Math Calendar

August 28, 2014 4:10 pm (Thursday)

The Mathematics of Three-Dimensional Structure Determination of Molecules by Cryo-Electron Microscopy

Amit Singer, Princeton University
Location: Stevenson 5211

Cryo-electron microscopy (EM) is used to acquire noisy 2D projection images of thousands of individual, identical frozen-hydrated macromolecules at random unknown orientations and positions. The goal is to reconstruct the 3D structure of the macromolecule with sufficiently high resolution. We will discuss algorithms for solving the cryo-EM problem and their relation to other branches of mathematics such as tomography, random matrix theory, representation theory, spectral geometry, convex optimization and semidefinite programming. Tea at 3:30 pm in SC 1425.



August 29, 2014 4:10 pm (Friday)

Fuglede-Kadison Determinats and Sofic Entropy

Ben Hayes, Vanderbilt University
Location: Stevenson 1432

Let G be a countable discrete group. An algebraic action of G is an action of G by automorphisms on a compact, metrizable, abelian group X. We will typically ignore the algebraic structure of X and think of the action of G on X as either an action on a compact metrizable space by homeomorphisms, or as a probablity measure-preserving action (giving X the Haar measure). When G is sofic, (to be defined in the talk) Lewis Bowen, with an extension by David Kerr and Hanfeng Li, defined the entropy of an action of G on a compact metrizable space or probability space. We will discuss results on the entropy of an algebraic action in the case that X is the Pontryagin dual of a finitely presented Z(G)-module. It turns out the answer is related to Fuglede-Kadison determinants (defined via the group von Neumann algebra) of finite matrices over Z(G). Our work extends results many others: Li-Thom,Kerr-Li,Bowen-Li etc, and in particular is a generalization of recent results of Li-Thom from amenable groups to sofic groups. Moreover, the techniques are the first in the subject to avoid a nontrivial determinant approximation. Time permitting, I will sketch a proof of the main result.



September 4, 2014 4:10 pm (Thursday)

Departmental Welcome Event


Location: Stevenson 5211

Department Chair Dietmar Bisch will introduce newcomers to the department. Refreshments will follow in Stevenson 1425.



September 5, 2014 4:10 pm (Friday)

A Center Construction for Braided Subfactors and Defects of Conformal Nets

Marcel Bischoff, Vanderbilt University
Location: Stevenson 1432

Braided subfactors are subfactors whose even part sits inside a given (non-degenerately) braided tensor category C. Using the braiding of C, there is a notion of commutativity for such subfactors. Maximal commutative subfactors in Z(C) can all be obtained by a subfactor in C via a double construction, the generalized Longo-Rehren construction. Given two commutative subfactors there is the notion of a defect between them, which is basically a commuting square containing both subfactors. We introduce a fusion product between defects and discuss how these defects describe topological defects in algebraic conformal quantum field theory. We give a classification of defects for subfactors coming from the double construction in terms of bimodules of the original subfactors. This classification will also show that the double construction is basically a special case of the "Functoriality of the center of an algebra" by Kong and Runkel.



September 11, 2014 4:10 pm (Thursday)

Talk Title TBA

Martin Kassabov, Cornell University
Location: Stevenson 5211



September 12, 2014 4:10 pm (Friday)

Talk Title TBA

Uffe Haagerup, Copenhagen University
Location: Stevenson 1432



September 18, 2014 4:10 pm (Thursday)

Talk Title TBA

Uffe Haagerup, University of Copenhagen
Location: Stevenson 5211



September 19, 2014 4:10 pm (Friday)

Talk Title TBA

François Le Maître, École Normale Supérieure de Lyon
Location: Stevenson 1432