MenuEvents for 10/12/2018 from all calendars
Algebra and Combinatorics Seminar
Time: 3:00PM - 4:00PM
Location: BLOC 628
Speaker: Andrew Maurer, University of Georgia
Title: Relative Cohomology of Classical Lie Superalgebras
Abstract: Cohomology is a powerful technique in representation theory. In this talk, I will define Lie superalgebras and their relative cohomology theory. We will see two classical results on geometric properties of relative cohomology, and I will present original results which relate the two aforementioned results.
Linear Analysis Seminar
Time: 4:00PM - 5:00PM
Location: BLOC 220
Speaker: Rufus Willet, University of Hawaii
Title: Representation stability and topology
Abstract: Let G be a discrete group with a fixed finite generating set S. A map from G into some (finite dimensional) unitary group U(n) is an epsilon-representation if it is a group homomorphism up to epsilon error (for the operator norm) on the finite set S. Thus a quasi-representation is a close to being a representation in some sense. The group G is stable if every epsilon representation is close to an actual representation, in a precise sense. For example, free groups are fairly obviously stable. However, a famous result of Voiculescu shows that the rank two free abelian group is not stable. In his thesis, Loring gave this a topological interpretation: it turns out that Voiculescu’s result is more-or-less equivalent to Bott periodicity. I’ll try to explain all this, and how topological information can be used to produce many other examples of non-stable groups.
Geometry Seminar
Time: 4:00PM - 5:00PM
Location: BLOC 628
Speaker: B. Ullery, Harvard
Title: The gonality of complete intersection curves (Postponed)
Abstract: The gonality of a smooth projective curve is the smallest degree of a map from the curve to the projective line. If a curve is embedded in projective space, it is natural to ask whether the gonality is related to the embedding. In my talk, I will discuss recent work with James Hotchkiss. Our main result is that, under mild degree hypotheses, the gonality of a general complete intersection curve in projective space is computed by projection from a codimension 2 linear space, and any minimal degree branched covering of P^1 arises in this way.
Noncommutative Geometry Seminar
Time: 4:00PM - 5:00PM
Location: BLOC 220
Speaker: Rufus Willett, University of Hawaii
Title: Representation stability and topology (Joint with Linear Analysis Seminar)
Abstract: Let G be a discrete group with a fixed finite generating set S. A map from G into some (finite dimensional) unitary group U(n) is an epsilon-representation if it is a group homomorphism up to epsilon error (for the operator norm) on the finite set S. Thus a quasi-representation is a close to being a representation in some sense. The group G is stable if every epsilon representation is close to an actual representation, in a precise sense. For example, free groups are fairly obviously stable. However, a famous result of Voiculescu shows that the rank two free abelian group is not stable. In his thesis, Loring gave this a topological interpretation: it turns out that Voiculescu’s result is more-or-less equivalent to Bott periodicity. I’ll try to explain all this, and how topological information can be used to produce many other examples of non-stable groups.
