIRS-21w5205/19
DESCRIPTION:Title: Algorithmic reduction of algebraic lattices\nby Thomas Espitau (
NTT Secure Platform Laboratories) as part of BIRS workshop: Lattices and C
ohomology of Arithmetic Groups\n\n\nAbstract\nAfter revisiting the basics
of algorithmic reduction theory\nfor lattices\nunder a more algebraic geom
etric prism\, we present generic strategies to\nenhance the reduction over
algebraic lattices over number fields (a.k.a.\nhermitian vector bundles o
ver arithmetic curves) and see how we can\nleverage\nsymplectic symmetries
to design faster processes. Such techniques can be\nused\nto parallelize
and speed up the core computations in algorithmic number\ntheory and\nfor
the tractable cohomologies of arithmetic groups.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5205/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabrielle Nebe (RWTH Aachen)
DTSTART:20211008T130000Z
DTEND:20211008T134500Z
DTSTAMP:20260422T185352Z
UID:BIRS-21w5205/20
DESCRIPTION:Title: Computational tools for G-invariant quadratic forms (\nby Gabrie
lle Nebe (RWTH Aachen) as part of BIRS workshop: Lattices and Cohomology o
f Arithmetic Groups\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5205/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathieu Dutour Sikiric (Rudjer Bosković Institute)
DTSTART:20211008T140000Z
DTEND:20211008T144500Z
DTSTAMP:20260422T185352Z
UID:BIRS-21w5205/21
DESCRIPTION:Title: ppermutalib/polyhedral tools for polyhedral computation\nby Math
ieu Dutour Sikiric (Rudjer Bosković Institute) as part of BIRS workshop:
Lattices and Cohomology of Arithmetic Groups\n\n\nAbstract\nOver several w
ork that I did\, I use a combination\nof tools from group theory\, polyhed
ral geometry in order to\ncompute geometric or topological information.\nI
have now shifted most of my programs to a C++ framework\nin order to achi
eve the best performance. All of the software\nis open source and I will p
resent what has been done\, the\nissues and what can be done in the future
. I will present here\nwhat parts are relevant to lattice and cohomology t
heories.\n\n---The foundational part of a lot of this is "permutalib" whic
h is\na permutation group library that allows to compute set-stabilizer\na
nd other operations needed for polyhedral computation which\nis 10 times f
aster than GAP.\n\n---A direct application of it is the computation of the
automorphism\ngroup of polytope. Another fundamental construction is the\
ncanonical form of a polytope which greatly helps with enumeration\ntasks.
\n\n---This also translates into an algorithm for the computation of the\n
canonical form of a quadratic form. An illustration of this\nwas the enume
ration of C-type in dimension 6 where we found\n55 million types in reason
able time.\n\n---We also provide efficient algorithms for dual description
using\nsymmetries where we achieve a two-fold improvement over GAP.\n---W
e also provide an implementation of the Vinberg algorithm\nusing all the a
bove that allows us to solve some 19 dimensional\nexamples easily.\n\nThe
point of this presentation is not really to concentrate on specific\nprobl
ems but to show approaches that allow us to treat large problems.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5205/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steffen Kionke (University of Hagen\, Germany)
DTSTART:20211008T154500Z
DTEND:20211008T160000Z
DTSTAMP:20260422T185352Z
UID:BIRS-21w5205/22
DESCRIPTION:Title: Profinite rigidity of lattices in higher rank Lie groups\nby Ste
ffen Kionke (University of Hagen\, Germany) as part of BIRS workshop: Latt
ices and Cohomology of Arithmetic Groups\n\n\nAbstract\nThe famous arithme
ticity and superrigidity results of Margulis allow to classify lattices in
higher rank Lie groups up to commensurability. It is known that two non-c
ommensurable lattices can still be profinitely commensurable\, i.e.\, thei
r profinite completions have isomorphic open subgroups. In this talk I wil
l explain how lattices in higher rank can be classified up to profinite co
mmensurability (modulo the congruence subgroup problem). We will see that
profinitely commensurable lattices exist in most simple Lie groups of high
er rank. More surprisingly\, such examples cannot exist in the complex Lie
groups of type E_8\, F_4 and G_2.\n\nThis is based on joint work with Hol
ger Kammeyer.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5205/22/
END:VEVENT
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