Seminars & Events for 2010-2011

March 3, 2011
4:30pm - 6:30pm
Nondistortedsubgroups of $Out(F_n)$, via Lipschitz retraction in spaces of trees (joint work with M. Handel)

We prove that various subgroups of $Out(F_n)$ — the outer automorphism group of a free group of rank $n$ — such as the stabilizer of the conjugacy class of a rank $n-1$ free factor, are undistorted in $Out(F_n)$.

Speaker: Lee Mosher, Rutgers University
Location:
Fine Hall 314
March 3, 2011
4:30pm - 6:30pm
Periods of quaternionic Shimura varieties

In the early 80's, Shimura made a precise conjecture relating Peterssoninner products of arithmetic automorphicforms on quaternion algebras over totally real fields, up to algebraic factors. This conjecture (which is a consequence of the Tate conjecture on algebraic cycles) was proved a few years later by Michael Harris.

Speaker: Kartik Prasanna, University of Michigan, Ann Arbor
Location:
IAS Room S-101
March 4, 2011
11:00am - 1:00pm
Geometry of quantum response in open systems

I shall describe a theory of adiabatic response for controlled open systems governed by Lindblad evolutions. The theory gives quantum response a geometric interpretation induced from the geometry of Hilbert space projections. For a two level system the metric turns out to be the Fubini-Study metric and the symplectic form the adiabatic curvature.

Speaker: Yosi Avron, Technion (Israel Institute of Technology)
Location:
Jadwin Hall A09
March 4, 2011
3:00pm - 5:00pm
An Aronsson type approach to extremal quasiconformal mappings

Quasiconformal mappings $u:\Omega\to \Omega'$ between open domains in $R^n$, are $ W^{1,n}$ homeomorphisms whose dilation $K=|du|/ (det du)^1/n$ is in $L^\infty$. A classical problem in geometric function theory consists in finding QC minimizers for the dilation within a given homotopy class or with prescribed boundary data. In a joint work with A.

Speaker: Luca Capogna, University of Arkansas
Location:
Fine Hall 314
March 7, 2011
4:00pm - 6:00pm
Generalized Markov models in population genetics

Population geneticists study the dynamics of alternative genetic types in a replicating population. Most theoretical works rests on a simple Markov chain, called the Wright-Fisher model, to describe how an allele's frequency changes from one generation to the next.

Speaker: Joshua Plotkin, University of Pennsylvania
Location:
Fine Hall 214
March 8, 2011
4:30pm - 6:30pm
Cluster Algebras and Quiver Grassmannians

A cluster algebra, which was introduced by Fomin and Zelevinsky, is a commutative algebra with a family of distinguished generators (the cluster variables) grouped into overlapping subsets (the clusters) which are constructed by mutations. A quiver Grassmannian is a projective variety parametrizing subrepresentations of a quiver representation with a given dimension vector.

Speaker: Kyungyong Lee, University of Connecticut
Location:
Fine Hall 322
March 9, 2011
4:30pm - 6:30pm
The spectrum of non-normal random matrices

We will discuss the asymptotics of the spectrum of non-normal random matrices with size going to infinity, and in particular the single ring phenomenon observed for unitary invariant models.

Speaker: Alice Guionnet, ENS, Lyon, France
Location:
Fine Hall 314
March 10, 2011
12:00pm - 2:00pm
Topological expansion for random matrices

Department Colloquium (joint with ORFE)

Speaker: Alice Guionnet, ENS, Lyon, France
Location:
Sherrerd Hall 101
March 10, 2011
2:30pm - 4:30pm
Linear systems modulo composites

Computation modulo composite numbers is much less understood than computation over primes; and sometimes surprisingly much more powerful. A positive example is that the best construction of locally decodable codes known today heavily relies on computations modulo composites.

Speaker: Shachar Lovett, IAS
Location:
Fine Hall 224
March 10, 2011
3:00pm - 4:30pm
Nonimmersions of real projective spaces and tmf

We use the spectrum tmf to obtain new nonimmersion results for many real projective spaces RP^n for n as small as 113. The only new ingredient is some new calculations of tmf-cohomology groups. We present an expanded table of nonimmersion results. We also present several questions about tmf.

Speaker: Don Davis, Lehigh University
Location:
Fine Hall 314
March 10, 2011
4:30pm - 6:30pm
Unlink detection and the Khovanov module

Kronheimer and Mrowka recently showed that Khovanov homology detects the unknot. Their proof does not obviously extend to show that Khovanov homology detects unlinks of more than one component, and one could reasonably question whether it actually does (the Jones polynomial, for instance, does not detect unlinks with multiple components).

Speaker: Matt Hedden, Michigan State University
Location:
Fine Hall 314
March 10, 2011
4:30pm - 6:30pm
Affine sieve and expanders

I will talk about the fundamental theorem of affine sieve (joint with Sarnak). The main black box in the proof of this result will be also explained. It is a theorem on a necessary and sufficient condition for a finitely generated subgroup of SL(n,Q) under which the Cayley graphs of such a group modulo square free integers form a family of expanders (joint with Varju).

Speaker: Alireza Golsefidy, Princeton University
Location:
Fine Hall 214
March 11, 2011
2:00pm - 4:00pm
Diffusion in a periodic Lorentz gas with narrow tunnels (P. Balint, N. Chernov, and D. Dolgopyat)

In a periodic Lorentz gas a particle moves bouncing off a regular array of fixed convex obstacles (scatterers), like in a pinball machine. When the horizon is finite, one observes a classical diffusion law. When the obstacles are so large that the tunnels between them become narrow (of width $\epsilon \to 0$) then the diffusion matrix scales with $\epsilon$.

Speaker: Nikolai Chernov, University of Alabama, Birmingham
Location:
Fine Hall 801
March 11, 2011
3:00pm - 5:00pm
CR moduli spaces on a contact 3-manifold

We study low-dimensional problems in topology and geometry via a study of contact and Cauchy-Riemann ($CR$) structures. In particular, we consider various $CR$ moduli spaces on a contact 3-manifold. A contact structure is called spherical if it admits a compatible spherical $CR$ structure.

Speaker: Jih-Hsin Cheng, Academia Sinica, Taiwan
Location:
Fine Hall 314
March 17, 2011
4:30pm - 6:30pm
Niebur Integrals and Mock Automorphic Forms

Among the bounty of brilliancies bequeathed to humanity by Srinivasa Ramanujan, the circle method and the notion of mock theta functions strike wonder and spark intrigue in number theorists fresh and seasoned alike. The former creation was honed to perfection for its original purpose of counting partitions by Hans Rademacher.

Speaker: Wladimir de Azevedo Pribitkin, College of Staten Island, CUNY
Location:
IAS Room S-101
March 21, 2011
4:00pm - 6:00pm
Brother, can you spare a compacton?

Unlike certain personal or national tragedies which may extend indefinitely, patterns observed in nature are of finite extent. Yet, as a rule, the solitary patterns predicted by almost all existing mathematical models extend indefinitely with their tails being a by product of their analytical nature.

Speaker: Philip Rosenau, Tel Aviv University
Location:
Fine Hall 214
March 22, 2011
4:00pm - 6:00pm
Pseudo-Anosov flows in Seifert fibered and solvable 3-manifolds

We discuss the following rigidity results: 1) A pseudo-Anosov flow in a Seifert fibered manifold is up to finite covers topologically conjugate to a geodesic flow; 2) A pseudo-Anosov flow in a solv manifold is topologically conjugate to a suspension Anosov flow. The proofs use the structure of the fundamental groups in these manifolds and the topological theory of pseudo-Anosov flows.

Speaker: Sergio Fenley, Florida State University and Princeton University
Location:
Fine Hall 601
March 22, 2011
5:00pm - 7:00pm
Massey Triple Products

A technique will be discussed to control the indeterminacy in cohomology Massey triple products. A variety of non-vanishing and vanishing results for Massey triple products are proved using this technique. Here are three examples. Many authors have noticed that non-trivial triple products in a submanifold produce non-trivial triple products in the blowup along the submanifold.

Speaker: Larry Taylor, IAS
Location:
Fine Hall 314
March 24, 2011
2:00pm - 4:00pm
Ergodic properties of infinite extensions of area-preserving flows

We consider infinite volume preserving flows that are obtained as extensions of flows on surfaces. Consider a smooth area-preserving flow on a surface $S$ given by a vector field $X$ and consider a real valued function $f$ on $X$.

Speaker: Corinna Ulcigrai, University of Bristol
Location:
Fine Hall 801
March 24, 2011
3:00pm - 5:00pm
Equivariant cohomology and orbit structure

Let T be a torus, and let X be a T-space. In this talk I will relate algebraic properties of the equivariant (co)homology of X to the structure of the T-orbits in X. This generalizes a result of Atiyah and Bredon.

Speaker: Matthias Franz, University of Western Ontario
Location:
Fine Hall 314

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