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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: Jan Rosinski

Mar 23, 2018 04:00 PM

Speaker: Jan Rosinski, University of Tennessee

Title: Series expansions of time-continuous random walks and solutions to random differential equations

Abstract: In 1923 N. Wiener constructed two random trigonometric series which converge uniformly to a limit satisfying conditions for a Brownian motion. The conditions were  earlier  postulated by A. Einstein in terms of partial differential equations.  K. Ito, the founder of Ito stochastic calculus, unified results on the convergence of these and other similar series expansions in the so-called  Ito-Nisio theorem (1968). O. Kallenberg (1974) gave the first generalization of the Ito-Nisio theorem to the uniform convergence of processes with jumps.

Brownian motion describes continuous in space random walk. In this talk we will concentrate on random walks with jumps, their series expansions, and strongest possible modes of their convergence. To this aim we will establish further generalization of the Ito-Nisio theorem.  We will discuss the Ito map, which is just an ODE with a rough input. Using these tools we obtain strong pathwise convergence in numerical solutions of stochastic differential equations driven by Levy processes.

This talk is based on a joint work with Andreas Basse-O’Connor and Jorgen Hoffmann-Jorgensen.

Faculty host: Erkan Nane

DMS Colloquium: Emily King

Mar 30, 2018 04:00 PM

Speaker: Emily King (U. Bremen)

Title: (Hilbert Space) Frames, Algebraic Combinatorics, and Geometry

Abstract: Frames are generalizations of orthonormal bases which yield "nice" decompositions of data. Such systems are the foundation of applied harmonic analysis and are also closely related to quantum measurements and linear codes.  When one wants an optimally robust representation of data, one often looks for frames that have some sort of spread, be it geometric (as non-parallel as possible) or algebraic (no nontrivial linear dependencies).  Over the last few years, it has been discovered that the relationship between these two types of spread is more complicated than had previously been believed. Furthermore, methods from algebra, geometry, and combinatorics have recently proven themselves to be very useful in the study of frames.

For example, algebraic graph theory and combinatorial design theory have led to new characterizations and novel constructions of optimal line (or, more generally, subspace) configurations which are also frames. Also, almost all desirable classes of frames form real algebraic varieties, and certain known results in frame theory have also been found to be equivalent to concepts in matroid theory and arrangements of hyperplanes.

In this talk, the currently known connections between these objects from harmonic analysis / quantum information theory and combinatorics / algebraic & discrete geometry will be presented.

(photo courtesy Uni Bremen/Kai Uwe Bohn)

DMS Colloquium: Claudiu Raicu

Apr 06, 2018 04:00 PM

Speaker: Claudiu Raicu (Notre Dame)

Title: TBA

DMS Colloquium: Gradimir V. Milovanovic

Apr 10, 2018 04:00 PM

Speaker: Gradimir V. Milovanovic, Serbian Academy of Sciences and Arts

Title: Special Quadrature Processes for Summation of Slowly Convergent Series

Abstract: Slowly convergent series  appear in many problems in mathematics, physics  and other  sciences. There are several numerical methods based on linear and nonlinear transformations (e.g., Cesàro-transformation,  Aitken $$\Delta^2$$-transformation, Wynn-Shanks $$\varepsilon$$-algorithm, $$E$$-algorithm, Levin's transformation,  $$\rho$$-algorithm, etc.). In this lecture  we present the so-called summation/integration methods, which are very efficient. Methods are based on certain transformations of sums to weighted integrals over the real line or the half-line and  on an application of special Gaussian quadrature formulas with respect to some non-classical weight functions (Bose-Einstein, Fermi-Dirac, hyperbolic weights, $$\ldots$$). For constructing such quadrature rules we use a recent progress in symbolic computation and variable-precision arithmetic, implemented through our Mathematica package “OrthogonalPolynomials.” Several interesting applications will also be presented.

Faculty host: Narendra K. Govil

DMS Colloquium: Honglang Wang

Apr 20, 2018 04:00 PM

Speaker: Honglang Wang, IUPUI (Indiana University--Purdue University Indianapolis)

Faculty host: Guanqun Cao

DMS AU-AUM Joint Colloquium: Robert Underwood

Mar 09, 2018 04:00 PM

AU-AUM Joint Math Colloquium

Speaker: Robert Underwood, AUM

Title: A Class of Automatic Sequences

Robert G. Underwood is an Ida Belle Young Endowed Professor at Auburn University at Montgomery. He is the author of three books on Hopf algebras and modern algebra, and has published over 30 papers on subjects including algebra, geometry and theoretical computer science.  He teaches modern algebra, number theory and applied cryptography at AUM.  He is currently a co-PI on an NSF STEM grant conducting an undergraduate research project relating entropy and secure encryption.

Faculty host: Huajun Huang

DMS Colloquium: Hans-Werner van Wyk

Feb 23, 2018 04:00 PM

Speaker: Hans-Werner van Wyk

Title: The Propagation of Uncertainty through Differential Equations

Abstract: Many complex physical processes can be adequately described in the deterministic language of partial differential equations (PDEs), yet operate in uncertain environments that can only be observed partially and/or indirectly. This aleatory uncertainty manifests itself in the underlying system parameters. My work centers on its identification and propagation through to quantities of interest related to the system's output. This talk highlights my contributions in this area, particularly in improving the efficiency of sampling methods by exploiting multiscale features of random inputs, by designing quadrature schemes tailored to the underlying density, or through the use of reduced order models. I will also discuss some applications of my work, ranging from the prediction of saltwater intrusion, to the development of reliable spectral diagnostics for astrophysical plasmas.

DMS Colloquium: Yifan Cui

Feb 19, 2018 04:00 PM

Speaker: Yifan Cui, University of North Carolina, Chapel Hill

Title: Tree-based Survival Models and Precision Medicine

Abstract: In the first part, we develop a theoretical framework for survival tree and forest models. We first investigate the method from the aspect of splitting rules. We show that existing approaches lead to a potentially biased estimation of the within-node survival and cause non-optimal selection of the splitting rules. Based on this observation, we develop an adaptive concentration bound result which quantifies the variance component for survival forest models. Furthermore, we show with two specific examples how these concentration bounds, combined with properly designed splitting rules, yield consistency results.

In the second part, we focus on one application of survival trees in precision medicine which estimates individualized treatment rules nonparametrically under right censoring. We extend the outcome weighted learning to right censored data without requiring either inverse probability of censoring weighting or semi-parametric modeling of the censoring and failure times. To accomplish this, we take advantage of the tree-based approach to nonparametrically impute the survival time in two different ways. In simulation studies, our estimators demonstrate improved performance compared to existing methods. We also illustrate the proposed method on a phase III clinical trial of non-small cell lung cancer.

DMS Colloquium: Jaehong Jeong

Feb 16, 2018 04:00 PM

Speaker: Jaehong Jeong, King Abdullah University of Science and Technology

Title: A Stochastic Generator of Global Monthly Wind Energy with Tukey g-and-h Autoregressive Processes

Abstract: Quantifying the uncertainty of wind energy potential from climate models is a very time-consuming task and requires a considerable amount of computational resources. A statistical model trained on a small set of runs can act as a stochastic approximation of the original climate model and can be used to assess the uncertainty considerably faster than by resorting to the original climate model for additional runs. While Gaussian models have been widely employed as means to approximate climate simulations, the Gaussianity assumption is not suitable for winds at policy-relevant time scales, i.e., sub-annual. We propose a trans-Gaussian model for monthly wind speed that relies on an autoregressive structure with Tukey g-and-h transformation, a flexible new class that can separately model skewness and tail behavior. This temporal structure is integrated into a multi-step spectral framework that is able to account for global nonstationarities across land/ocean boundaries, as well as across mountain ranges. Inference can be achieved by balancing memory storage and distributed computation for a data set of 220 million points. Once fitted with as few as five runs, the statistical model can generate surrogates fast and efficiently on a simple laptop and can provide uncertainty assessments very close to those obtained from all the available climate simulations on a monthly scale.

This is joint work with Yuan Yan, Stefano Castruccio, and Marc G. Genton.

DMS Colloquium: Yiwen Liu

Feb 14, 2018 04:00 PM

Speaker: Yiwen Liu, University of Georgia

Title: B-scaling: a novel nonparametric data fusion method

Abstract: With the rapid development in science and technology, massive data has been collected from different sources, which leads to a large amount of data with different types and formats, such as the image data and omics data. Each type of the data only captures part of the contained information, and the data has to be integrated or fused to provide a complete understanding of the whole picture. Thus, there is an urgent call of powerful data fusion method. In this talk, I will introduce a B-scaling method to integrate multisource data. The asymptotic property of the B-scaling method will be discussed to provide theoretical underpinning of the method. The application of the method on epigenetic and biomedical research will be highlighted in the talk.

DMS Colloquium: Stefan Friedenberg

Feb 09, 2018 04:00 PM

Speaker: Professor Stefan Friedenberg, Hochschule Stralsund

Title: Extensions of rational groups

Faculty host: Ulrich Albrecht

Last Updated: 09/11/2015