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# Departmental Colloquia

Our department is proud to host weekly colloquium talks featuring research by leading mathematicians from around the world. Most colloquia are held on Fridays at 4pm in Parker Hall, Room 250 (unless otherwise advertised) with refreshments preceding at 3:30pm in Parker Hall, Room 244.

**DMS Colloquium: Jian-Guo Liu**

**Dec 01, 2017 04:00 PM**

Speaker: **Jian-Guo Liu**, Duke University

Host: Wenxian Shen

**DMS Colloquium Steve Qin**

**Nov 10, 2017 04:00 PM**

Speaker: **Steve Qin**, Department of Biostatistics and Bioinformatics, Rollins School of Public Health, Emory University

Title: Utilizing historical data to aid statistical inference of high throughput data with low sample size

Abstract: Modern high-throughput biotechnologies such as microarray and next generation sequencing produce a massive amount of information for each sample assayed. However, in a typical high throughput experiment, only limited amount of data are observed for each individual feature, thus the classical "large p, small n" problem. Bayesian hierarchical model, capable of borrowing strength across features within the same dataset, has been recognized as an effective tool in analyzing such data. However, the shrinkage effect, the most prominent feature of hierarchical models, can lead to undesirable over-correction for some features. In this work, we discuss possible causes of the drawback and propose several alternative solutions. Our strategy is rooted in the facts that in the Big Data era, large amount of historical data are available which can and should be taken advantage of. Our strategy presents a new framework to enhance the Bayesian hierarchical model.

This is a joint work with Ben Li.

Host: Peng Zeng

**DMS Colloquium: Graeme Milton**

**Nov 03, 2017 04:00 PM**

Speaker: **Professor Graeme Milton**, University of Utah

Title: Metamaterials and Mathematics

Abstract: Metamaterials are basically composite materials with properties or a combination of properties not found in nature. Typically they are made by combining materials with highly contrasting phases. There has been an explosion of interest in them due to a wealth of potential applications, and the unprecedented ability we now have to tailor make desired microstructures. In practice the operation of many metamaterials is not in the homogenization limit so mathematics needs to be developed to satisfactorily account for their properties. Numerical algorithms and particularly optimization codes also need to be developed as a tool for designing new microstructures. In addition there is a wealth of relatively unexplored areas, such as non-linear metamaterials, metamaterials with dynamic microstructures, and more generally active metamaterials with controllable properties.

Progress in developing an understanding of them would be greatly accelerated by mathematicians. There is a lot of excitement in the field, and as a result a lot of speculative and some dubious claims have been made. Mathematics is needed to separate truth from fiction.

Host: Junshan Lin

**DMS Colloquium: Prof. Fadil Santosa**

**Oct 27, 2017 04:00 PM**

Speaker: **Prof. Fadil Santosa,** University of Minnesota

Title: An Approach to Statistical Shape Analysis

Abstract: In statistical shape analysis the goal is to obtain characteristics such as mean, standard deviation, etc., from a set of shapes. While much progress in this area has occurred in the past four decades, many challenges remain. This presentation will review several of the important developments in this field. An approach based on Fourier analysis is proposed and its capabilities demonstrated.

Hosts: Yanzhao Cao and Junshan Lin

**DMS Colloquium: Yin**

**Oct 20, 2017 04:00 PM**

Speaker: **Professor Gang George Yin**, Wayne State University

Title: Switching Random Dynamic Systems and Applications

Abstract: Many problems in control and optimization require the treatment of systems in which continuous dynamics and discrete events coexist. This talk presents a survey on some of our recent work on such systems. In the setup, the discrete event is formulated as a random process with a finite state space, and the continuous component is the solution of a deterministic or stochastic differential equation. Seemingly similar to the systems without switching, the processes have a number of features that are distinctly different from processes without switching. After providing motivational examples arising from wireless communications, finance, singular perturbed Markovian systems, manufacturing, and consensus controls, we present necessary and sufficient conditions for the existence of unique invariant measure, stability, stabilization, and numerical solutions of control and game problems.

Host: Xiaoying Han

**DMS Colloquium: Dr. Tianran Chen**

**Oct 06, 2017 04:00 PM**

Speaker: **Dr. Tianran Chen**, AUM

Title: Algebraic aspects of network induced systems of nonlinear equations

Abstract: Networks, or graphs, can represent a great variety of systems in the real world including neural networks, power grid, the Internet, and our social networks. Mathematical models for such systems naturally reflect the graph theoretical information of the underlying network. This talk explores some common themes in such models from the point of view of systems of nonlinear equations. In particular, we will discuss recent results from the root counting problem for the algebraic Kuramoto equations.

**DMS Colloquium: Ji Li**

**Sep 29, 2017 04:00 PM**

Speaker: **Ji Li**, Macquarie University, Sydney, Australia

Title: Nehari type theorem: Commutator and BMO space associated with operators

Aabstract: In this talk we will discuss the Nehari type theorem, i.e., the characterization of the BMO space via the commutator of Riesz transforms, associated with operators in several different settings, where the analyticity or Fourier transform is not available. This is motivated by concrete examples arisen from harmonic analysis and differential equations, including the Cauchy integrals, the Reisz transforms associated with Neumann Laplacian, Bessel operators, and the sub-Laplacian on stratified nilpotent Lie groups (e.g. Heisenberg groups).

Host: Yongsheng Han

Last Updated: 09/11/2015