Department of Mathematics
Central Michigan University
Colloquia - Spring 2014

The following list is updated regularly.

Speaker: Dr. Kyu-Hwan Lee (University of Connecticut) February 6, 2014
Title: Infinite Dimensional Lie Algebras and Modular Forms
Abstract: In this talk, we will observe how modular forms naturally arise from the theory of infinite dimensional Lie algebras. In particular, we will consider affine and rank 2 hyperbolic Kac--Moody algebras and see their relationship to Jacobi modular forms and Hilbert modular forms, respectively.
Speaker: Dr. Brian Lukoff (Program Director, Learning Catalytics, Pearson Education, Boston, MA) February 7, 2014
Title: Using Learning Catalytics to Create an Interactive Classroom
Abstract: Peer instruction and other interactive teaching methods have been shown to dramatically improve conceptual understanding. While no technology is necessary to take advantage of these teaching methods, technology can enable the instructor to better understand student understanding, differentiate instruction, and facilitate more productive student discussions in the classroom. This workshop will introduce Learning Catalytics, a cloud-based platform for interactive teaching that allows students to use web-enabled devices—laptops, smartphones, and tablets—to engage in rich, authentic tasks in class and allows instructors to go beyond clickers and other response systems to create an interactive environment that integrates assessment with learning.

This presentation is sponsored by Pearson Education.

*** Time and Location: 10:00 a.m. - 11:00 a.m., Pearce Hall, Room 123A ***

*** Refreshments: 9:30 a.m. - 10:00 p.m., Pearce Hall, Room 216 ***

Speaker: Professor Hugh Montgomery (University of Michigan) March 6, 2014
Title: Primes, Zeros, and Random Matrix Theory
Abstract: In 1859, Riemann showed that the distribution of prime numbers depends on the location of the zeros of the Riemann zeta function. Hilbert and Pólya independently speculated that the Riemann Hypothesis (RH) is true because the zeros are related to some (still undiscovered) Hermitian operator. For forty years we have had some limited evidence that the zeros are spectral. Today, Random Matrix Theory is a valuable tool that enables us to generate deep conjectures concerning the zeta function.
Speaker: Dr. Benjamin Linowitz (University of Michigan) March 25, 2014
Title: Isospectral Surfaces of Small Volume
Abstract: In 1980 Vigneras used orders in quaternion algebras to exhibit pairs of hyperbolic 2-manifolds which were isospectral but not isometric, thereby proving that one cannot hear the shape of a 'hyperbolic drum'. The example which appeared in Vigneras' paper turned out to be incorrect for a technical reason, and was subsequently corrected in her book on quaternion orders. The corrected manifolds turn out to have enormous genus: 100801. In this talk we will exhibit substantially simpler examples; for instance, a pair of isospectral hyperbolic 2-orbifolds whose underlying surfaces have genus 0. These examples are further distinguished in that they have minimal volume amongst those arising from maximal arithmetic Fuchsian groups and cannot be obtained via Sunada's method. This is joint work with John Voight.
Speaker: Tim Rey (Director, Advanced Analytics, Steelcase, Inc., Grand Rapids, MI) April 3, 2014
Title: The Curse of Dimensionality in a Real Life Industrial Problem
Abstract: Industrial data mining (supervised learning) problems generally involve wrestling with the “curse of dimensionality”. Data collected in an industrial transaction environment is rarely if ever intended to be used in a modeling problem, let alone in a “cause and effect” modeling problem. Thus the contradiction between cause and effect (ala the use of the scientific method and proper design of experiments) and “prediction” is before us. This curse of dimensionality seems to prevent analytics professionals from finding true cause and effect. Data sets not intended for modeling generally have significant multicollinearity, lack of balance and often are too wide (p being inappropriate for n). Approaches for solving these issues can be broken down in three classes; dimension reduction, parameter adjustment and data structure adjustment. This talk will show an industrial data mining problem where the curse is present in all its glory. Each of the three basic methods for supposed “solutions” to the problem will be presented using modern day technologies.
Speaker: Dr. Rachelle DeCoste (Wheaton College) April 4, 2014
Title: Geometric Properties of 2-Step Nilpotent Lie Groups
Abstract: 2-step nilpotent Lie groups with a left invariant metric are objects that admit both positive and negative sectional and Ricci curvatures. The geometry of such an object reflects strongly the algebraic structure of the associated Lie algebra. We will discuss various geometric properties of Lie groups such as the presence of closed geodesics. We will also define some classes of 2-step nilpotent Lie groups, namely Heisenberg type and Heisenberg-like, and give examples of each. Finally, new and ongoing research into the properties of 2-step nilpotent Lie groups associated to simple graphs will be introduced.

*** Time and Location: 1:00 p.m. - 2:00 p.m., Pearce Hall, Room 227 ***

*** Refreshments: 2:00 p.m. - 2:30 p.m., Pearce Hall, Room 216 ***

Speaker: Professor Aaron Yip (Purdue University) April 10, 2014
Title: Examples of Singular Perturbations in Variational Problems
Abstract: We will discuss the idea of Gamma convergence which is used to identify limiting description of singularly perturbed problems in variational settings. The prototype is the Allen-Cahn Functional which is used in the modeling of phase transitions and phase boundary motions. It can also be connected to minimal surfaces and motion by mean curvature. Examples will be given to demonstrate the versatility of this framework. On the other hand, I will also give some examples that might not be easily handled by this approach.
Speaker: Dr. Mark Johnson (University of Arkansas) April 15, 2014
Title: Symbolic Powers of Ideals: Containments and Conjectures
Abstract: The symbolic power of an ideal, in a commutative noetherian ring, is the "pure" part of the ordinary power of the ideal - in the sense of the Lasker-Noether primary decomposition. Symbolic powers occur frequently in commutative algebra and algebraic geometry and there are many open problems about them, roughly concerning their growth - how much larger they are compared to the ordinary power. In this talk, we will give a survey of recent progress on a number of these problems regarding them.
Speaker: Dr. Rabeya Basu (Indian Institute of Science Education and Research, Pune) April 29, 2014
Title: On Applications of Suslin's Local Global Principle
Abstract: In 1975 Daniel Quillen and Andrei Suslin independently proved the problem posed by J-P. Serre in 1955 on finitely generated projective modules, which asks whether finitely generated projective modules over a polynomial ring over a field are free. In this talk we shall concentrate on A. Suslin's local-global principle which is one of the main ingredient for Suslin's proof of Serre's conjecture. We shall discuss various applications of this theorem in the field of classical K-theory.

Colloquia - Fall 2013
Speaker: Professor Alan Freed (Saginaw Valley State University) September 12, 2013
Title: Mechanics of Soft Tissues: Reflecting On Roads Traveled and The Road Just Taken
Abstract: About three-quarters of a century ago saw the emergence of a finite strain theory suitable for modeling natural rubber, which was critical to the war effort. This theory was derived from thermodynamics and has a solid foundation in statistical mechanics. With an application of invariant theory in the 1950's, the explicit theory for rubber elasticity became complete. In the decades that have ensued, rubber elasticity (hyperelasticity) has been applied to a broad selection of materials - some successfully, some not. Of particular interest for this talk are the soft solids of biologic origin. The presentation will reexamine the road well traveled in our attempts to secure a mathematical description for these materials, and it will show that a new fork in the road is worth exploring and developing. In 2003, Prof. K. Rajagopal from Texas A&M introduced an idea that the thermodynamic structure of an elastic material might be implicit in its dependence upon state. This simple notion is causing a profound revolution in our thinking of what an elastic solid is or can be - a revolution that is, unfortunately, slowed by the inertia of bias. Much of this presentation will present what such a theory is capable of predicting. Implicit elasticity today is where explicit elasticity was in the 1950's. There are great opportunities that lie ahead in the continued development of this theory, and in the construction of tools that can apply this technology for use in engineering applications.
Speaker: Professor Shihshu Walter Wei (University of Oklahoma) September 19, 2013
Title: Some Simple Ideas and Methods in Mathematics and their Recent Developments
Abstract: In this talk we'll discuss several elegant ideas and simple methods in mathematics that have made strong impacts on the study of algebra, analysis, geometry, topology, differential equations, mathematical physics, applied mathematics and their interconnectedness.

We'll begin with a very simple idea in middle school algebra, or a philosophy of Lao-Zi, then we'll quickly move to some ideas in calculus and in classical geometry. Along these frame works, we'll explore their roles in real and complex geometry, several complex variables, algebraic topology, calculus of variations, optimization problems, Gauge theory, Lie group representation theory and transcendental algebraic geometry.

Some related problems, further applications, and recent developments, especially in p-harmonic geometry will also be addressed. It is our effort to make the talk comprehensible to graduate students of any fields.

Speaker: Professor Richard J. Fleming (Central Michigan University) October 3, 2013
Title: On a Measure of the Distance to 1(2)
Abstract: For a Banach space X, let λ0(X) denote the infimum of the Banach-Mazur distances between the two-dimensional subspaces of X and the two-dimensional L1-space 1(2). The condition that λ0(X) > 1 has been used to establish certain isomorphic Banach-Stone theorems. We investigate some elementary properties of λ0(X) and consider conditions on X that imply that λ0(X) > 1 or λ0(X) > 1.
Speaker: Professor Mei-Ling Ting Lee (University of Maryland) October 15, 2013
Title: Boundary Crossing Based Threshold Regression Models for Lifetime Data
Abstract: Cox regression methods are well-known. It has, however, a strong proportional hazards assumption. In many medical contexts, a disease progresses until a failure event (such as death) is triggered when the health level first reaches a failure threshold. I’ll present a model for the health process that requires few assumptions and, hence, is quite general in its potential application. Distribution-free methods for estimation and prediction are developed. Computational aspects of the approach are straightforward. Case examples are presented that demonstrate the methodology and its practical use. The methodology provides medical researchers and biostatisticians with new and robust statistical tools for estimating treatment effects and assessing a survivor’s remaining life.

This is a joint work with G.A. Whitmore of McGill University.

*** Time: 3:30 p.m. - 4:30 p.m. ***

*** Refreshments: 3:00 p.m. - 3:30 p.m. ***

Speaker: Dr. Keri Kornelson (University of Oklahoma) November 7, 2013
Title: Fourier Bases on Fractals
Abstract: In this talk, we use an iterated function system (IFS) approach to describe the Bernoulli convolution measures. These measures are supported on Cantor sets which are subsets of the real line, and have a variety of interesting properties. In particular, one can find examples in which there exist Fourier bases for the associated L2 Hilbert space. We describe some of these bases, and the associated operators that arise from them. One interesting such operator exhibits its own fractal-like self-similarity.
Speaker: Dr. Kun Zhao (Tulane University) November 14, 2013
Title: A System of Hyperbolic Balance Laws Arising from Chemotaxis
Abstract: In contrast to diffusion (random diffusion without orientation), chemotaxis is the biased movement of cells/particles toward the region that contains higher concentration of beneficial or lower concentration of unfavorable chemicals. The former often refers to the attractive chemotaxis and latter to the repulsive chemotaxis. Chemotaxis has been advocated as a leading mechanism to account for the morphogenesis and self-organization of a variety of biological coherent structures such as aggregates, fruiting bodies, clusters, spirals, spots, rings, labyrinthine patterns and stripes, which have been observed in experiments.

In this talk, I will present recent results on the rigorous analysis of a partial differential equation model arising from repulsive chemotaxis, which is a system of hyperbolic balance laws consisting of nonlinear and coupled parabolic and hyperbolic type PDEs. In particular, global wellposedness, large-time asymptotic behavior of classical solutions to such model are obtained which indicate that chemorepulsion problem with non-diffusible chemical signal and logarithmic chemotactic sensitivity exhibits strong tendency against pattern formation. The results are consistent with general results for classical repulsive chemotaxis models.

Speaker: Dr. Philip Lombardo (Saint Joseph's College of New York) November 22, 2013
Title: From Modular Forms to Crystal Bases
Abstract: Riemann's 1859 paper introducing his zeta function as a means of proving the prime number theorem marked the beginning of a beautiful interaction between complex analysis and number theory. As the study of L-functions and modular forms progressed into a more general theory of automorphic forms, representation theory soon became an important part of the story. The Casselman-Shalika formula is one example of the strong connection between automorphic forms and representation theory. In this talk, I will highlight some important ideas in the development of the theory of automorphic forms while providing context for a more recent result connecting the Casselman-Shalika formula to the combinatorics of crystal bases.

*** Time: 2:00 p.m. - 3:00 p.m. ***

*** Refreshments: 1:30 p.m. - 2:00 p.m. ***

Speaker: Dr. Matías Salibián-Barrera (University of British Columbia) December 3, 2013
Title: S-estimators for Functional Principal Component Analysis
Abstract: Principal components analysis is a widely used technique that provides an optimal lower-dimensional approximation to multivariate observations. In the functional case, a new and simple characterization of elliptical distributions on separable Hilbert spaces allows us to obtain an equivalent stochastic optimality property for the principal component subspaces associated with elliptically distributed random elements. This property holds even when second moments do not exist.

These lower-dimensional approximations can be very useful in identifying potential outliers among high-dimensional or functional observations. In this talk we propose a new class of robust estimators for principal components. For a fixed dimension q, we robustly estimate the q-dimensional linear space that best fits the data, in the sense of minimizing the sum of coordinate-wise robust residual scale estimators. The extension to the infinite-dimensional case is also studied. In analogy to the linear regression case, we call this proposal S-estimators. Our method is consistent for elliptical random vectors, and is Fisher-consistent for elliptically distributed random elements on arbitrary Hilbert spaces. Numerical experiments show that our proposal is highly competitive when compared with other existing methods when the data are generated both by finite- or infinite-rank stochastic processes. We also illustrate our approach using two real functional data sets, where the robust estimator is able to discover atypical observations in the data that would have been missed otherwise.

This talk is the result of recent collaborations with Graciela Boente and David Tyler.

Speaker: Professor Marcus Jobe (Miami University) December 5, 2013
Title: Elementary Statistical Methods and Measurement Error
Abstract: How the sources of physical variation interact with a data collection plan determines what can be learned from the resulting dataset, and in particular, how measurement error is reflected in the dataset. The implications of this fact are rarely given much attention in most statistics courses. Even the most elementary statistical methods have their practical effectiveness limited by measurement variation; and understanding how measurement variation interacts with data collection and the methods is helpful in quantifying the nature of measurement error. We illustrate how simple one- and two-sample statistical methods can be effectively used in introducing important concepts of metrology and the implications of those concepts when drawing conclusions from data.

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