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BEGIN:VEVENT
SUMMARY:Avner Ash (Boston College)
DTSTART:20211011T140000Z
DTEND:20211011T144500Z
DTSTAMP:20260404T042016Z
UID:BIRS-21w5011/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/BIRS-
 21w5011/1/">Homology of arithmetic groups and Galois representations</a>\n
 by Avner Ash (Boston College) as part of BIRS workshop: Cohomology of Arit
 hmetic Groups: Duality\, Stability\, and Computations\n\n\nAbstract\nI giv
 e a few examples of how Galois representations can help in the understandi
 ng and computation of the homology of congruence subgroups of $\\mathrm{GL
 }_n(\\mathbb{Z})$.   Then I sketch a current project of mine with Darrin D
 oud in which we hope to prove the following:  If $\\rho=\\sigma_1 \\oplus 
 \\sigma_2$ is an $n$-dimensional odd mod $p$ Galois representation\, with 
 $\\sigma_1$ and $\\sigma_2$ irreducible odd Galois representations that ar
 e attached to Hecke eigenclasses in the homology of the predicted congruen
 ce subgroups\, with predicted weights\, then $\\rho$ is attached to a Heck
 e eigenclasses in the homology of the predicted congruence subgroup of $\\
 mathrm{GL}_n(\\mathbb{Z})$\, with predicted weight.  Here\, "predicted" re
 fers to the Serre-type conjecture of Ash–Doud–Pollack–Sinnott.  We a
 ssume that $p$ is greater than $n+1$ and that the Serre conductor of $\\rh
 o$ is square-free.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5011/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Patzt (Copenhagen University/ University of Oklahoma)
DTSTART:20211011T150000Z
DTEND:20211011T154500Z
DTSTAMP:20260404T042016Z
UID:BIRS-21w5011/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/BIRS-
 21w5011/2/">Rognes' connectivity conjecture and the Koszul dual of Steinbe
 rg</a>\nby Peter Patzt (Copenhagen University/ University of Oklahoma) as 
 part of BIRS workshop: Cohomology of Arithmetic Groups: Duality\, Stabilit
 y\, and Computations\n\n\nAbstract\nIn this talk\, I will explain how a ho
 motopy equivalence\nbetween certain $E_k$-buildings both proves Rognes' co
 nnectivity\nconjecture for fields and computes the Koszul dual of Steinber
 g. Rognes'\nconnectivity conjecture states that the common basis complex i
 s highly\nconnected. This is relevant as the equivariant homology of this 
 complex\nappears in a rank filtration spectral sequence computing the homo
 logy of\nthe $K$-theory spectrum. The Steinberg modules appear in various 
 contexts\,\nimportantly as the dualizing modules of special linear groups 
 of number\nrings. They can be put together to form a ring. When considered
 \nequivariantly over the general linear groups of fields\, one can show\nt
 hat this ring is Koszul and we compute its Koszul dual. Results in this\nt
 alk include joint work with Jeremy Miller\, Rohit Nagpal\, and Jennifer\nW
 ilson.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5011/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Kupers
DTSTART:20211011T163000Z
DTEND:20211011T171500Z
DTSTAMP:20260404T042016Z
UID:BIRS-21w5011/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/BIRS-
 21w5011/3/">On homological stability for GL_n(Z)</a>\nby Alexander Kupers 
 as part of BIRS workshop: Cohomology of Arithmetic Groups: Duality\, Stabi
 lity\, and Computations\n\n\nAbstract\nI will explain what is known about 
 homological stability for the general linear groups of the integers. In pa
 rticular\, I will discuss a recent result\, joint work with Jeremy Miller 
 and Peter Patzt\, that improves the homological stability range to slope 1
 . It builds on machinery developed with Soren Galatius and Oscar Randal-Wi
 lliams\, and is closely related to homology with coefficients in the Stein
 berg module.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5011/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathilde Gerbelli-Gauthier
DTSTART:20211011T210000Z
DTEND:20211011T212000Z
DTSTAMP:20260404T042016Z
UID:BIRS-21w5011/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/BIRS-
 21w5011/4/">Growth of cohomology in towers and endoscopy</a>\nby Mathilde 
 Gerbelli-Gauthier as part of BIRS workshop: Cohomology of Arithmetic Group
 s: Duality\, Stability\, and Computations\n\n\nAbstract\nHow fast do Betti
  numbers grow in a congruence tower of compact arithmetic manifolds? The d
 imension 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-l
 inear. I’ll discuss this question from the point of view of automorphic 
 forms\, and outline how the phenomenon of endoscopy can be used to explain
  the slow rates of growth and to compute upper bounds.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5011/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathalie Wahl (University of Copenhagen)
DTSTART:20211012T140000Z
DTEND:20211012T144500Z
DTSTAMP:20260404T042016Z
UID:BIRS-21w5011/5
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/BIRS-
 21w5011/5/">Stability in the homology of classical groups</a>\nby Nathalie
  Wahl (University of Copenhagen) as part of BIRS workshop: Cohomology of A
 rithmetic Groups: Duality\, Stability\, and Computations\n\n\nAbstract\nGe
 neral linear groups\, symplectic groups\, unitary groups and orthogonal gr
 oups have long been known to satisfy homological stability under appropria
 te conditions. In joint work with David Sprehn\, we improved the earlier k
 nown homological stability ranges for $\\mathrm{Sp}_{2n}(\\mathbb{F})$\, $
 \\mathrm{O}_{n\,n}(\\mathbb{F})$ and $\\mathrm{U}_{2n}(\\mathbb{F})$ over 
 any field $\\mathbb{F}$ other than $\\mathbb{F}_2$\, following a strategy 
 of Quillen for general linear groups $\\mathrm{GL}_n(\\mathbb{F})$. Under 
 more restricted assumptions\, we deduce a stability theorem for the orthog
 onal group $\\mathrm{O}_n(\\mathbb{F})$. I'll present these results\, focu
 ssing on what these groups have in common\, and presenting this maybe less
  well-known strategy of Quillen that gives a slope 1 stability range for $
 \\mathrm{GL}_n(\\mathbb{F})$.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5011/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Putman
DTSTART:20211012T150000Z
DTEND:20211012T154500Z
DTSTAMP:20260404T042016Z
UID:BIRS-21w5011/6
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/BIRS-
 21w5011/6/">The Steinberg representation is irreducible</a>\nby Andrew Put
 man as part of BIRS workshop: Cohomology of Arithmetic Groups: Duality\, S
 tability\, and Computations\n\n\nAbstract\nWe prove that the Steinberg rep
 resentation of $\\mathrm{GL}_n$ (or\, more generally\, a connected reducti
 ve group) over an infinite field is irreducible. For finite fields\, this 
 is a classical theorem of Steinberg and Curtis.  This is joint work with A
 ndrew Snowden.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5011/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Broaddus (The Ohio State University)
DTSTART:20211012T163000Z
DTEND:20211012T171500Z
DTSTAMP:20260404T042016Z
UID:BIRS-21w5011/7
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/BIRS-
 21w5011/7/">Level structures and images of the Steinberg module for surfac
 es with marked points</a>\nby Nathan Broaddus (The Ohio State University) 
 as part of BIRS workshop: Cohomology of Arithmetic Groups: Duality\, Stabi
 lity\, and Computations\n\n\nAbstract\nThe moduli space $\\mathcal{M}$ of 
 complex curves of fixed topology is an\norbifold classifying space for sur
 face bundles. As such the cohomology\nrings of $\\mathcal{M}$ and its vari
 ous orbifold covers give characteristic classes\nfor surface bundles. I wi
 ll discuss the Steinberg module which is\ncentral to the duality present i
 n these cohomology rings. I will then\nexplain current joint work with T. 
 Brendle and A. Putman on surfaces\nwith marked points which expands on res
 ults of N. Fullarton and A.\nPutman for surfaces without marked points. We
  show that certain\nfinite-sheeted orbifold covers $\\mathcal{M}[l]$ of $\
 \mathcal{M}$ have large nontrivial\n$Q$-cohomology in their cohomological 
 dimension.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5011/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frank Calegari (University of Chicago)
DTSTART:20211012T190000Z
DTEND:20211012T194500Z
DTSTAMP:20260404T042016Z
UID:BIRS-21w5011/8
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/BIRS-
 21w5011/8/">The stable cohomology of SL(F_p)</a>\nby Frank Calegari (Unive
 rsity of Chicago) as part of BIRS workshop: Cohomology of Arithmetic Group
 s: Duality\, Stability\, and Computations\n\n\nAbstract\nLet $p$ be a prim
 e. One can make sense of various “compatible” algebraic representation
 s of $\\mathrm{SL}_N(\\mathbb{F}_p)$ as $p$ is fixed and as $N$ varies (fo
 r example\, the standard representation\, or the adjoint representation\, 
 or the trivial representation). It turns out that the cohomology groups of
  these representations are stable as $N$ gets large. So what are they? We 
 discuss a conjectural answer to this. We also discuss how this relates to 
 a conjectural computation of $H^i(\\mathrm{SL}_N(\\mathbb{F}_p)\,\\mathbb{
 F}_p)$ for $i$ fixed and $N$ going off to infinity which should be true fo
 r “almost all $p$”.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5011/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Yasaki
DTSTART:20211012T203000Z
DTEND:20211012T211500Z
DTSTAMP:20260404T042016Z
UID:BIRS-21w5011/9
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/BIRS-
 21w5011/9/">Cohomology of Congruence Subgroups\, Steinberg Modules\, and R
 eal Quadratic Fields</a>\nby Dan Yasaki as part of BIRS workshop: Cohomolo
 gy of Arithmetic Groups: Duality\, Stability\, and Computations\n\n\nAbstr
 act\nGiven a real quadratic field\, there is a naturally defined Hecke-sta
 ble subspace of the cohomology of a congruence subgroup of $\\mathrm{SL}_3
 (\\mathbb{Z})$.  We investigate this subspace and make  conjectures about 
 its dependence on the real quadratic field and the relationship to boundar
 y cohomology.  This is joint work with Avner Ash.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5011/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melody Chan (Brown University)
DTSTART:20211013T140000Z
DTEND:20211013T144500Z
DTSTAMP:20260404T042016Z
UID:BIRS-21w5011/10
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/BIRS-
 21w5011/10/">The top-weight rational cohomology of $\\mathcal{A}_g$</a>\nb
 y Melody Chan (Brown University) as part of BIRS workshop: Cohomology of A
 rithmetic Groups: Duality\, Stability\, and Computations\n\n\nAbstract\nIn
  joint work with Madeline Brandt\, Juliette Bruce\, Margarida Melo\,\nGwyn
 eth Moreland\, and Corey Wolfe\, we recently identified new\ntop-weight ra
 tional cohomology classes for moduli spaces $\\mathcal{A}_g$ of\nabelian v
 arieties\, by using computations of Voronoi complexes for\n$\\mathrm{GL}(g
 \,\\mathbb{Z})$ of Elbaz-Vincent--Gangl--Soulé.  In this talk\, I will tr
 y to\nexplain these results from the beginning\, surveying some of the mai
 n\ntechniques and ingredients.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5011/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Gunnells (University of Massachusetts)
DTSTART:20211013T150000Z
DTEND:20211013T154500Z
DTSTAMP:20260404T042016Z
UID:BIRS-21w5011/11
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/BIRS-
 21w5011/11/">Modular symbols over function fields</a>\nby Paul Gunnells (U
 niversity of Massachusetts) as part of BIRS workshop: Cohomology of Arithm
 etic Groups: Duality\, Stability\, and Computations\n\n\nAbstract\nModular
  symbols\, due to Birch and Manin\, provide a very\nconcrete way to comput
 e with classical holomorphic modular forms.\nLater modular symbols were ex
 tended to $\\mathrm{GL}(n)$ by Ash and Rudolph\, and\nsince then such symb
 ols and variations have played a central role in\ncomputational investigat
 ion of the cohomology of arithmetic groups\nover number fields\, and in pa
 rticular in explicitly computing the\nHecke action on cohomology. $$ \\qqu
 ad \\\\[-2em]$$ \n\nA theory of modular symbols for $\\mathrm{GL}(2)$ over
  the rational function field\nwas developed by Teitelbaum and later by Arm
 ana.  In this talk we extend\nthis construction to $\\mathrm{GL}(n)$ and s
 how how it can be used to compute Hecke\noperators on cohomology.  This is
  joint work with Dan Yasaki.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5011/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark McConnell (Princeton University)
DTSTART:20211013T163000Z
DTEND:20211013T171500Z
DTSTAMP:20260404T042016Z
UID:BIRS-21w5011/12
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/BIRS-
 21w5011/12/">Binary Quadratic Forms and Hecke Operators for $\\mathrm{SL}(
 2\,\\mathbb{Z})$</a>\nby Mark McConnell (Princeton University) as part of 
 BIRS workshop: Cohomology of Arithmetic Groups: Duality\, Stability\, and 
 Computations\n\n\nAbstract\nRobert MacPherson and I developed an algorithm
  for computing the Hecke operators on the cohomology $H^d$ of arithmetic s
 ubgroups of $\\mathrm{SL}(n)$ defined over any division algebra\, for all 
 $d$ and all $n$.  It extends Voronoi's notion of perfect forms by introduc
 ing tempered perfect forms.  To find the tempered perfect forms\, our code
  must compute the facets of a large convex polytope of $n(n+1)/2$ dimensio
 ns\, which is slow even for $n = 3$ or $4$.  The talk will report on recen
 t work\, in the classical case of $\\mathrm{SL}(2\,\\mathbb{Z})$\, where w
 e have succeeded in identifying the tempered perfect forms directly.  The 
 story comes down to binary quadratic forms in the spirit of Lagrange and G
 auss\, together with some modern class field theory.  This is joint work w
 ith Erik Bahnson and Kyrie McIntosh.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5011/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oscar Randal-Williams (University of Cambridge)
DTSTART:20211014T140000Z
DTEND:20211014T144500Z
DTSTAMP:20260404T042016Z
UID:BIRS-21w5011/13
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/BIRS-
 21w5011/13/">$E_\\infty$-algebras and general linear groups</a>\nby Oscar 
 Randal-Williams (University of Cambridge) as part of BIRS workshop: Cohomo
 logy of Arithmetic Groups: Duality\, Stability\, and Computations\n\n\nAbs
 tract\nI will discuss joint work with S. Galatius and A. Kupers in which w
 e investigate the homology of general linear groups over a ring $A$ by con
 sidering the collection of all their classifying spaces as a graded $E_\\i
 nfty$-algebra. I will first explain diverse results that we obtained in th
 is investigation\, which can be understood without reference to $E_\\infty
 $-algebras but which seem unrelated to each other: I will then explain how
  the point of view of cellular $E_\\infty$-algebras unites them.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5011/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bena Tshishiku
DTSTART:20211014T150000Z
DTEND:20211014T154500Z
DTSTAMP:20260404T042016Z
UID:BIRS-21w5011/14
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/BIRS-
 21w5011/14/">Unstable cohomology of arithmetic groups and geometric cycles
 </a>\nby Bena Tshishiku as part of BIRS workshop: Cohomology of Arithmetic
  Groups: Duality\, Stability\, and Computations\n\n\nAbstract\nWe construc
 t unstable cohomology classes of nonuniform arithmetic subgroups of $\\mat
 hrm{SO}(p\,q)$ using ideas of Millson-Raghunathan and more recent work of 
 Avramidi and Nguyen-Phan. The classes we construct are dual to maximal per
 iodic flats in the locally symmetric space. One motivation for this result
  is to produce characteristic classes for certain manifold bundles that ar
 e not in the algebra generated by the stable (MMM) classes.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5011/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benson Farb (University of Chicago)
DTSTART:20211014T163000Z
DTEND:20211014T171500Z
DTSTAMP:20260404T042016Z
UID:BIRS-21w5011/15
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/BIRS-
 21w5011/15/">Rigidity of moduli spaces</a>\nby Benson Farb (University of 
 Chicago) as part of BIRS workshop: Cohomology of Arithmetic Groups: Dualit
 y\, Stability\, and Computations\n\n\nAbstract\nAlgebraic geometry contain
 s an abundance of miraculous constructions.  Examples include ``resolving 
 the quartic''\; the existence of 9 flex points on a smooth plane cubic\; t
 he Jacobian of a genus $g$ curve\; and the 27 lines on a smooth cubic surf
 ace. In this talk I will explain some ways to systematize and formalize th
 e idea that such constructions are special: conjecturally\, they should be
  the only ones of their kind. I will state a few of these many (mostly ope
 n) conjectures. They can be viewed as forms of rigidity (a la Mostow and M
 argulis) for various moduli spaces and maps between them.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5011/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Emerton (University of Chicago)
DTSTART:20211014T190000Z
DTEND:20211014T194500Z
DTSTAMP:20260404T042016Z
UID:BIRS-21w5011/16
DESCRIPTION:by Matthew Emerton (University of Chicago) as part of BIRS wor
 kshop: Cohomology of Arithmetic Groups: Duality\, Stability\, and Computat
 ions\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5011/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Feng (Massachusetts Institute of Technology)
DTSTART:20211014T200000Z
DTEND:20211014T202000Z
DTSTAMP:20260404T042016Z
UID:BIRS-21w5011/17
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/BIRS-
 21w5011/17/">The Galois action on symplectic K-theory</a>\nby Tony Feng (M
 assachusetts Institute of Technology) as part of BIRS workshop: Cohomology
  of Arithmetic Groups: Duality\, Stability\, and Computations\n\n\nAbstrac
 t\nI will talk about some connections between the cohomology of arithmetic
  groups\, $K$-theory\, and number theory. One reason for these connections
  is the fact that there is a natural Galois action on the cohomology of sy
 mplectic groups of integers\, which turns out to provide Galois representa
 tions important in the Langlands correspondence. The same mechanism leads 
 to a Galois action on a symplectic variant of K-theory of the integers. In
  joint work with Soren Galatius and Akshay Venkatesh\, we compute this Gal
 ois action and find that it also enjoys a certain universality.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5011/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Brück
DTSTART:20211014T210000Z
DTEND:20211014T212000Z
DTSTAMP:20260404T042016Z
UID:BIRS-21w5011/18
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/BIRS-
 21w5011/18/">High-dimensional rational cohomology of $\\operatorname{SL}_n
 (\\mathbb{Z})$ and $\\operatorname{Sp}_{2n}(\\mathbb{Z})$</a>\nby Benjamin
  Brück as part of BIRS workshop: Cohomology of Arithmetic Groups: Duality
 \, Stability\, and Computations\n\n\nAbstract\nBy results of Lee-Szarba an
 d Church-Putman\, the rational cohomology of $\\operatorname{SL}_n(\\mathb
 b{Z})$ vanishes in "codimensions zero and one"\, i.e. $H^{{n \\choose 2} -
 i}(\\operatorname{SL}_n(\\mathbb{Z})\;\\mathbb{Q}) = 0$ for $i\\in \\{0\,1
 \\}$ and $n \\geq i+2$\, where ${n \\choose 2}$ is the virtual cohomologic
 al dimension of $\\operatorname{SL}_n(\\mathbb{Z})$. I will talk about wor
 k in progress on two generalisations of these results: The first project i
 s joint work with Miller-Patzt-Sroka-Wilson. We show that the rational coh
 omology of $\\operatorname{SL}_n(\\mathbb{Z})$ vanishes in codimension two
 \, i.e. $H^{{n \\choose 2} -2}(\\operatorname{SL}_n(\\mathbb{Z})\;\\mathbb
 {Q}) = 0$ for $n \\geq 4$. The second project is joint with Patzt-Sroka. I
 ts aim is to study whether the rational cohomology of the symplectic group
  $\\operatorname{Sp}_{2n}(\\mathbb{Z})$ vanishes in codimension one\, i.e.
  whether $H^{n^2 -1}(\\operatorname{Sp}_{2n}(\\mathbb{Z})\;\\mathbb{Q}) = 
 0$ for $n \\geq 2$.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5011/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Orsola Tommas (University of Padova)
DTSTART:20211015T140000Z
DTEND:20211015T144500Z
DTSTAMP:20260404T042016Z
UID:BIRS-21w5011/19
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/BIRS-
 21w5011/19/">Stability results for toroidal compactifications of $\\mathca
 l{A}_g$</a>\nby Orsola Tommas (University of Padova) as part of BIRS works
 hop: Cohomology of Arithmetic Groups: Duality\, Stability\, and Computatio
 ns\n\n\nAbstract\nIn this talk\, we will discuss the geometry of the modul
 i space $\\mathcal{A}_g$ of\nprincipally polarized abelian varieties of di
 mension $g$ and its\ncompactifications. As is well known\, in degree $k < 
 g$ the rational\ncohomology of $\\mathcal{A}_g$\, which coincides with the
  cohomology of the symplectic\ngroup\, is freely generated by the odd Cher
 n classes of the Hodge bundle\nby a classical result of Borel. Work of Cha
 rney and Lee provides an\nanalogous result for the stable cohomology of th
 e minimal\ncompactification of $\\mathcal{A}_g$\, the Satake compactificat
 ion.\nHowever\, for most geometric applications it is more natural to work
  with\nthe toroidal compactifications of $\\mathcal{A}_g$. We will report 
 on joint work with\nSam Grushevsky and Klaus Hulek on the toroidal compact
 ifications of $\\mathcal{A}_g$\,\nand describe stability results for the p
 erfect cone compactification and\nthe matroidal partial compactification a
 nd their combinatorial features.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5011/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabian Hebestreit (University of Bonn)
DTSTART:20211015T150000Z
DTEND:20211015T152000Z
DTSTAMP:20260404T042016Z
UID:BIRS-21w5011/20
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/BIRS-
 21w5011/20/">The stable cohomology of symplectic groups over the integers<
 /a>\nby Fabian Hebestreit (University of Bonn) as part of BIRS workshop: C
 ohomology of Arithmetic Groups: Duality\, Stability\, and Computations\n\n
 \nAbstract\nI will report on joint work with M. Land and T. Nikolaus in wh
 ich we compute the stable part of the cohomology of both symplectic groups
  and orthogonal groups with vanishing signature over the integers at regul
 ar primes\, in particular at the prime 2. Our approach is by identifying t
 he stable cohomology with that of a certain Grothendieck-Witt space\, whos
 e homotopy type can be analysed using recent advances in hermitian $K$-the
 ory.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5011/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jordan Ellenberg (University of Wisconsin)
DTSTART:20211015T153000Z
DTEND:20211015T155000Z
DTSTAMP:20260404T042016Z
UID:BIRS-21w5011/21
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/BIRS-
 21w5011/21/">Legendre symbols and secondary stability</a>\nby Jordan Ellen
 berg (University of Wisconsin) as part of BIRS workshop: Cohomology of Ari
 thmetic Groups: Duality\, Stability\, and Computations\n\n\nAbstract\nThis
  talk is really a problem proposal.  Mark Shusterman and I have been talk
 ing about the problem of controlling sums of Legendre symbols $\\left(\\fr
 ac{f}{g}\\right)$ as $f$ and $g$ range over squarefree polynomials of degr
 ee $m$ and $n$ over $\\mathbb{F}_q$\, with $m$ and $n$ growing while the f
 inite field $\\mathbb{F}_q$ stays the same.  This can be expressed as a p
 roblem about the trace of Frobenius acting on the etal cohomology of a spa
 ce whose complex points are a $K(\\pi\,1)$ for a certain finite-index subg
 roup of a colored braid group\; it seems to me that the behavior we expect
  to see for these averages would follow from a good result on secondary 
 homological stability for these subgroups.  The question is whether the a
 ssembled topological might of this workshop can help figure out whether su
 ch a statement is true and provable with current methods.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5011/21/
END:VEVENT
END:VCALENDAR