 October 21, Clayton Petsche (OSU)
The Dynamical MordellLang Problem
Abstract: The Dynamical MordellLang Problem combines dynamical systems, algebraic geometry, and number theory in interesting and exciting new ways. One starts in the simple setting of a map from a algebraic variety to itself; for example, one might consider a polynomial function from Euclidean nspace to Euclidean nspace. The goal is to find a simple law or pattern governing the distribution, in the Zariski topology, of forward orbits of points with respect to this map. The problem in full generality is still very much open, but we will survey interesting partial results, and we will give a new result whose proof combines methods from ergodic theory as well as the theory of Berkovich analytic spaces.
 November 11, Ivan Loseu (Northeastern)
Counting finite dimensional irreducible representations over quantizations of symplectic resolutions
Abstract: A basic problem in Representation theory is, given an algebraic object such as a group, an associative algebra or a Lie algebra, to study its finite dimensional irreducible representations. The first question, perhaps, is how many there are. In my talk I will address this question for associative algebras that are quantizations of algebraic varieties admitting symplectic resolutions. Algebras arising this way include universal enveloping algebras of semisimple Lie algebras, as well as Walgebras and symplectic reflection algebras. The counting problem is a part of a more general program due to Bezrukavnikov and Okounkov relating the representation theory of quantizations to Quantum cohomology of the underlying symplectic varieties. It is also supposed to have other connections to Geometry.

November 25, Mock AMS Session
 December 2, Hans Ringstrom (KTH)
On the topology and future stability of the universe
Abstract: The current standard model of the universe is spatially homogeneous, isotropic and spatially flat. Furthermore, the matter content is described by two perfect fluids (dust and radiation) and there is a positive cosmological constant. Such a model can be well approximated by a solution to the EinsteinVlasov equations with a positive cosmological constant. As a consequence, it is of interest to study stability properties of solutions in the Vlasov setting. The talk will contain a description of recent results on this topic. Moreover, the restriction on the global topology of the universe imposed by the data collected by observers will be discussed.
 February 10, Vera Serganova (UC Berkeley)
The Lie superalgebra P(n) and Brauer algebras with signs
Abstract: The “strange” Lie superalgebra P(n) is the algebra of endomorphisms of an (nn)dimensional vector space V equipped with a nondegenerate odd symmetric form. Representations of P(n) in tensor powers of V are not completely reducible. The centralizer of the P(n)action in the kth tensor power of V is given by a certain analogue of the Brauer algebra.Using this algebra one can construct a pseudoabelian tensor category Prep, which is a natural analogue of the Deligne categories GL(t)rep and SO(t)rep.
Then we construct an abelian tensor category C which satisfy certain universal properties with respect to the categories of representations of P(n) for all n. We discuss combinatorial properties of C and its relationship with Prep.

April 14, Krzysztof Burdzy (UW)
On the meteor process
Abstract: The meteor process is a model of mass redistribution on a graph. I will present results on existence of the process and existence, uniqueness and properties of the stationary distribution. I will also discuss special questions arising in the case when the graph is a cycle or the set of integers.

April 21, Jerry Folland (UW)
From the applicable to the abstruse: an example in representation theory
Abstract: The operations of time shift (f(t)→ f(t+1)) and frequency shift (f(t)→ exp(2πiωt)f(t)) are fundamental ingredients of applied Fourier analysis, and the group of operators on L²(R) that they generate gives a unitary representation of the socalled discrete Heisenberg group. How does this representation decompose into irreducible representations? The answer provides illustrations of (i) some useful tools of modern harmonic analysis, when ω is rational, and (ii) some pathological phenomena from the dark side of representation theory, when ω is irrational. We shall discuss these results after providing a bit of background on unitary representation theory.

May 12, Emanuel Carneiro (IMPA)
Extremal Fourier analysis and some consequences of the Riemann hypothesis
Abstract: In this talk I will show how some extremal problems in Fourier analysis come into play when bounding some objects related to the Riemann zetafunction, under the assumption of the Riemann hypothesis. Most of the talk should be accessible to graduate students with a good knowledge of real and complex analysis.

May 30, Andre Henriques (Utrecht)
An introduction to conformal field theory
Abstract: I’ll give an overview of the definition of a chiral conformal field theory, talk about some examples, and discuss their representation theory.