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Date  Speaker  Talk 

Current Talks: 

Thursday, November 20, 2014 at 3:30 p.m. in ILB 370 This talk is part of the Student Symposium Series, organized and conducted by the graduate students.  Nemanja Kosovalic, University of South Alabama 
The LyapunovSchmidt Reduction in Nonlinear Analysis
Abstract: We introduce and give a survey of a functional analytic approach to solving problems in bifurcation theory and nonlinear analysis called the LyapunovSchmidt reduction. We illustrate how this method works in the context of a Hopf bifurcation in a system of ordinary differential equations, and indicate how it applies to other problems in nonlinear analysis. If time permits, we discuss some limitations of the method in the context of partial differential equations. The talk is aimed to be accessible to students and outsiders of the field. 
Tuesday, November 25, 2014 at 3:30 p.m. in ILB 370 
Erwin MinaDiaz, University of Mississippi Note the different day! 
Orthogonal Polynomials over the Unit Disk: Some Examples and Asymptotic Results
Abstract: Generally speaking, orthogonal polynomials refers to a sequence of polynomials p_{0}(z), p_{1}(z), ..., p_{n}(z), ..., of a complex variable z, each p_{n} of degree n, that are orthogonal with respect to some inner product (orthogonal polynomials of several variables can also be considered). Typically, the inner product is given by an integral with respect to a (positive) measure whose support is a compact subset of the complex plane. Two particular cases stand out for the richness of the theory: orthogonal polynomials over the real line (the support of the measure is contained in R), and orthogonal polynomials over the unit circle (the support of the measure is contained in {z:z=1}). The richness is due to some special features of the real line and the circle. In contrast, when the orthogonality measure is no longer supported on the line or the circle, the wealth of results is much more limited, and in some aspects, nonexistent. We will discuss some recent results in this more general context, mainly concerning the behavior of p_{n}(z) as n approaching infinity for planar type orthogonality measures supported on the unit disk. 
Thursday, February 5, 2015 at 3:30 p.m. in ILB 370  Thomas Brüstle, Université de Sherbrooke and Université Bishop’s, Canada 
TBA
Abstract: TBA 
Thursday, February 12, 2015 at 3:30 p.m. in ILB 370 This talk is part of the Student Symposium Series, organized and conducted by the graduate students.  Sytske Kimball, Department of Meteorology, University of South Alabama 
TBA
Abstract: TBA 
Past Talks: 

Thursday, November 13, 2014 This talk is part of the Student Symposium Series, organized and conducted by the graduate students.  Frazier Bindele, University of South Alabama 
SignedRank with Responses Missing at Random
Abstract: In this talk, we will start by introducing some asymptotic results on nonparametric kernel estimation. Next we will show how kernel estimation can be used in the study of the signedrank estimator of the regression coefficients under the assumption that some responses are missing at random in the regression model. Strong consistency and asymptotic normality of the proposed estimator will be established under mild conditions. To demonstrate the performance of the signedrank estimator, a simulation study under different settings of errors’ distributions will show that the proposed estimator is more efficient than the least squares estimator whenever the error distribution is heavy tailed or contaminated. When the errors follow a normal distribution, the simulation experiment also will show that the signedrank estimator is more efficient than its least squares counterpart whenever a large proportion of the responses are missing. 
Thursday, November 6, 2014  David Sprehn, University of Washington 
Characteristic Classes in Group Cohomology
Abstract: I will introduce the theory of characteristic classes for permutation representations of groups, and illustrate the technique by playing around with the natural representation of S_{4} and constructing generators for its "mod2 cohomology ring." Then we will meet the Dickson invariants, and construct some nonzero cohomology classes on the general linear groups over F_{2}. Lastly, I'll describe how finding a nonzero Chern class on GL_{n}F_{p} inspired my recent work on cohomology of finite groups of Lie type. 
Thursday, October 30, 2014  Masaaki Suzuki, Meiji University, Tokyo, Japan 
Meridional and NonMeridional Epimorphisms between Knot Groups
Abstract: We will consider epimorphisms between knot groups. Especially, we will focus on the image of a meridian under such an epimorphism. A homomorphism between knot groups is called meridional if it preserves their meridians. The existence of a meridional epimorphism introduces a partial order on the set of prime knots. We will determine the pairs of prime knots with up to 11 crossings which admit meridional epimorphisms between their knot groups. Moreover, we will describe some examples of nonmeridional epimorphisms explicitly. 
Thursday, October 23, 2014  Nutan Mishra, University of South Alabama 
Constructing Partially Balanced Incomplete Block Designs from Strongly Regular Graphs
Abstract: An undirected graph without loops, is strongly regular when each vertex is of equal degree with any two vertices with an edge are joined with exactly m common vertices and any two vertices without an edge are joined to n common vertices. R.C. Bose, in his 1963 paper, has shown that a two class association scheme can be expressed as a strongly regular graph. And thus strongly regular graphs has close connections with two classes of partially balanced incomplete block designs (PBIBD). Basic concepts, definitions, interrelationships of graph theory and design theory will be discussed along with a few construction theorems for partially balanced incomplete block designs. 
Thursday, October 16, 2014  Nutan Mishra, University of South Alabama 
Optimal Properties of Variance Balanced Designs
Abstract: It is well known that for a proper block design the combinatorial property of pairwise balance is sufficient to ensure the statistical property of variance balance. The variance balance property of a block design implies the complete symmetry of the information matrix. Using these facts we discuss the optimality in a class of proper variance balanced designs with unequal replications. Further unequal replications force the variance balanced designs to be nonbinary designs. Hence instead of using the usual optimality criteria given by J. Keifer, we compare the designs with respect to the functions based on efficiency factors of the design, namely eigenvalues of the matrix (RinverseC). 
Thursday, October 9, 2014  Ash Abebe, Auburn University 
Nonparametric Methods for Classification and Feature Selection
Abstract: In this talk, I will discuss some nonparametric maxcentral classifiers as well as methods for selecting features that are relevant for discrimination. The feature selection method rewards features for information towards discrimination but penalizes them for their similarity to already selected features. Monte Carlo simulation studies demonstrate that there are several situations where the proposed procedures provide lower misclassification error rates than classical methods. Finally, I will discuss results of application of the proposed procedures on food safety and gene expression data. 
Thursday, October 2, 2014 This talk is part of the Student Symposium Series, organized and conducted by the graduate students.  David Mullens, University of South Alabama 
What is a Scissors Congruence?
Abstract: We will define what it means to be Scissors Congruent for polygons and polyhedra. We'll see a scissors congruence proof of the Pythagorean Theorem and show that scissors congruence is an invariant of area. Next, we'll understand scissors congruence in terms of the distributive law and various other properties. We will define the Dehn Invariant. Noting that volume is an invariant of scissors congruence we'll recall Hilbert's Third Problem and see a simple proof that the converse is not true. We will explore a scissors congruence proof of Heron's Formula. Finally, if we have time, we will define scissors congruence in terms of the group of isometries and explore this notion in a group theoretic context. 
Thursday, September 25, 2014 This talk is part of the Student Symposium Series, organized and conducted by the graduate students.  David Benko, University of South Alabama 
Fractalicious Dogs and Potential Theory
Abstract: We give a brief introduction to potential theory. Then we explain how to use balayage to get beautiful fractalicious images such as dogs. 
Thursday, September 18, 2014 This talk is part of the Student Symposium Series, organized and conducted by the graduate students.  Scott Carter, University of South Alabama 
Sierpinski Figures in All Dimensions, The Chaos Game, and Multinomial Coefficients
Abstract: It is wellknown among mathematicians that the result of the Chaos Game on 3 equidistant vertices yields a figure that approximates the Sierpinski triangle. It is also known that the binomial coefficients when read modulo 2 resemble this figure. In this talk, I want to show you some interesting ndimensional generalizations of these phenomena. 
Thursday, September 11, 2014 This talk is part of the Student Symposium Series, organized and conducted by the graduate students.  Cornelius Pillen, University of South Alabama 
Plutarch’s Box, O’Halloran Numbers, and the Riemann Hypothesis
Abstract: During our last summer camp some Mobile County six graders were given a rectangular prism of size 5 by 2 by 2. They were asked to calculate its surface area and then find another rectangular prism with integer dimensions and identical surface area. While daydreaming in the back of the class I started thinking about these rectangular “integer prisms”. Are there any such prisms whose surface area equals their volume? Can every (large) even number be realized as the surface area of some rectangular prism with integer dimension? The answer to these questions leads to some heavyduty mathematics. Even the Riemann Hypothesis appears. 
Thursday, September 4, 2014 This talk is part of the Student Symposium Series, organized and conducted by the graduate students.  Dan Silver, University of South Alabama 
Dimer Coverings
Abstract: A dimer covering (also called a perfect matching) of a graph is a collection of edges that covers each vertex exactly once. The term “dimer” comes from chemistry: a dimer is a polymer with only two atoms. If we think of vertices as univalent atoms, then dimer coverings provide simple models for studying certain phase transitions. We explain how dimer coverings arise in both topology and algebraic dynamical systems. 
Department of Mathematics and Statistics 
