2013-14 Colloquia talks


Date Speaker Talk
Wednesday, May 14, 2014 Albert J. Todd, University of California, Riverside Vector Cross Products and G2-Geometry

Abstract: In this talk, I will focus primarily on giving the motivation for my work in G2- and multisymplectic geometry. I will begin with a brief introduction to general vector cross products and their relation to various geometries of current interest. I will then focus on specifically G2-geometry, a 7-dimensional geometry based on 2-fold vector cross products, wherein I will also give a brief introduction to differential forms. Finally, we will put the pieces together, and I will discuss how all of this ties in to my research. Throughout, I will give glimpses of applications to various areas of physics.

Thursday, May 8, 2014 David Mullens, University of South Alabama An Opportunity to study Na+ Signaling

Abstract: Action potentials are short-lasting events in which the electrical membrane potential of a cell rapidly rises and falls. Ca2+ signaling through ion channels is well understood at the plasma membrane, i.e, movement of Ca2+ ions from the extracellular space through Ca2+ channels to the intracellular space (cytosol). Ca2+ channels are also present on membranes of intracellular organelles such as the mitochondria and the ER. The channels control the flux of Ca2+ from intracellular stores to the cytosol. Cytosolic Ca2+ levels in turn regulate hundreds of cellular functions. While we know a great deal about Ca2+ regulated signaling pathways, we know much less about how other cations regulate cellular function(s). Recently Ning Xu et al. provided data indicating that intracellular Na+ may be modulated in a similar fashion to Ca2+. However, little is know about the regulation of intracellular Na+. Using well described ODEs, such as the Hodgkin Huxley and Nernst equations, we have explored how to model action potentials and how the release from intracellular stores may alter Na+ levels in the cytosol. Simulation results indicate that there is much we do not understand about the role(s) intracellular stores play in regulating cytosolic Na+.

Thursday, April 24, 2014 Oliver Dasbach, Louisiana State University Knots, and q-Series Identities from Number Theory

Abstract: The colored Jones polynomial is one of the more fascinating objects in knot theory. We will show how to rediscover some well-known and less known q-Series Identities such as the (second) Rogers-Ramanujan identity from studying the colored Jones polynomial.

Thursday, April 17, 2014 Nemanja Kosovalić, York University, Canada Age Structured Population Dynamics, Age of Maturity, and State Dependent Delay

Abstract: Consider a population of individuals occupying some habitat, which is structured by age. Suppose that there are two distinct life stages, the immature stage and the mature stage. Suppose that the mature and immature population are not competing in the sense that they are consuming different resources, e.g. think of frogs and tadpoles. A natural question is "What determines the age of maturity?". In many biological contexts, the age of maturity is not merely constant but is more accurately determined by whether or not the quantity of food consumed by the immature population, reaches a prescribed threshold. In this talk we discuss some past work related to this idea, and new research directions it has inspired.

Tuesday, April 8, 2014 Mary Clair Thompson, Lafayette College Decompositions and Asymptotic Results in Semisimple Lie Groups

Abstract: Kostant's seminal paper "On Convexity, the Weyl Group, and the Iwasawa Decomposition" provides an elegant generalization of many results in matrix theory to the setting of a real semisimple Lie group. For example, there is a sense in which matrix spectra correspond to convex hulls of Weyl group orbits of elements of the semisimple group G, leading to a generalization of the Horn-Thompson theorem to the Lie group context.

Our research follows the spirit of Kostant's work. In this talk, we examine generalizations of well-known matrix results to the Lie group setting. In particular, we discuss two converging matrix sequences, the iterated Aluthge sequence and the iterated LR sequence, and examine the context in which these results may be generalized to the elements of a Lie group. We also discuss ongoing research on the inverse-adjoint decomposition and equivalent conditions. As in Kostant's work, we see that the available group decompositions play an important role in controlling group behavior, once again confirming that many well-known matrix behaviors are not so much due to the concrete matrix structure, but rather to the much deeper Lie group structure.

Thursday, April 3, 2014 Moshe Adrian, University of Utah The Local Converse Problem for GL(n,F)

Abstract: Let F be a non-archimdean local field of characteristic zero. The local converse problem, an important problem in the Langlands program, asks to what extent the "twisted gamma factors" determine a representation of GL(n,F). Jacquet has formulated a conjecture on precisely which family of twisted gamma factors can uniquely determine a representation of GL(n,F). I will first give an overview of the Langlands program, and then report on recent progress on Jacquet's conjecture, which is joint work with Baiying Liu, Shaun Stevens, and Peng Xu.

Tuesday, April 1, 2014 Jesse Ratzkin, University of Cape Town, South Africa Geometry vs. PDE

Abstract: I will discuss several problems at the intersection of geometry and partial differential equations (PDEs), all of which arise from optimization problems. One can associate many measurements to a bounded domain D in n-dimensional Euclidean space, such as volume, perimeter, diameter, inradius, principle frequency, and torsional rigidity (which is also the maximum of the expected first exit time of a Brownian particle). An isoperimetric inequality, in the sense of Polya and Szego, seeks to extremize one measurement while holding another fixed. For instance, the classical isoperimetric inequality seeks to minimize perimeter while fixing volume, the Faber-Krahn inequality seeks to minimize the principle frequency while fixing volume (of all drumheads with an equal area, the round drum has the lowest base note). I will discuss several similar domain optimization problems associated to a nonlinear, second order PDE, which arises from extremal Sobolev functions and interpolates nicely between torsional rigidity and principle frequency.

Time allowing, I will also discuss a problem arising from conformal geometry on the sphere, which is associated to a fourth order PDE, as well as some interesting open questions.

Part of this is joint work with Tom Carroll, of the University of Cork in Ireland.

Thursday, March 20, 2014 Ajit C. Tamhane, Northwestern University A Class of Improved Hybrid Hochberg-Hommel Type Step-Up Multiple Test Procedures

Abstract: We derive a new p-value based procedure which improves upon the Hommel procedure by gaining power as well as having a simpler step-up structure similar to the Hochberg procedure. The key to this improvement is that the Hommel procedure is nonconsonant and can be improved by a consonant procedure. Exact critical constants of this new procedure can be numerically determined and tabled. The 0th order approximations to the exact critical constants, albeit slightly conservative, are simple to use and need no tabling, and hence are recommended in practice. An analytical proof is given to show that the proposed procedure controls the familywise error rate under independence among the p-values. Simulations are performed to empirically exhibit familywise error rate control under both positive and negative dependence. Power superiority of the proposed procedure over competing procedures is also empirically exhibited via simulations. Illustrative examples are given.

Wednesday, March 19, 2014
This talk is aimed at a general audience.
Ajit C. Tamhane, Northwestern University
First Satya Mishra Memorial Lecture
False Findings in Scientific Research

Abstract: A scientific experiment typically addresses many research questions and therefore involves testing multiple hypotheses. The incidence of false positives can become very high if proper adjustment is not made for multiplicity of tests. Some researchers selectively report only positive findings from their experiments. This selective inference problem is also a multiplicity problem in another disguise. In this talk I will present examples of multiple testing from various published studies. Next I will discuss some simple statistical methods for multiplicity adjustment. Finally, I will conclude with some remarks about the need for reproducible and replicable experiments to confirm research findings.

Thursday, March 13, 2014
This talk is aimed in particular at undergraduate and graduate students.
Xin-Min Zhang, University of South Alabama The Calculus and Dynamic Geometry of Pedal Triangles

Abstract: In this presentation, we shall examine some interesting properties of pedal triangles. A few of these properties are well-known in classical geometry, but many are observed and proved only in recent years. In particular, we pay attention to the sequences of pedal triangles, the fractals generated by pedal triangles, some extreme properties associated with pedal triangles and its relationship with the parental triangle. Basic multi-variable calculus can be applied nicely to the study of dynamical systems in classical geometry. Anyone with some knowledge in high school geometry and calculus should be able to appreciate the special role played by pedal triangles.

Thursday, February 27, 2014
This talk is aimed in particular at undergraduate and graduate students.
Jörg Feldvoss, University of South Alabama Why Space is 3-Dimensional or the Scarcity of Vector Products and Division Algebras

Abstract: The cross product of vectors in Euclidean 3-space can be introduced in undergraduate linear algebra courses. One might wonder why contrary to the dot product, which is available for any finite-dimensional real vector space, the cross product is only defined for 3-space. In my talk I will discuss the existence of cross products of vectors in Euclidean n-space for arbitrary n. It turns out that this is only the case if n = 0, 1, 3, 7.

This result is equivalent to a theorem of Hurwitz on the existence of real composition algebras (1898) and to a theorem of Zorn on the structure of finite-dimensional alternative division algebras over the real numbers (1932). Both kinds of algebras only exist in dimensions 1, 2, 4, or 8 (and are realized by the real numbers, the complex numbers, Hamilton's quaternions, and Cayley's octonions, respectively). All proofs are very elementary and can be done in a purely algebraic manner.

If time permits, I will also discuss a theorem of Hopf on the existence of finite-dimensional commutative division algebras over the real numbers (1940), for which no (elementary) purely algebraic proof is known. The goal of my talk is to present a lot of interesting mathematics from different areas (algebra, number theory, and topology) and the intimate relation between them.

Thursday, February 20, 2014 Yichuan Zhao, Georgia State University Smoothed Jackknife Empirical Likelihood Inference for ROC Curves with Missing Data

Abstract: In this paper, we apply smoothed jackknife empirical likelihood (JEL) method to construct confidence intervals for the receiver operating characteristic (ROC) curve with missing data. After using hot deck imputation, we generate pseudo-jackknife sample to develop jackknife empirical likelihood. Comparing to traditional empirical likelihood method, the smoothed JEL has a great advantage in saving computational cost. Under mild conditions, the smoothed jackknife empirical likelihood ratio converges to a scaled chi-square distribution. Furthermore, simulation studies in terms of coverage probability and average length of confidence intervals demonstrate this proposed method has the good performance in small sample sizes. A real data set is used to illustrate our proposed JEL method. This is joint work with Dr. Hanfang Yang.

Tuesday, February 18, 2014
This talk is aimed at a general audience.
Ming-Wen An, Vassar College & University of South Alabama Predicting Survival from Tumor-Measurement Based Endpoints in Phase II Cancer Clinical Trials

Abstract: In the final stages of a long and costly drug discovery process, a drug compound is introduced into humans through different phases of clinical trials. In oncology, as many as 60% of drug compounds that reach the last phase (Phase III) fail to show an improvement in survival. One possible reason for this high failure rate could be inappropriate evaluation of compounds in preceding Phase II trials, in which the primary endpoint is often binary tumor response measured by the Response Evaluation Criteria for Solid Tumors (RECIST). Extensive efforts have been ongoing to identify alternative tumor measurement (TM)-based endpoints, with the goal of improved prediction of overall survival (OS). We evaluate alternative categorical and continuous TM-based endpoints for their ability to predict OS using the RECIST 1.1 data warehouse (13 breast, lung, and colon cancer trials). We fit Cox models, using a landmark analysis to allow for early endpoint evaluation, and measure predictive ability via the c-index, Hosmer-Lemeshow goodness of fit statistic, positive/negative predictive value and prediction error. Absolute and relative change in TMs demonstrate potential, but not convincing, improvements in predicting OS compared to RECIST tumor response.

The talk should be accessible to a general audience. I will begin with a brief background to the problem, then describe our methods and results, and conclude with discussion and and open statistical questions.

This is joint work with Sumithra Mandrekar, Dan Sargent, Jeff Meyers, Axel Grothey, Xinxin Dong, Yu Han and Jan Bogaerts.

Thursday, February 6, 2014
This talk is aimed in particular at undergraduate and graduate students.
David Benko, University of South Alabama The Basel Problem

Abstract: The Basel problem, to find 1 + 1/4 + 1/9 + 1/16 + ... was open for a long period of time during the 17-18th century. Euler was the first one to give a beautiful although incomplete solution. We will discuss the problem and related questions.

Tuesday, November 19, 2013 David Auckly, Kansas State University Stable Equivalence of Surfaces in 4-Manifolds

Abstract: It is well known that there are homeomorphic 4-manifolds that are not smoothly equivalent, which become smoothly equivalent after taking the connected sum with one copy of a special manifold. Similar behavior may be found in other geometric settings, including diffeomorphisms up to isotopy, positive scalar curvature and knotted surfaces. In this talk we will prove that there is an infinite family of spheres in a connected sum of complex projective spaces with assorted orientations, so that no two spheres in the family are smoothly equivalent, yet every pair is topologically isotopic. Furthermore we will show that the spheres become smoothly isotopic after one stabilization. We will do so with an explicit description of the spheres and the isotopies. This is joint work with Danny Ruberman, Paul Melvin, and Hee Jung Kim.

Thursday, November 14, 2013
This talk is aimed in particular at undergraduate and graduate students.
Michael Francis, University of South Alabama Mathematical Modeling of Endothelial Calcium Dynamics

Abstract: Ca2+ is an important regulator of various physiological functions, including modulation of vascular tone via the endothelium, a thin cell layer which lines the interior of blood vessels. Endothelium-mediated blood vessel relaxation is essential for maintenance of blood flow, where stimulation of Ca2+-dependent effectors produces robust dilatory responses. In endothelial cells, the Ca2+ permeable inositol 1,4,5-trisphosphate receptor (IP3R) is a major regulator of Ca2+ activity. Recent evidence suggests that IP3R-dependent Ca2+ activity leads to continuous attenuation of vascular tone in pig coronary arteries. This effect is amplified by stimulated production of inositol 1,4,5-trisphosphate (IP3), a phospholipid metabolite which increases IP3R activation. Fluorescent Ca2+ measurements using microscopy have revealed spatially and temporally complex IP3R-dependent Ca2+ signals, but critical aspects of their regulation by IP3 remain unresolved because real-time measurements of IP3 dynamics are not currently possible. However, mathematical modeling may be employed as a valuable tool in determining the impact of IP3R regulation on endothelial Ca2+ activity. Using a combination of fluorescence microscopy, novel calcium signal analysis techniques, and mathematical modeling, we tested the hypothesis that IP3 gradients and IP3R distribution determines the magnitude, speed, and duration of Ca2+ wave propagation in pig coronary endothelial cells.

Thursday, November 7, 2013
This talk is aimed in particular at undergraduate and graduate students.
Abey López-García, University of South Alabama An Introduction to Totally Positive Matrices

Abstract: A totally positive matrix is a matrix all of whose minors are strictly positive. This class of matrices is of great importance in mathematics, from a theoretical and a practical point of view. In this talk I will explain some of the basic properties of these matrices, especially those concerning their eigenvalues. In particular, I will discuss the Gantmacher-Krein theorem, which states that the eigenvalues of a totally positive matrix are all positive and simple. Along the way, I will also discuss the Perron-Frobenius theorem on strictly positive matrices.

Tuesday, November 5, 2013 Dimitar Grantcharov, University of Texas at Arlington Weight Representations of Lie Algebras

Abstract: Following works of G. Benkart, D. Britten, S. Fernando, V. Futorny, A. Joseph, F. Lemire, and others, in 2000 O. Mathieu achieved a major breakthrough in representation theory by classifying the simple weight representations of finite dimensional reductive Lie algebras. The next step in the study of weight representations is to look at the indecomposable representations. In this talk we will discuss some recent results related to the structure of the indecomposable weight representations and connections with algebraic geometry. This is a joint work with Vera Serganova.

Thursday, October 31, 2013 Chris Drupieski, DePaul University Polynomial Functors and Cohomology

Abstract: Strict polynomial functors were defined by Friedlander and Suslin in 1997 in order to investigate cohomology for the general linear group, and ultimately to prove that the cohomology ring of a finite group scheme (equivalently, a finite-dimensional cocommutative Hopf algebra) is a finitely generated algebra. In this talk I'll give an overview of what a (strict) polynomial functor is, and how these objects are connected to the cohomology of the general linear group. Toward the end of the talk, I will describe some questions I am currently investigating in a "super" analogue of the above setup. The speaker will endeavor to make this talk accessible to open-minded non-algebraists (and graduate students).

Thursday, October 24, 2013
This talk is aimed in particular at undergraduate and graduate students.
Xin-Min Zhang, University of South Alabama From the Napoleon Theorem to the PDN Theorem: Some Authorship Disputes in Mathematics

Abstract: It is not uncommon in mathematical research that different people prove the same theorem independently around the same period of time. It is also not unheard of for a mathematical result to be discovered, forgotten, and then rediscovered in the history of mathematics. Therefore, the attribution of a mathematical theorem to the appropriate author(s) often caused dispute or controversy, sometimes even involving unpleasant personal attacks. In this presentation, we shall take a closer look at the Napoleon theorem in classical geometry and its generalizations in modern mathematics. In addition to some interesting geometric, algebraic, and analytic results related to the Napoleon theorem and its generalizations, we will also review some mathematicians' personal experience as they challenged themselves with ambitious problems.

Thursday, October 17, 2013
This talk is aimed in particular at undergraduate and graduate students.
Thomas Weigel, Università degli Studi di Milano-Bicocca, Italy The Spectrum of a Finite Cayley Graph

Abstract: For a finite graph Λ its spectrum is defined to be the set of eigenvalues of the adjacency matrix AΛ counted with their multiplicities. In particular, it is possible to compute the spectrum for any explicitly given finite graph, but the isomorphism type of a graph is not determined by its spectrum.

In the talk it will be shown that for the Cayley graph Γ(G,S) of a finite group G with finite generating set S the representation theory of the group G yields a decomposition of the spectrum of Γ(G,S) in pieces which are related to the irreducible complex characters of G. This phenomenon has interesting applications in group theory and combinatorics.

Thursday, October 10, 2013
This talk is aimed in particular at undergraduate and graduate students.
Cornelius Pillen, University of South Alabama Integer Matrices of Finite Order

Abstract: We say a square matrix has finite order if there exists a positive integer m such that the matrix raised to the mth power is the identity matrix. A few weeks ago some of our most talented graduate students were experiencing sleepless nights trying to find integer matrices of finite order. Fortunately, someone in this picture will help us to avoid such nightmares in the future.

Thursday, October 3, 2013
This talk is aimed in particular at undergraduate and graduate students.
David Mullens, University of South Alabama What is the Fundamental Group?

Abstract: We will begin be defining when two paths α and β are homotopic. Next, we will define the multiplication of paths, and the multiplication of equivalence classes. Namely, the equivalence classes of loops based at a fixed point, x0, of an arbitrary surface X. The description of the fundamental group of the circle, S1, will be given. Also, it will be shown that the fundamental group is indeed a group. If there is time, we will define covering spaces, by illustration, using the circle and torus. Lastly, we will ambitiously try to explore the relationship between covering spaces and the fundamental group. This talk is aimed at undergraduates and graduates who have not had a course in Algebraic Topology.

Thursday, September 26, 2013 Dan Silver, University of South Alabama Knots in the Nursery: "(Cats) Cradle Song" of James Clerk Maxwell

Abstract: PETER the Repeater
Platted round a platter
Slips of slivered paper,
Basting them with batter.

So begins "(Cats) Cradle Song," verse composed by James Clerk Maxwell, probably in 1877. It was Maxwell's response to the manuscript of "On Knots," written by his friend Peter Guthrie Tait, who had hoped for constructive criticism.

Maxwell wrote poems to amuse his friends and express personal sentiments. The purpose of "(Cats) Cradle Song" was to have a bit of good-natured fun at Tait's expense. Between its references to nursery rhymes, we discover mathematical ideas that were novel at the time. Some of the ideas would endure and inspire every succeeding generation.

Thursday, September 19, 2013
This talk is aimed in particular at undergraduate and graduate students.
David Benko, University of South Alabama Dividing the Indivisible

Abstract: The idea of atoms dates back to ancient India (6th century BC) and Greece (5th century BC). Democritus coined the term atomos, meaning indivisible. We now know that atoms are divisible: physicists find smaller and smaller particles. In Mathematics points are indivisible. We will challenge this and define a new world where points are divisible and functions like signum(x) are continuous ... Please attend the talk only if you can sing "What a Wonderful World".

Thursday, September 12, 2013
This talk is aimed in particular at undergraduate and graduate students.
Scott Carter, University of South Alabama Models of the Projective Plane

Abstract: In this talk, I will describe several embeddings or immersions of the projective plane in 4-dimensional space. The descriptions will follow from movie parameterizations and their associated charts. A movie is a sequence of 3-dimensional cross-sections of the surface while a chart is a transverse projection onto the plane of the blackboard. By including depth considerations in the chart, we can give full descriptions of the surface. In this way, a detailed understanding can be achieved.

Thursday, September 5, 2013
This talk is aimed in particular at undergraduate and graduate students.
Susan Williams, University of South Alabama Who's D.H. Lehmer and what's his Problem, anyhow?

Abstract: Lehmer's interest in large primes inspired him to construct a mechanical computer out of bicycle chains in 1928, when he was 23. It also led him to pose a deceptively simple question about polynomials with integer coefficients. Eighty years later, Lehmer's problem remains unsolved. It has turned out to have repercussions in graph theory, group theory, dynamics and topology.

Thursday, August 29, 2013
This talk is aimed in particular at undergraduate and graduate students.
Sera Kim, University of South Alabama Virtual Knot Theory

Abstract: Virtual knot theory is introduced by L. H. Kauffman as a generalization of classical knot theory in the sense that if two classical link diagrams are equivalent as virtual links, then they are equivalent as classical links. I will talk about the history of the virtual links and introduce some invariants for classifying them.

For colloquium talks from other years click here