BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Mikhail Belolipetsky (IMPA) DTSTART:20211004T130000Z DTEND:20211004T134500Z DTSTAMP:20260404T060945Z UID:BIRS-21w5205/1 DESCRIPTION:Title: Subspace stabilisers in hyperbolic lattices\nby Mikhail Be lolipetsky (IMPA) as part of BIRS workshop: Lattices and Cohomology of Ari thmetic Groups\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5205/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Jeremy Miller (Purdue University) DTSTART:20211004T141000Z DTEND:20211004T145500Z DTSTAMP:20260404T060945Z UID:BIRS-21w5205/2 DESCRIPTION:Title: Stability patterns in the cohomology of SLn(Z) and its congrue nce subgroups\nby Jeremy Miller (Purdue University) as part of BIRS wo rkshop: Lattices and Cohomology of Arithmetic Groups\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5205/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Patzt (Copenhagen University/ University of Oklahoma) DTSTART:20211004T160000Z DTEND:20211004T164500Z DTSTAMP:20260404T060945Z UID:BIRS-21w5205/3 DESCRIPTION:Title: Top cohomology of congruence subgroups of SL_n(Z)\nby Pete r Patzt (Copenhagen University/ University of Oklahoma) as part of BIRS wo rkshop: Lattices and Cohomology of Arithmetic Groups\n\n\nAbstract\nThe pr incipal 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 a bove n(n-1)/2. Lee and Szczarba gave a comparison\nmap of its cohomology i n top degree n(n-1)/2 to the top homology of an\n"oriented" version of the Tits building of F_p. We prove this map is\nsurjective for all primes p a nd injective 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 wi th Jeremy Miller and Andrew Putman.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5205/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Jennifer Wilson (University of Michigan) DTSTART:20211004T170000Z DTEND:20211004T174500Z DTSTAMP:20260404T060945Z UID:BIRS-21w5205/4 DESCRIPTION:Title: The high-degree cohomology of the special linear group\nby Jennifer Wilson (University of Michigan) as part of BIRS workshop: Lattic es and Cohomology of Arithmetic Groups\n\n\nAbstract\nIn this talk I will describe some current efforts to understand the\nhigh-degree rational coho mology of SL_n(Z)\, or more generally the\ncohomology of SL_n(O) when O is a number ring. I will survey some results\,\nconjectures\, and ongoing wo rk toward this goal. We will see that a key\napproach is to construct appr opriately "small" flat resolutions of an\nSL_n(O)-representation called th e Steinberg module\, and overview how we may\nhope to accomplish this by s tudying the topology of certain associated\nsimplicial complexes. This tal k includes work joint with Brück\, Kupers\,\nMiller\, Patzt\, Sroka\, and Yasaki.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5205/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Haluk Sengun (University of Sheffield) DTSTART:20211005T130000Z DTEND:20211005T134500Z DTSTAMP:20260404T060945Z UID:BIRS-21w5205/5 DESCRIPTION:Title: Periods of mod p Bianchi modular forms and Selmer groups\n by Haluk Sengun (University of Sheffield) as part of BIRS workshop: Lattic es and Cohomology of Arithmetic Groups\n\n\nAbstract\nThe relationship bet ween special values of L-functions modular\nforms and Selmer group of modu lar p-adic Galois representations is a\nmajor theme in number theory. Give n the developing mod p Langlands\nprogram\, it is natural to ask whether t here some kind of mod p analogue\nof the above theme. Notice that mod p mo dular forms do not have\nassociated L-functions! In this talk\, I will rep ort on ongoing work with\nLewis Combes in which we formulate\, and computa tionally test\, a\nconnection between Selmer groups of mod p Galois repres entations and mod\np Bianchi modular forms. This is inspired by a speculat ion of Calegari\nand Venkatesh.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5205/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Renaud Coulangeon (Institut de Mathematiques de Bordeaux) DTSTART:20211005T140000Z DTEND:20211005T144500Z DTSTAMP:20260404T060945Z UID:BIRS-21w5205/6 DESCRIPTION:Title: On Grayson-Stuhler filtration of Euclidean lattices\nby Re naud Coulangeon (Institut de Mathematiques de Bordeaux) as part of BIRS wo rkshop: Lattices and Cohomology of Arithmetic Groups\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5205/6/ END:VEVENT BEGIN:VEVENT SUMMARY:James Rickards (University of Colorado Boulder) DTSTART:20211005T160000Z DTEND:20211005T163000Z DTSTAMP:20260404T060945Z UID:BIRS-21w5205/7 DESCRIPTION:Title: Improved computation of fundamental domains for arithmetic Fuc hsian groups\nby James Rickards (University of Colorado Boulder) as pa rt of BIRS workshop: Lattices and Cohomology of Arithmetic Groups\n\n\nAbs tract\nThe fundamental domain of an arithmetic Fuchsian group $\\Gamma$ re veals a lot of interesting information about the group. An algorithm to co mpute this 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 per forms significantly better in practice. In this talk\, we describe work to improve the geometric algorithms\, and specialize Page's enumeration down to Fuchsian groups\, to produce a final algorithm that is much more effic ient. Optimal choices of constants in the enumeration are given by heurist ics\, which are supported by large amounts of data. This algorithm has bee n implemented in PARI/GP\, and we demonstrate its practicality by comparin g running times versus the live Magma implementation of Voight's algorithm .\n LOCATION:https://stable.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:20260404T060945Z UID:BIRS-21w5205/8 DESCRIPTION:Title: Perfect Forms Over Imaginary Quadratic Fields\nby Dan Yasa ki (The University of North Carolina at Greensboro) as part of BIRS worksh op: Lattices and Cohomology of Arithmetic Groups\n\n\nAbstract\nGiven an i maginary quadratic field\, there is a finite number of\nequivalence classe s of perfect forms over that field. We investigate these\nforms in the ra nk 2 case using a Voronoi's reduction theory. We show that\nthe perfect f orms cannot get too complicated\, which allows us to give a\nlower bound o n the number such perfect forms in terms of the discriminant\nof the field and the value of the Dedekind zeta function at 2. This is\njoint work wi th Kristen Scheckelhoff and Kalani Thalagoda.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5205/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Ruth Kellerhals (University of Fribourg) DTSTART:20211007T130000Z DTEND:20211007T134500Z DTSTAMP:20260404T060945Z UID:BIRS-21w5205/13 DESCRIPTION:Title: A polyhedral approach to the arithmetic and geometry of hyper bolic link complements\nby Ruth Kellerhals (University of Fribourg) as part of BIRS workshop: Lattices and Cohomology of Arithmetic Groups\n\n\n Abstract\nMotivated by the work of Meyer\, Millichap and Trapp [MMT] and b y Thurston\, I shall present an elementary polyhedral approach to study an d deduce results about the arithmeticity and commensurability of an infini te family of hyperbolic link complements M_n for n>2. The manifold M_n is the complement of the 3-sphere by the (2n)-link chain. \nThe hyperbolic s tructure of M_n stems from an ideal right-angled polyhedron that can be cu t into four copies of an ideal right-angled n-gonal antiprism. \nEach of t hese polyhedra gives rise to a hyperbolic Coxeter orbifold that is commens urable to a hyperbolic orbifold with a single cusp. Vinberg's arithmeticit y criterion and certain cusp density and volume computations allow us to r eproduce some of the main results in [MMT] about M_n in a comparatively el ementary and direct way. This approach works in several other cases of lin k complements as well.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5205/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean Raimbault ((Institut de Mathematiques de Toulouse) DTSTART:20211007T140000Z DTEND:20211007T144500Z DTSTAMP:20260404T060945Z UID:BIRS-21w5205/14 DESCRIPTION:Title: Asymptotic bounds for the homology of arithmetic lattices \nby Jean Raimbault ((Institut de Mathematiques de Toulouse) as part of BI RS workshop: Lattices and Cohomology of Arithmetic Groups\n\n\nAbstract\nI will discuss work with M. Frączyk and S. Hurtado which implies the follo wing statements: given a semisimple Lie group G there is a constant C such that for any (torsion-free) lattice Γ\\Gamma in G\, the size of the tors ion subgroups of all its homology groups is at most C^v where v is its cov olume in G. We prove this by constructing a simplicial complex with O(v) v ertices and bounded degree which is a classifying space for Γ\\Gamma\, so lving a conjecture of T. Gelande\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5205/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Ha Tran (Concordia University of Edmonton) DTSTART:20211007T160000Z DTEND:20211007T163000Z DTSTAMP:20260404T060945Z UID:BIRS-21w5205/15 DESCRIPTION:Title: The size function for imaginary sextic fields\nby Ha Tran (Concordia University of Edmonton) as part of BIRS workshop: Lattices and Cohomology of Arithmetic Groups\n\n\nAbstract\nLet $F$ be an imaginary cy lic sextic field with discriminant $\\Delta$ and the ring of integers $O_F $. \n The size function $h^0$ for $F$ is an analogue of t he dimension 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) i deal lattices of covolume $\\sqrt{|\\Delta|}$ the function $h^0$ attains its maximum at the trivial ideal lattice $O_F$. In this talk we will discu ss the main idea to prove that the conjecture holds for $F$.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5205/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Tamar Blanks (Rutgers University) DTSTART:20211007T164500Z DTEND:20211007T171500Z DTSTAMP:20260404T060945Z UID:BIRS-21w5205/16 DESCRIPTION:Title: Generating Cryptographically-Strong Random Lattice Bases and Recognizing Rotations of Z^n\nby Tamar Blanks (Rutgers University) as part of BIRS workshop: Lattices and Cohomology of Arithmetic Groups\n\n\nA bstract\nLattice-based cryptography relies on generating random bases whic h are difficult to fully reduce. Given a lattice basis (such as the privat e basis for a cryptosystem)\, all other bases are related by multiplicatio n by matrices in GL(n\, Z). We compare the strengths of various methods to sample random elements of SL(n\, Z)\, finding some are stronger than othe rs with respect to the problem of recognizing rotations of the Z^n lattice . In particular\, the standard algorithm of multiplying unipotent generato rs together (as implemented in Magma's RandomSLnZ command) generates insta nces of this last problem which can be efficiently broken\, even in dimens ions nearing 1\,500. We also can efficiently break the random basis genera tion method in one of the NIST Post-Quantum Cryptography competition submi ssions (DRS). Other random basis generation algorithms (some older\, some newer) are described which appear to be much stronger.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5205/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Tian An Wong (University of Michigan-Dearborn) DTSTART:20211006T130000Z DTEND:20211006T134500Z DTSTAMP:20260404T060945Z UID:BIRS-21w5205/17 DESCRIPTION:Title: On Eisenstein cocycles over imaginary quadratic fields\nb y Tian An Wong (University of Michigan-Dearborn) as part of BIRS workshop: Lattices and Cohomology of Arithmetic Groups\n\n\nAbstract\nEisenstein co cyles are elements in the group cohomology of\nGL(n) that parametrize spec ial values of L-functions. I will report on\njoint work with J. Flórez an d C. Karabulut on our construction of\nEisenstein cocyles over imaginary q uadratic fields $K$\, proving the\nintegrality of Hecke L-functions attach ed to degree $n$ extensions of\n$K$. This gives a new proof of a result pr eviously obtained by P. Colmez\nand L. Schneps\, and most recently by N. B ergeron\, P. Charollois\, and L.\nGarcia. Time permitting\, I will discuss work in progress on the\ninterpolation of these special values via a p-ad ic L-function.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5205/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Ling Long (Louisiana State University) DTSTART:20211006T140000Z DTEND:20211006T144500Z DTSTAMP:20260404T060945Z UID:BIRS-21w5205/18 DESCRIPTION:Title: From hypergeometric functions to lattices of generalized Lege ndre curves and beyond\nby Ling Long (Louisiana State University) as p art of BIRS workshop: Lattices and Cohomology of Arithmetic Groups\n\n\nAb stract\nIn this talk\, we will explain how to use hypergeometric functions to compute period lattices of generalized Legendre curves based on the wo rk of Archinard and Wolfart and automorphic forms on arithmetic triangle g roups based on the work of Yang. From which we will see how some recent de velopments on hypergeometric functions over finite fields can be used to c ompute the action of Hecke operators on automorphic forms on arithmetic tr iangle groups.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5205/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Espitau (NTT Secure Platform Laboratories) DTSTART:20211008T121500Z DTEND:20211008T124500Z DTSTAMP:20260404T060945Z UID:BIRS-21w5205/19 DESCRIPTION:Title: Algorithmic reduction of algebraic lattices\nby Thomas Es pitau (NTT Secure Platform Laboratories) as part of BIRS workshop: Lattice s and Cohomology of Arithmetic Groups\n\n\nAbstract\nAfter revisiting the basics of algorithmic reduction theory\nfor lattices\nunder a more algebra ic geometric prism\, we present generic strategies to\nenhance the reducti on over algebraic lattices over number fields (a.k.a.\nhermitian vector bu ndles over arithmetic curves) and see how we can\nleverage\nsymplectic sym metries to design faster processes. Such techniques can be\nused\nto paral lelize and speed up the core computations in algorithmic number\ntheory an d\nfor the tractable cohomologies of arithmetic groups.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5205/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabrielle Nebe (RWTH Aachen) DTSTART:20211008T130000Z DTEND:20211008T134500Z DTSTAMP:20260404T060945Z UID:BIRS-21w5205/20 DESCRIPTION:Title: Computational tools for G-invariant quadratic forms (\nby Gabrielle Nebe (RWTH Aachen) as part of BIRS workshop: Lattices and Cohom ology of Arithmetic Groups\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5205/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Mathieu Dutour Sikiric (Rudjer Bosković Institute) DTSTART:20211008T140000Z DTEND:20211008T144500Z DTSTAMP:20260404T060945Z UID:BIRS-21w5205/21 DESCRIPTION:Title: ppermutalib/polyhedral tools for polyhedral computation\n by Mathieu Dutour Sikiric (Rudjer Bosković Institute) as part of BIRS wor kshop: Lattices and Cohomology of Arithmetic Groups\n\n\nAbstract\nOver se veral work that I did\, I use a combination\nof tools from group theory\, polyhedral geometry in order to\ncompute geometric or topological informat ion.\nI have now shifted most of my programs to a C++ framework\nin order to achieve the best performance. All of the software\nis open source and I will present 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 cohom ology theories.\n\n---The foundational part of a lot of this is "permutali b" which is\na permutation group library that allows to compute set-stabil izer\nand other operations needed for polyhedral computation which\nis 10 times faster 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 o f the\ncanonical form of a quadratic form. An illustration of this\nwas th e enumeration of C-type in dimension 6 where we found\n55 million types in reasonable time.\n\n---We also provide efficient algorithms for dual desc ription using\nsymmetries where we achieve a two-fold improvement over GAP .\n---We also provide an implementation of the Vinberg algorithm\nusing al l the above that allows us to solve some 19 dimensional\nexamples easily.\ n\nThe point of this presentation is not really to concentrate on specific \nproblems but to show approaches that allow us to treat large problems.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5205/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Steffen Kionke (University of Hagen\, Germany) DTSTART:20211008T154500Z DTEND:20211008T160000Z DTSTAMP:20260404T060945Z UID:BIRS-21w5205/22 DESCRIPTION:Title: Profinite rigidity of lattices in higher rank Lie groups\ nby Steffen Kionke (University of Hagen\, Germany) as part of BIRS worksho p: Lattices and Cohomology of Arithmetic Groups\n\n\nAbstract\nThe famous arithmeticity and superrigidity results of Margulis allow to classify latt ices in higher rank Lie groups up to commensurability. It is known that tw o non-commensurable lattices can still be profinitely commensurable\, i.e. \, their profinite completions have isomorphic open subgroups. In this tal k I will explain how lattices in higher rank can be classified up to profi nite commensurability (modulo the congruence subgroup problem). We will se e that profinitely commensurable lattices exist in most simple Lie groups of higher rank. More surprisingly\, such examples cannot exist in the comp lex Lie groups of type E_8\, F_4 and G_2.\n\nThis is based on joint work w ith Holger Kammeyer.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5205/22/ END:VEVENT END:VCALENDAR