Peter Hinow, University of Wisconsin, Milwaukee
Computational Analysis Seminar page for Zoom meeting information

A new multi-electrode array-based application for the long-term recording of action potentials from electrogenic cells makes possible exciting cardiac electrophysiology studies in health and disease. With hundreds of simultaneous electrode recordings being acquired over a period of days, the main challenge becomes achieving reliable signal identification and quantification. We set out to develop an algorithm capable of automatically extracting regions of high-quality action potentials from terabyte size experimental results and to map the trains of action potentials into a low-dimensional feature space for analysis. Our automatic segmentation algorithm finds regions of acceptable action potentials in large data sets of electrophysiological readings. We use spectral methods and support vector machines to classify our readings and to extract relevant features. We are able to show that action potentials from the same cell site can be recorded over days without detrimental effects to the cell membrane. The variability between measurements 24 h apart is comparable to the natural variability of the features at a single time point. Our work contributes towards a non-invasive approach for cardiomyocyte functional maturation, as well as developmental, pathological and pharmacological studies. As the human-derived cardiac model tissue has the genetic makeup of its donor, a powerful tool for individual drug toxicity screening emerges. This is a Joint work with Stacie Kroboth, Viviana Zlochiver (Advocate Aurora Health) and John Jurkiewicz (UWM).

Clover May, NTNU

For spaces with an action by a group G, one can compute an equivariant analogue of singular cohomology called RO(G)-graded Bredon cohomology.  Computations in this setting are often challenging and not well understood, even for G = C_2, the cyclic group of order 2.  In this talk, I will start with an introduction to RO(G)-graded cohomology and describe a structure theorem for RO(C_2)-graded cohomology with (the equivariant analogue of) Z/2-coefficients.  The structure theorem describes the building blocks for the cohomology of C_2-spaces and makes computations significantly easier.  It shows the cohomology of a finite C_2 space depends only on the cohomology of two types of spheres, representation spheres and antipodal spheres.  I will give some applications and talk about work in progress generalizing the structure theorem to other settings. (Contact Person: Anna Marie Bohmann)

Ákos Nagy, UC Santa Barbara
PDE Seminar page for Zoom meeting information

The Keller–Segel equations provide a mathematical model for chemotaxis, that is the organisms (typically bacteria) in the presence of a (chemical) substance. These equations have been intensively studied on R^n with its flat metric, and the most interesting and difficult case is the planar, n = 2. Less is known about solutions in the presence of nonzero curvature. In the talk, I will introduce the Keller–Segel equations in dimension 2, and then briefly recall a few relevant known facts about them. After that I will present my main results. First I prove sharp decay estimates for stationary solutions and prove that such a solution must have mass 8π. Some aspects of this result are novel already in the flat case. Furthermore, using a duality to the “hard” Kazdan–Warner equation on the round sphere, I prove that there are arbitrarily small perturbations of the flat metric on the plane that do not support a stationary solution to the Keller–Segel equations. I will also prove a curved version of the logarithmic Hardy–Littlewood–Sobolev inequality, which I use to prove a result that is complementary to the above ones, as it shows that the functional corresponding to the Keller–Segel equations is bounded from below only when the mass is 8π.

Finally, if time permits, I will present a few results about the nonstationary case, that is a work in progress. In particular, I show long time existence for small masses for certain metrics.

Yi Ling, Vanderbilt University
Zoom link is: https://vanderbilt.zoom.us/j/92800454642 The meeting ID is 928 0045 4642.

 Abstract: Schur functions are one of the most important symmetric functions as they are closely related to representation theory and geometry. The Heisenberg product is an associative product defined on symmetric functions which interpolates between the ordinary product and the Kronecker product. Heisenberg coefficients are Schur structure constants of the Heisenberg product and generalization of the well-known Littlewood-Richardson coefficients and Kronecker coefficients. In this talk, I will describe Schur functions and the Heisenberg product. I will also introduce stability results related to the Kronecker coefficient and the Heisenberg coefficient.

James Tener, ANU Mathematical Sciences Institute
https://vanderbilt.zoom.us/j/94393956397?pwd=Ulg2TWpHZURyR09WejIxbEVUVFRwUT09
Meeting ID: 943 9395 6397  Passcode: 810797

In this talk I’ll present joint work in progress with André Henriques which shows that any conformal net (i.e. a net of factors corresponding to intervals of the unit circle) has a geometric origin. More precisely, I’ll explain how the factors are generated by insertion operators built from a two-dimensional geometric field theory, or alternatively from a vertex operator algebra. A similar analysis is possible for representations of a conformal net, which correspond to subfactors.

After the talk, all participants are invited to stay on the Zoom call and chat with the speaker. Please feel free to pass the Zoom meeting information on to your students and postdocs.

Maxime Van de Moortel, Princeton University
PDE Seminar page for Zoom meeting information

Abstract: TBD