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# Events for October 12, 2018 from General and Seminar calendars

## Algebra and Combinatorics Seminar

**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

**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

**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

**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.

**Time:** 3:00PM - 4:00PM

**Location:** BLOC 628

**Speaker:** Andrew Maurer, University of Georgia

**Title:** *Relative Cohomology of Classical Lie Superalgebras*

**Time:** 4:00PM - 5:00PM

**Location:** BLOC 220

**Speaker:** Rufus Willet, University of Hawaii

**Title:** *Representation stability and topology*

**Time:** 4:00PM - 5:00PM

**Location:** BLOC 628

**Speaker:** B. Ullery, Harvard

**Title:** *The gonality of complete intersection curves (Postponed)*

**Time:** 4:00PM - 5:00PM

**Location:** BLOC 220

**Speaker:** Rufus Willett, University of Hawaii

**Title:** *Representation stability and topology (Joint with Linear Analysis Seminar)*