Schedule
Tentative schedule: talks Monday, and Tuesday will be held in Grace Ford Salvatori Hall 106.
CHANGE in venue: Talks on Wednesday and Thursday morning will be held in Grace Ford Salvatori Hall 116 because of construction in the room previously announced.
Titles and Abstracts
Speaker: Christopher Bendel (U Wisconsin-Stout)
Title: Cohomology of finite groups of Lie type
Abstract: Let G be a semisimple algebraic group over an algebraically closed field of prime characteristic p, and consider the associated finite subgroups of Lie type obtained by taking points over a finite field of characteristic p. This talk will discuss recent results of Bendel, Nakano and Pillen on the cohomology of such finite groups in the defining characteristic. Of particular interest will be the relationship between the cohomology of the finite group and that of the ambient algebraic group for a rational G-module. Another question that will be discussed is the vanishing of the cohomology of the finite groups for the trivial module in low degrees.
Speaker: Dave Benson (Aberdeen)
Title: Matrix factorisations and modules for elementary abelian p-groups
Abstract: My talk is about joint work with my recent student Fergus Reid, giving an application of the theory of matrix factorisations in modular representation theory of elementary abelian p-groups.
A module of complexity c for E \cong (Z/p)^r in characteristic p has Loewy length at least (p-1)(r-c)+1. We study the case of equality. If p is odd, the only rank varieties possible are finite unions of linear subspaces of dimension c, and every such rank variety occurs. If p=2, the variety has to be equidimensional. If such a variety is a finite union of set theoretic complete intersections then it occurs for such a module, but otherwise the situation is unclear. Exterior algebras in any characteristic are also treated, and follow the same behaviour as the case p=2 above.
Speaker: Jon F. Carlson (U Georgia)
Title: A new look at endotrivial modules
Abstract: Let G be a finite group and k a field of characteristic p, dividing the order of G. A kG-module is endotrivial if its endomorphism ring Hom_k(M,M), as a kG-module, is isomorphic to k in the stable category, stmod(kG). Tensoring with an endotrivial module is a self-equivalence of Morita type on stmod(kG). The endotrivial module have been classified in the case that G$ is a p-group and in many other cases. Recent new techniques suggested by work of Balmer, have greatly enhanced the machinery for such characterizations. It is now possible to give a complete and elementary local description of the group of endotrival modules in the case that the Sylow p-subgroup of G is abelian. The talk with will highly joint work with Jacques Thevenaz, Nadia Mazza and Dan Nakano.
Speaker: Christian Haesemeyer (UCLA)
Title: Homology theories of singular schemes
Abstract: We will endeavour to give an introduction to our joint work with Cortinas, Schlichting, Walker and Weibel regarding algebraic homology theories of singular schemes, guided by a concrete application that can be described in a very elementary fashion in the context of linear algebra over rings.
Speaker: Roy Joshua (Ohio)
Title: Notions of Purity and the Cohomology of Quiver moduli
Abstract: We explore several variations of the notion of purity for the action of Frobenius on schemes defined over finite fields. In particular, we study how these notions are preserved under certain natural operations like quotients for principal bundles and also geometric quotients for reductive group actions. We then apply these results to study the cohomology of quiver moduli. We prove that a natural stratification of the space of representations of a quiver with a fixed dimension vector is equivariantly perfect and from it deduce that each of the l-adic cohomology groups of the quiver moduli space is strongly pure. This is joint work with Michel Brion.
Speaker: Alexander Merkurjev (UCLA)
Title: Motivic decomposition of compactifications of certain group varieties
Abstract: Let D be a central simple algebra of prime degree over a field and let G be the algebraic group of norm 1 elements of D. We determine motivic decomposition of certain compactifications of G and of any G-torsor E. We also compute the Chow ring of G and E. This a joint work with Nikita Karpenko.
Speaker: Paul Arne Østvær (Oslo)
Title: Motivic slices and quadratic forms
Abstract: We compute the motivic slices of hermitian K-theory and
higher Witt-theory. The corresponding slice spectral sequences relate
motivic cohomology to hermitian K-groups and Witt groups, respectively.
Using this we (re)prove Milnor's conjecture on quadratic forms for fields
of characteristic different from 2. Joint work with Oliver Röndigs.
http://arxiv.org/abs/1311.5833
Speaker: Julia Pevtsova (U Washington)
Title: Representations and cohomology of finite group schemes
Abstract: I’ll describe some of Eric Friedlander’s contributions to the subject which happened in the last twenty years starting with the celebrated “Finite generation of cohomology” theorem of Friedlander and Suslin.
Speaker: Alexander Premet (Manchester)
Title: Regular Derivations of Truncated Polynomial Rings.
Abstract: TBA
Speaker: Zinovy Reichstein (UBC)
Title: A numerical invariant for linear representations of finite groups
Abstract: Let K/k be fields of characteristic zero, G be a finite group and \rho \colon G \to \operatorname{GL}_n(K) be a non-modular linear representation of G whose character \chi takes values in k. A theorem of Brauer says that if k contains a primitive e-th root of unity, where e is the exponent of G, then \rho is defined over k, i.e., \rho has the same character as some representation \rho' \colon G \to \operatorname{GL}_n(k).
If k is not assumed to contain a primitive e-th root of unity, one would like to know ``how far" \rho is from being defined over k. In the case, where \rho is absolutely irreducible, a classical answer to this question is given by the Schur index of \rho, which is the smallest degree of a finite field extension L/k such that \rho is defined over L. In this talk based on joint work with Nikita Karpenko, I will discuss another invariant, the essential dimension of
\rho, which measures ``how far" \rho is from being defined over k by considering all (not necessarily algebraic) intermediate fields of definition k \subset L \subset K for \rho.
Speaker: Raphaël Rouquier (UCLA)
Title: Genericity in modular representation theory
Abstract: Certain aspects of the mod l representation theory of finite groups of Lie type over a field with q elements (l prime to q) are expected to depend only on the type of the group and the order of q modulo l. I will discuss a new setting to study homological and character-theoretic aspects, based on perverse equivalences and A-infinity deformations. (joint with David Craven).
Speaker: Andrei Suslin (Northwestern)
Title: Modules of constant Jordan type in characteristic 0
Abstract: TBA
Speaker: Wilberd van der Kallen (Utrecht)
Title: Cohomological finite generation and bifunctors
Abstract: Let k be a field. Let G be a reductive algebraic k-group acting algebraically on a finitely generated k-algebra A. Then the cohomological finite generation property (CFG) holds: the cohomology algebra H^*(G,A) is a finitely generated k-algebra. This result fits into a long story, going from the First Fundamental Theorem of invariant theory to strict polynomial bifunctors and their cohomology. We will sample this story.
Speaker: Mark Walker (U Nebraska-Lincoln)
Title: On Ext modules over complete intersection rings
Abstract: Let R be the quotient of a regular ring by a regular sequence of elements. For example, R could be the group ring of an elementary abelian p- group over a field of characteristic p. For a pair of finitely generated R-modules M and N, the direct sum of all their Ext-modules, Ext^*_R(M,N), is a finitely generated graded module over the ring of Eisenbud operators. In this talk, I discuss some recent results about the structure of these graded modules.
Speaker: Charles Weibel (Rutgers)
Title: Witt groups of real varieties
Abstract: We approximate the Witt groups of a variety V over the reals using a 8-periodic topological invariant: the Witt groups of Real vector bundles on the space of complex points of V. This is a better approximation than one might expect, and has the advantage of being finitely generated; this is based on joint work with M. Karoubi.