**COLLOQUIA 2015 -- 2016**

Refreshments are served in Parker Hall, Room 244, beginning at 3:30.

**September 4, 2015**

Speaker: Yichen Qin, University of Cincinnati

Title: Maximum Tangent Likelihood Estimation and Robust Regression

Abstract: In this article, we introduce a new robust estimation procedure for linear regression called maximum tangent likelihood estimation. By robustifying the traditional log-likelihood function, we are able to generate a class of robust estimates of the regression coefficients by adjusting the trade-off between efficiency and robustness. Furthermore, we propose a penalized tangent likelihood estimation for variable selection. We prove the consistency and oracle properties for such a method and show that it achieves the breakdown point of 0.5. We demonstrate the superior performance of our estimator by several simulation studies as well as real data examples.

Faculty host: Guanqun Cao

Brief Description of the Speaker’s Academic and Professional Achievements/Credentials:

Dr. Yichen Qin received a Bachelor in Statistics at Renmin University in 2005 and a Master of Science in Statistics at Columbia University in 2007. After that, he studied with Dr. Carey E. Priebe, a Senior Member of the IEEE, a Lifetime Member of the Institute of Mathematical Statistics, and a Fellow of the American Statistical Association, in Johns Hopkins University. Qin obtained a Ph.D. in Applied Mathematics and Statistics from Johns Hopkins University in 2013. In the same year, he joined the Department of Operations, Business Analytics, and Information Systems in the Lindner College of Business at the University of Cincinnati as an Assistant Professor. His current line of research focuses on computational statistics, robust statistics, clustering analysis, mixture models, variable selection, financial statistics, social network analysis. He has published over 8 papers in high impact statistics journals including *Journal of the American Statistical Association*, *Statistics in Medicine*, etc.

**September 11, 2015 **

**Speaker:** Hongkai Zhao (University of California at Irvine)

Title: Approximate separability of Green’s function and intrinsic complexity of differential operators

Abstract: Approximate separable representation of the Green’s functions for differential operators is a fundamental question in the analysis of differential equations and development of efficient numerical algorithms. It can reveal intrinsic complexity, e.g., Kolmogorov n-width or degrees of freedom of the corresponding differential equation. Computationally, being able to approximate a Green’s function as a sum with few separable terms is equivalent to the existence of low rank approximation of the discretized system which can be explored for matrix compression and fast solution techniques such as in fast multiple method and direct matrix inverse solver. In this talk, we will mainly focus on Helmholtz equation in the high frequency limit for which we developed a new approach to study the approximate separability of Green’s function based on an geometric characterization of the relation between two Green's functions and a tight dimension estimate for the best linear subspace approximating a set of almost orthogonal vectors. We derive both lower bounds and upper bounds and show their sharpness and implications for computation setups that are commonly used in practice. We will also make comparisons with other types of differential operators such as coercive elliptic differential operator with rough coefficients in divergence form and hyperbolic differential operator. This is a joint work with Bjorn Engquist.

Faculty host: Yanzhao Cao

**September 18, 2015**

Paul Martin, Colorado School of Mines

Faculty host: Junshan Lin

**October 23, 2015**

Speaker: Elton Hsu, Northwest University

Faculty host: Ming Liao

**October 30, 2015**

Speaker: Zhong-Zhi Bai, Chinese Academy of Sciences

Faculty host: Tin-Yau Tam

**November 6, 2015**

Speaker: Caroline Uhler, Institute for Science and Technology, Austria/MIT

Faculty host: Luke Oeding

**PAST COLLOQUIA**

**August 28, 2015 ROOM 249**

Speaker: Peter Nyikos, University of South Carolina

ABSTRACT: A quarter of a century after Peano caused a sensation with his space filling curves, the Hahn-Mazurkiewicz theorem gave a beautiful characterization of which spaces are a continuous image of the closed unit interval. They are precisely the compact, connected, locally connected, metrizable spaces. A problem that remained open for about six decades was to find a characterization of continuous images of orderable continua that was a natural generalization of this theorem. It was finally solved by Mary Ellen Rudin in 2000: all one needs is to change "metrizable" to "monotonically normal"; however, the proof was arguably the most difficult proof in all of point set topology, hence the long lag time. Moreover, Rudin needed some exceptionally deep theorems of Treybig and Nikiel to complement her proof, which actually showed that every compact monotonically normal space is the continuous image of an orderable compact space. This talk will review the highlights of this epic mathematical journey, and consider one minor improvement and one problem which, if answered affirmatively, would replace monotone normality with the much simpler and more general condition that every subspace is normal. However, this would require powerful axioms that are independent of the usual (ZFC) axioms of set theory.

Faculty host: Gary Gruenhage

Brief Description of the Speaker’s Academic and Professional Achievements/Credentials:

Peter Nyikos has been a leader in the field of set theoretic topology ever since he obtained his Ph.D. in 1971 at Carnegie-Mellon. He has approximately 100 publications in refereed journals and many invited conference addresses. He is on the editorial board of *Topology and its Applications* and has organized several AMS Special Sessions as well as a Spring Topology and Dynamics Conference. A long-standing interest of his is the theory of non-metrizable manifolds.

**TUESDAY, September 1, 2015**

Speaker: Wayne M. Lawton, Mahidol University, Thailand

Title: Multivariate Prediction and Spectral Factorization

Abstract: Prediction theory studies stationary random functions on ordered groups. Time series are functions on the integer group and characterized by classical harmonic analysis results such as Szego's spectral factorization theorem. Images are functions on higher rank groups. We use results about entire functions and ergodic theory to derive new results for these functions.

Faculty host: Richard Zalik

Brief Description of the Speaker’s Academic and Professional Achievements/Credentials:

Research Interests: Harmonic Analysis and its Applications to Engineering and Physics. His research addresses both fundamental mathematics and physics. Positions held include G. C. Evans Instructor, Dept. Math, Rice University; Research member, Institute for Advanced Study, Princeton; Lecturer at UCLA and at USC; Member of Technical Staff at Jet Propulsion Lab; Senior Project Engineer at TRW; Co-founder and Chief Scientist, AWARE, Inc; Visiting Scientist at Harvard/Smithsonian Center for Astrophysics; Adjunct Professor of Electrical Engineering at Rice University and Northeastern University; Associate Professor, University of Newcastle, Australia.

Author of numerous research publications in pure mathematics, applied mathematics and physics, Lawton is widely cited and well known in the applied harmonic analysis and signal processing communities. Editor for the *Journal of High Performance Computing* and the *Journal of Southeast Asian Mathematical Society,* and currently an editor for the *Thai Journal of Mathematics*.

Lawton was the 1998 Winner of the National Science Award, National Science and Technology Board, Republic of Singapore; 1972 Rice Math Prize; 1968 Bausch and Lomb Science Award.

Lawton received a PhD from Wesleyan University, 1972. He is a member of Phi Beta Kappa and Sigma Xi. He speaks Thai, German, and Mandarin. Recently retired from the National University of Singapore, he is currently an Adjunct Professor at the University of Western Australia and a Visiting Lecturer at Mahidol University in Thailand.