Speaker: Radu Dascaliuc
Date: Monday 10/5/15
Place: 4PM in Deady 208

I will talk about a probabilistic cascade structure that can be naturally associated with certain partial differential equations and how it can be used to study well-posedness questions.
In the context of the still unsolved uniqueness problem for the 3D Navier-Stokes equations, our aim will be to see how the explosion properties of such cascades help establish a connection between the uniqueness of symmetry-preserving (self-similar) solutions and the uniqueness of the general problem.

Based on the joint work with N. Michalowski, E. Thomann, and E. Waymire.

Speaker: Valentino Tosatti
Date: Monday 9/28/15
Place: 4PM in Deady 208

Abstract: I will give an introduction to the study of Ricci flow on
compact Kahler manifolds, and explain how its behavior reflects the
structure of the complex manifold. I will then describe a result (joint
with T.Collins) which gives a geometric description of the set where
finite-time singularities occur, answering a conjecture of
Feldman-Ilmanen-Knopf and Campana.

Speaker: Emanuel Carneiro

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 zeta-function, 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.

Speaker: André Henriques

Abstract: I’ll give an overview of the definition of a chiral conformal field theory, talk about some examples, and discuss their representation theory.

Speaker: Jerry Folland, University of Washington

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 so-called 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.

Speaker: Krzysztof Burdzy

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.

Speaker: Vera Serganova, UC Berkeley.

Abstract:

The “strange” Lie superalgebra P(n) is the algebra of endomorphisms of an (n|n)-dimensional vector space V equipped with a non-degenerate 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 k-th tensor power of V is given by a certain analogue of the Brauer algebra.Using this algebra one can construct a pseudo-abelian tensor category P-rep, 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 P-rep.

Speaker: Hans Ringstrom

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 Einstein-Vlasov 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.

Speaker: Ivan Loseu

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 W-algebras 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.

Date: Oct 21, 2013

Speaker: Clayton Petsche, OSU

Abstract: The Dynamical Mordell-Lang 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 n-space to Euclidean n-space.  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.