Mon, Mar 31

Algebra Seminar
Jintao Deng, UB
Higher index theory for spaces with an FCE-by-FCEstructure 
4:00PM, Mathematics Building 250

The coarse Novikov conjecture claims that a certain assembly map from the K-homology of a metric space to the K-theory of its Roe algebra is injective. It has significant applications in geometry and topology of manifolds. Let \((1\to N_m\to G_m\to Q_m \to 1)_{m}\) be a sequence of extensions of finite groups. Assume that the coarse disjoint unions of\((N_m)_m\), \((G_m)_m\) and \( (Q_m)_m\) have bounded geometry. The sequence\((G_m)_m\) is said to have an FCE-by-FCE structure, if the sequence \((N_m)_m\) and the sequence \((Q_m)_m\) admit fibered coarse embeddings into Hilbert spaces. In this talk, I will talk about the coarse Novikov conjecture for a space with an FCE-by-FCE structure.  This is based a joint work with L. Guo, Q. Wang and G. Yu.

Wed, Apr 2

Analysis Seminar
Yusheng Luo, Cornell University
Uniformization of gasket Julia set
4:00PM, 250 Math Building

The quasiconformal uniformization problem for fractal sets is a classical question that has seen significant recent progress. In the 1970s, Ahlfors provided a geometric characterization of when a Jordan curve can be quasiconformally uniformized to a round circle. A closely related question--when a Sierpinski carpet can be quasiconformally mapped to a round carpet--has been extensively studied in both geometric and dynamical settings, with key contributions from McMullen, Bonk, and Bonk-Lyubich-Merenkov.   
In contrast, the problem of determining when a gasket can be quasiconformally mapped to a circle packing is more subtle. In this talk, I will discuss recent joint work with D.Ntalampekos that provides a characterization of when a gasket Julia set is quasiconformally equivalent to a circle packing. The proof builds on new results from some joint work with Y.Zhang on renormalization theory for circle packings.

Fri, Apr 4

Applied Math Seminar
Tamas Horvath (applied math, Oakland U)
Space-Time Finite Element Methods - The Good, the Bad and the Ugly
3:00PM, Math 250

Partial differential equations posed on moving domains arise in many applications such as air turbine modeling, flow past airplane wings, etc. The time-dependent nature of the flow domain poses an additional challenge when devising numerical methods for the discretization of such problems. One alternative when dealing with time-dependent domains is to pose the problem on a space-time domain and apply, for example, a finite element method in both space and time. These space-time methods can easily handle the time-dependent nature of the domain. In this talk, we present a space-time hybridizable discontinuous Galerkin method for the discretization of the incompressible Navier-Stokes equations on moving domains. This discretization is pointwise mass conserving and pressure robust, even on time-dependent domains. Moreover, high order can be achieved both in space and time. Numerical experiments will demonstrate the capabilities of the method.

Wed, Apr 9

Analysis Seminar
Hanfeng Li, SUNY at Buffalo
Local entropy theory, combinatorics, and local theory of Banach spaces
4:00PM, 250 Math Building

In 1995 Glasner and Weiss showed that if a continuous action of a countably infinite amenable group on a compact metrizable space X has zero entropy, then so does the induced action on the space of Borel probability measures on X. I will discuss a strengthening of the Glasner-Weiss result, in the framework of local entropy theory,  based on a new combinatorial lemma. I will also present an application of the combinatorial lemma to the local theory of Banach spaces. This is joint work with Kairan Liu.

Fri, Apr 18

Applied Math Seminar
Abner Salgado (University of Tennessee, Knoxville)
Energy, pointwise, and free boundary approximation of the obstacle problem for nonlocal operators

3:00PM, Math 250

We consider the obstacle problem for a nonlocal elliptic operator, like the integral fractional Laplacian of order 0<s<1. We derive regularity results in weighted Sobolev spaces, where the weight is a power of the distance to the boundary. These are then used to obtain optimal error estimates in the energy norm. 

Next, we develop a monotone, two-scale discretization of the operator, and apply it to develop numerical schemes. We derive pointwise convergence rates for linear and obstacle problems governed by such operators. As applications of the monotonicity, we provide error estimates for free boundaries and a convergent numerical scheme for a concave fully nonlinear, nonlocal, problem.

This presentation is based on several works in collaboration with: A. Bonito, J.P. Borthagaray, W. Lei, R.H. Nochetto, and C. Torres.

Fri, Apr 25

Applied Math Seminar
Sathyanarayanan Chandramouli (University of Massachusetts Amherst)
TBD
3:00PM, Math 250

TBD