Refreshments are served 30 minutes before each talk in the Conference Room MSPB 335
|February 8, 2018||Mrinal Roychowdhury, University of Texas - Rio Grande Valley||
Abstract: The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability distribution by a discrete distribution. Though the term 'quantization' is known to electrical engineers for the last several decades, it is still a new area of research to the mathematical community. In my presentation, first I will give the basic definitions that one needs to know to work in this area. Then, I will give some examples, and talk about the quantization on mixed distributions. Mixed distributions are an exciting new area for optimal quantization. I will also tell some open problems relating to mixed distributions.
|February 6, 2018||Jeff Mermin, Oklahoma State University||
Monomial Resolutions and CW Complexes
Abstract: Let R be a polynomial ring, and I a homogeneous ideal. Almost all algebraic and geometric information about I is encoded in a related object called a minimal free resolution: a long exact sequence of free modules terminating in I. Finding these free resolutions is thus a central problem in modern commutative algebra.
I'll work some examples showing that the problem is prohibitively difficult even for monomial ideals, and discuss modern techniques that can (in good situations) describe the resolution of a monomial ideal in terms of a suitable topological object, such as a simplicial or CW complex.
The talk should be accessible to students who are comfortable computing the homology of a simplicial complex.
|November 9, 2017||William Hardesty, Louisiana State University||
The Representation Theory of p-Restricted Lie Algebras
Abstract: A p-restricted Lie algebra is defined to be a Lie algebra over an (algebraically closed field) k of characteristic p > 0 which is equipped with an additional structure called the "p-power map". Unlike the characteristic 0 case, the study of finite-dimensional representations for (restricted) reductive Lie algebras (such as gln) is an incredibly deep and complicated subject. The goal of the talk will be to give a brief overview of this area of research. I will begin with a quick review of the representation theory for complex Lie algebras. Then I will define and give some important examples of p-restricted Lie algebras and their representations, as well as a summary of their basic properties. In the remainder of the talk various problems of interest to representation theorists will be discussed, such as computing extension groups, multiplicity formulas and radical filtrations for various types of representations. If time permits, I may also mention some results from my ongoing joint work with V. Nandakumar.
|November 2, 2017||Jonas Hartwig, Iowa State University||
Galois Orders and Gelfand-Zeitlin Modules
Abstract: Galois orders form a class of noncommutative algebras introduced by Futorny and Ovsienko in 2010. They appear in many places in Lie theory and quantum algebra. We present new constructions of Galois orders and their representations, generalizing recent results by several different authors. I will end by stating some current open problems in the area.
|October 19, 2017||H. N. Nagaraja, College of Public Health, The Ohio State University||
Some Applications of Ordered Data Models
Abstract: We introduce three probability models for ordered data viewing them as (i) order statistics, (ii) record values, and (iii) order statistics and their concomitants. Applications of spacings of order statistics to auction theory and actuarial science will be illustrated with two examples: (a) properties of expected rent in regular and reverse auctions and (b) finding approximation to finite-time ruin probabilities for a company with large initial reserves. The problem of estimating mobility rates in search models using record value theory will be discussed. We will see how the concept of concomitants of order statistics can be used to model data-snooping biases in search engines, two-stage designs, and tests of financial asset pricing models. Some recent work on order statistics and spacings will be introduced.
|October 18, 2017
This talk is aimed at a general audience!
|H. N. Nagaraja, College of Public Health, The Ohio State University
Fourth Satya Mishra Memorial Lecture
Statistical Methods for Public Health and Medicine
Abstract: Probabilistic modeling, statistical design, and inferential methods form the backbone of the remarkable advances in medicine and public health. General goals of inference are hypothesis testing (as in clinical trials), estimation (of risk for a disease), and prediction (of a future condition). We illustrate them by introducing examples, data types, statistical models, and methods. With summary statistics on commonly used statistical concepts in major public health and medical journals, we discuss popular statistical methods that drive current research in public health and medical science. We examine trends in biostatistical research and observe the evolving field of data science and bioinformatics.
|September 21 & 28, 2017||Selvi Beyarslan, University of South Alabama||
Algebraic Properties of Toric Rings of Graphs I & II
Abstract: Let G = (V,E) be a simple graph. We investigate the Cohen-Macaulayness and algebraic invariants, such as the Castelnuovo-Mumford regularity and the projective dimension, of the toric ring k[G] via those toric rings associated to induced subgraphs of G.
|September 19, 2017||Kodai Wada, Waseda University, Tokyo, Japan||
Linking Invariants of Virtual Links
Abstract: In the first half of the talk, we introduce the notion of an even virtual link and define a certain linking invariant of even virtual links, which is similar to the linking number. Here, a virtual link diagram is even if the virtual crossings divide each component into an even number of arcs. The set of even virtual link diagrams is closed under classical and virtual Reidemeister moves, and it contains the set of classical link diagrams. For two even virtual link diagrams, the difference between the linking invariants of them gives a lower bound of the minimal number of forbidden moves needed to deform one into the other. Moreover, we give an example which shows that the lower bound is best possible.
In the second half of the talk, we define a polynomial invariant of any virtual link which is a generalization of the linking invariant above. The polynomial invariant is a natural extension of the index type invariants of virtual knots, for example, the writhe polynomial and the affine index polynomial.
|September 7 & 14, 2017||Bin Wang, University of South Alabama||
A Mixture Model for Next-Generation Sequencing Gene Expression Data I & II
Abstract: Gene expression data are usually highly skewed with a lot of weakly- or non-expressed genes. As a result, gene expression data profiled using next-generation sequencing (NGS) techniques usually contain a large amount of zero measurements. We propose to model the NGS data using a mixture model. Via data binning, the expectation-maximization algorithm performs well to estimate the distributions of gene profiles. We also propose a novel normalization method by assuming the existence of a common distribution among all gene profiles.
|August 24, 2017||Andrei Pavelescu, University of South Alabama||
Complete Minors of Self-Complementary Graphs
Abstract: Some topological properties of graphs are connected to the existence of complete minors. For a simple non-oriented graph G, a minor of G is any graph that can be obtained from G by a sequence of edge deletions and contractions. In this talk, we show that any self-complementary graph with n vertices contains a K[(n+1)/2] minor. We also prove that this bound is the best possible and present some consequences about which self-complementary graphs are planar, intrinsically linked or intrinsically knotted. This is joint work with Dr. Elena Pavelescu.