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BEGIN:VEVENT
SUMMARY:Uriya First (University of Haifa)
DTSTART:20210628T150000Z
DTEND:20210628T155000Z
DTSTAMP:20260413T023352Z
UID:zoomnovy/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/zoomnovy/1/"
 >Generating algebras via versality</a>\nby Uriya First (University of Haif
 a) as part of Algebraic groups and algebraic geometry: in honor of Zinovy 
 Reichstein's 60th birthday\n\n\nAbstract\nLet R be a noetherian (commutati
 ve) ring of Krull dimension d. A classical theorem of Forster states that 
 a rank-n locally free R-module can be generated by n+d elements. Swan and 
 Chase observed that this upper bound cannot be improved in general. I will
  discuss joint works with Zinovy Reichstein and Ben Williams where similar
  upper and lower bounds are obtained for R-algebras\, provided that R is o
 f finite type over an infinite field k. For example\, every Azumaya R-alge
 bra of degree n (i.e. an n-by-n matrix algebra bundle over Spec R) can be 
 generated by floor(d/(n-1))+2 elements\, and there exist degree-n Azumaya 
 algebras over d-dimensional rings which cannot be generated by fewer than 
 floor(d/(2n-2))+2 elements. The case d=0 recovers the folklore fact that e
 very central simple algebra is generated by 2 elements over its center. Th
 e proof reinterprets the problem as a question on "how much versal" are ce
 rtain algebraic spaces approximating the classifying stack of the automorp
 hism scheme of the algebra in question.\n
LOCATION:https://researchseminars.org/talk/zoomnovy/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Merkurjev (UCLA)
DTSTART:20210628T161500Z
DTEND:20210628T170500Z
DTSTAMP:20260413T023352Z
UID:zoomnovy/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/zoomnovy/2/"
 >Classification of special reductive groups</a>\nby Alexander Merkurjev (U
 CLA) as part of Algebraic groups and algebraic geometry: in honor of Zinov
 y Reichstein's 60th birthday\n\n\nAbstract\nWe give a classification of sp
 ecial reductive groups over arbitrary fields that improves a theorem of M.
  Huruguen.\n
LOCATION:https://researchseminars.org/talk/zoomnovy/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Danny Krashen (University of Pennsylvania/Rutgers University)
DTSTART:20210628T181500Z
DTEND:20210628T190500Z
DTSTAMP:20260413T023352Z
UID:zoomnovy/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/zoomnovy/3/"
 >Hearing the shapes of division algebras</a>\nby Danny Krashen (University
  of Pennsylvania/Rutgers University) as part of Algebraic groups and algeb
 raic geometry: in honor of Zinovy Reichstein's 60th birthday\n\n\nAbstract
 \nTo what extent to the splitting fields of a division algebra determine i
 ts structure? In the case of maximal subfields\, it turns out that this qu
 estion is closely related to the famous problem "can you hear the shape of
  a drum?" In this talk\, I'll describe some work in progress with Max Lieb
 lich\, where we consider what happens when one considers splitting fields 
 of small transcendence degree.\n
LOCATION:https://researchseminars.org/talk/zoomnovy/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Scavia (UBC)
DTSTART:20210628T191500Z
DTEND:20210628T200500Z
DTSTAMP:20260413T023352Z
UID:zoomnovy/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/zoomnovy/4/"
 >The behavior of essential dimension under deformations</a>\nby Federico S
 cavia (UBC) as part of Algebraic groups and algebraic geometry: in honor o
 f Zinovy Reichstein's 60th birthday\n\n\nAbstract\nLet k be a field of cha
 racteristic zero\, G be a linear algebraic k-group\, and n a non-negative 
 integer. We show that in a flat family of primitive generically free G-var
 ieties over a base k-variety B\, the points of B whose geometric fiber has
  essential dimension at most n form a countable union of closed subsets of
  B. As an application\, we construct unramified non-versal G-torsors of ma
 ximal essential dimension. This is joint work with Zinovy Reichstein.\n
LOCATION:https://researchseminars.org/talk/zoomnovy/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathieu Florence (Jussieu)
DTSTART:20210629T150000Z
DTEND:20210629T155000Z
DTSTAMP:20260413T023352Z
UID:zoomnovy/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/zoomnovy/5/"
 >Heisenberg representations and indecomposable division algebras</a>\nby M
 athieu Florence (Jussieu) as part of Algebraic groups and algebraic geomet
 ry: in honor of Zinovy Reichstein's 60th birthday\n\n\nAbstract\nLet $F$ b
 e a field\, with absolute Galois group G. Let $p$ be a prime. Denote by $B
 _d$ the Borel subgroup of $GL_d$\, and by $U_d$ its unipotent radical. We 
  consider the question of lifting a triangular Galois representation $G \\
 longrightarrow B_d(\\mathbb Z/p)$\, to its mod $p^2$ analogue $G \\longrig
 htarrow B_d(\\mathbb Z/p^2)$. It has a rich history\, which we will recall
 . We'll then explain positive results\, up to  $d=3$\, under the presence 
 of $p^2$-th root of unity in $F$. Using an indecomposability result for di
 visions algebras\, due to Karpenko\, we'll show that the answer to the ana
 logous question\, with $U_3$ in place of $B_3$\, is negative.\n
LOCATION:https://researchseminars.org/talk/zoomnovy/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Chernousov (University of Alberta)
DTSTART:20210629T161500Z
DTEND:20210629T170500Z
DTSTAMP:20260413T023352Z
UID:zoomnovy/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/zoomnovy/6/"
 >R-triviality of groups of type F_4 arising from the first Tits constructi
 on.</a>\nby Vladimir Chernousov (University of Alberta) as part of Algebra
 ic groups and algebraic geometry: in honor of Zinovy Reichstein's 60th bir
 thday\n\n\nAbstract\nJoint work with S. Alsaody and A. Pianzola. Any group
  of type F_4 is obtained as the automorphism group of an Albert algebra. I
 n the talk we show that such a group is R-trivial  whenever the Albert alg
 ebra is obtained from the first Tits construction.\n
LOCATION:https://researchseminars.org/talk/zoomnovy/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesse Wolfson (UC Irvine)
DTSTART:20210629T181500Z
DTEND:20210629T190500Z
DTSTAMP:20260413T023352Z
UID:zoomnovy/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/zoomnovy/7/"
 >Essential dimension via prismatic cohomology</a>\nby Jesse Wolfson (UC Ir
 vine) as part of Algebraic groups and algebraic geometry: in honor of Zino
 vy Reichstein's 60th birthday\n\n\nAbstract\nLet A be a complex abelian va
 riety.  Using prismatic cohomology\, we show that for all but finitely man
 y primes p\, the multiplication-by-p cover p:A\\to A is p-incompressible\,
  as conjectured by Brosnan. As an application\, we obtain new p-incompress
 ibility results for congruence covers of Shimura varieties\, extending pre
 vious work of Farb-Kisin-W\, Brosnan-Fakhruddin\, and Fakhruddin-Saini. Th
 is is joint work with Benson Farb and Mark Kisin.\n
LOCATION:https://researchseminars.org/talk/zoomnovy/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Burt Totaro (UCLA)
DTSTART:20210629T191500Z
DTEND:20210629T200500Z
DTSTAMP:20260413T023352Z
UID:zoomnovy/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/zoomnovy/8/"
 >The Hilbert scheme of points on affine space</a>\nby Burt Totaro (UCLA) a
 s part of Algebraic groups and algebraic geometry: in honor of Zinovy Reic
 hstein's 60th birthday\n\n\nAbstract\nI will discuss the Hilbert scheme of
  d points in affine n-space\, with some examples. This space has many irre
 ducible components for n at least 3 and has been poorly understood. For n 
 greater than d\, we determine the homotopy type of the Hilbert scheme in a
  range of dimensions. The proof uses the homotopy theory of algebraic stac
 ks. Many questions remain. (Joint with Marc Hoyois\, Joachim Jelisiejew\, 
 Denis Nardin\, Maria Yakerson.)\n
LOCATION:https://researchseminars.org/talk/zoomnovy/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Pirisi (La Sapienza Università di Roma)
DTSTART:20210630T150000Z
DTEND:20210630T155000Z
DTSTAMP:20260413T023352Z
UID:zoomnovy/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/zoomnovy/9/"
 >Unramified cohomology\, cohomological invariants and root stacks</a>\nby 
 Roberto Pirisi (La Sapienza Università di Roma) as part of Algebraic grou
 ps and algebraic geometry: in honor of Zinovy Reichstein's 60th birthday\n
 \n\nAbstract\nGiven a smooth algebraic variety X/k\, its (Bloch-Ogus-Rost)
  unramified cohomology H_nr(X\,M) with coefficients in a cycle module M is
  the subgroup of M(k(X)) given by the elements whose residue at each codim
 ension one point is zero. When X is proper\, this group is a birational in
 variant and it being non-trivial disproves stable rationality. It was firs
 t used in this way\, in the form of the unramified Brauer group\, by Artin
 ⁠–Mumford and Saltman\, and then in higher degrees by Colliot-Thélèn
 e⁠–Ojanguren. \nGiven an algebraic group G/k\, the cohomological invar
 iants Inv(G\,M) are the natural transformations between the functor of G-t
 orsors over fields and the cycle module M. There are many examples dating 
 back up to the beginning of the 20th century\, but they were introduced in
  the present form by Serre. A result by Totaro shows that given a G-repres
 entation V such that the subset U where G acts freely has complement of co
 dimension 2 or more\, we have Inv(G\,M)=H_nr(U/G\,M). A few years ago\, I 
 reinterpreted the idea of cohomological invariants as invariants of the cl
 assifying stack BG\, extended them to invariants of general algebraic stac
 ks\, and showed that on schemes we have Inv(X\,M) = H_nr(X\,M) and in fact
  they can be seen as the "only possible" extension of Bloch-Ogus-Rost unra
 mified cohomology to algebraic stacks. Moreover\, cohomological invariants
  can be used to compute Brauer groups\, which I and Andrea di Lorenzo rece
 ntly did for the moduli stacks of smooth Hyperelliptic curves.\nUnfortunat
 ely\, it's easy to see that even for smooth\, projective Deligne Mumford s
 tacks cohomological invariants are not a birational invariant. One way to 
 see this is that while any birational map between smooth proper schemes is
  given\, at least in char(k)=0\, by a sequence of blow-ups and blow-downs\
 , which leave cohomological invariants unchanged\, for DM stacks we have t
 o add root stacks\, which can modify cohomological invariants rather drast
 ically. I will describe recent work with Andrea Di Lorenzo in which we fin
 d a formula to describe the cohomological invariants of a root stack and u
 se it to show that different natural compactifications of the moduli stack
 s of Hyperelliptic curves\, while being seemingly almost identical\, have 
 vastly different cohomological invariants.\n
LOCATION:https://researchseminars.org/talk/zoomnovy/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raman Parimala (Emory University)
DTSTART:20210630T161500Z
DTEND:20210630T170500Z
DTSTAMP:20260413T023352Z
UID:zoomnovy/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/zoomnovy/10/
 ">Period-Index questions for function fields of hyperelliptic curves</a>\n
 by Raman Parimala (Emory University) as part of Algebraic groups and algeb
 raic geometry: in honor of Zinovy Reichstein's 60th birthday\n\n\nAbstract
 \nWe shall discuss period/index questions for the Brauer group of function
  fields of hyperelliptic curves over number fields. We will relate this qu
 estion to a Hasse principle for certain orthogonal Grassmannians of pencil
 s of quadrics. We derive some consequences concerning the u-invariant in t
 he case of genus 2 curves.\n
LOCATION:https://researchseminars.org/talk/zoomnovy/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kirill Zainoulline (University of Ottawa)
DTSTART:20210630T181500Z
DTEND:20210630T190500Z
DTSTAMP:20260413T023352Z
UID:zoomnovy/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/zoomnovy/11/
 ">Localized cohomological operations</a>\nby Kirill Zainoulline (Universit
 y of Ottawa) as part of Algebraic groups and algebraic geometry: in honor 
 of Zinovy Reichstein's 60th birthday\n\n\nAbstract\nCohomological operatio
 ns in algebraic oriented cohomology theories of Levine-Morel (Steenrod ope
 rations in Chow groups\; Adams operations in connective K-theory of Cai-Me
 rkurjev\; Landweber-Novikov operations and Vishik symmetric operations in 
 algebraic cobordism) provide a useful tool to study algebraic cycles on pr
 ojective homogeneous varieties G/P.\nIn the talk\, I will show how to exte
 nd these operations to a T-equivariant setup\, where T is a split maximal 
 torus of a semisimple linear algebraic group G over a field of characteris
 tic zero. More generally\, I will show how to extend it to structure algeb
 ras of moment graphs (rings of global sections of structure sheaves on mom
 ent graphs).\nI will explain a uniform algorithm that computes the usual (
 non-equivariant) operations for G/Ps using such extended (localized) opera
 tions and equivariant Schubert calculus techniques. This generalizes the a
 pproach suggested by Garibaldi-Petrov-Semenov for Steenrod operations. Exa
 mples include Adams operations\, L.-N. operations and Vishik's Mod-p opera
 tions.\n
LOCATION:https://researchseminars.org/talk/zoomnovy/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brendan Hassett (Brown University)
DTSTART:20210630T191500Z
DTEND:20210630T200500Z
DTSTAMP:20260413T023352Z
UID:zoomnovy/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/zoomnovy/12/
 ">Equivariant rationality: invariants and constructions</a>\nby Brendan Ha
 ssett (Brown University) as part of Algebraic groups and algebraic geometr
 y: in honor of Zinovy Reichstein's 60th birthday\n\n\nAbstract\nAbout 20 y
 ears ago\, Reichstein obtained fundamental results on equivariant rational
 ity for varieties with actions of finite and linear algebraic groups. New 
 perspectives have come with the symbol invariants developed by Kontsevich\
 , Kresch\, and Tschinkel. We will discuss some implications of these ideas
  for rationality questions central to arithmetic geometry: complete inters
 ections of two quadrics.\n
LOCATION:https://researchseminars.org/talk/zoomnovy/12/
END:VEVENT
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