Department of Mathematics
Central Michigan University
Graduate Student Seminar - Spring 2014

The following list is updated regularly.

Speaker: Tibor Marcinek & Christine Phelps (Central Michigan University) February 4, 2014
Title: Mathematics Education Area Spotlight
Abstract: In this seminar we will have the following two 20-minute presentations.

Speaker: Tibor Marcinek

Title: Designing and Studying Interpretation Tasks in Mathematics Content Courses for Elementary Teachers

Abstract: Mathematics content courses for teachers are often specifically designed to go beyond common knowledge of mathematics and expose students to the multifaceted nature of mathematics for teaching. In the presentation, we will explain how one such facet is studied in our mathematics courses for elementary teachers. We will describe activities that facilitate students’ involvement in interpreting and responding to the mathematical ideas and thinking of others (their peers) and how such activities are studied and evaluated. This presentation will also bring up the importance of practitioner knowledge in mathematics education and a fuzzy borderline that separates it from the research knowledge.

Speaker: Christine Phelps

Title: Using a Discussion Board to Support Prospective Teachers in Analyzing a Lesson

Abstract: I present the results on an online discussion board intervention designed to help prospective teachers (PTs) learn to systematically analyze student thinking and mathematics teaching. Findings suggest that the intervention helped PTs to look past surface features of the lesson and focus on students' mathematical thinking, although gaps remained in their analysis skills. Results of this work can help improve teacher education.

Speaker: Cleland Loszewski (Central Michigan University) February 11, 2014
Title: The Symplectic Volume of the Ribbon Graph Complex $\overline{\mathrm{RG}}_{g,n}^{(1,0,0,\ldots)}$
Abstract: In a result dating back to the 1980's, Penner, Mumford, Thurston, and Harer showed that, through the Strebel differential, there is an equivalence between the moduli space of $n$-pointed genus $g$ algebraic curves, $\mathcal{M}_{g,n}$, and $\mathrm{RG}_{g,n}$ the moduli space of ribbon graphs. In 1992, Kontsevich used this equivalence to publish results proving the Witten Conjecture. The equivalence between these spaces allowed him to combinatorially define a differential $2$-form $\Omega$ on the compactified ribbon graph complex $\overline{\mathrm{RG}}_{g,n}$ whose pull-back represents the scaled sum of $\psi$-classes on the Deligne-Mumford compactification of the moduli space of algebraic curves $\overline{\mathcal{M}}_{g,n}$. Kontsevich showed that $\Omega$ is non-degenerate on cells of the complex that correspond to ribbon graphs with only odd-valent vertices, however, he made no particular use of this.

It was in 2010 when Bennett, Cochran, Safnuk, and Woskoff used the non-degeneracy of $\Omega$, and the fact that the top-dimensional cells of $\mathrm{RG}_{g,n}$ have all trivalent vertices, to calculate the symplectic volume of $\mathrm{RG}_{g,n}$. Creating a hamiltonian torus action on the top-dimension of $\mathrm{RG}_{g,n}$, they use symplectic reduction techniques to create a recursive formula for the volume.

In this talk, I discuss my dissertation research which extends the work done by Bennett et al. I define the sub-complexes $\overline{\mathrm{RG}}_{g,n}^{(\alpha_1, \alpha_2, \ldots)}$ of $\overline{\mathrm{RG}}_{g,n}$ which, roughly, is the ribbon graph complex cosisting of ribbon graphs with exactly $\alpha_i$ vertices of degree $2i+3$. I pay particular attention to $\overline{\mathrm{RG}}_{g,n}^{(1,0,0,\ldots)}$, finding a hamiltonian torus action on the top-dimensional cells and using symplectic reduction to recursively calculate its volume.

Speaker: Panel Discussion (J. Angelos (moderator), S. Cooper, S. Graham, C. Lee, S. Narayan) February 18, 2014
Title: Getting the Most Out of Conferences and Talks
Abstract: Do you know how to get the most out of conferences? Need tips on how to follow talks? Want to know why you should attend colloquia? This seminar will be a panel discussion with faculty members who will share their experiences and answer your questions. The discussion will be moderated by Professor Angelos.

We hope to see you there!

Speaker: Debraj Chakrabarti & Ben Salisbury (Central Michigan University) February 25, 2014
Title: Mathematics Area Spotlight
Abstract: In this seminar we will have the following two 20-minute presentations.

Speaker: Debraj Chakrabarti

Title: Several Complex Variables Are Better Than Just One

Abstract: In this talk we discuss how the properties of holomorphic functions of several complex variables differ from those of one complex variable. In particular, we discuss the Hartogs phenomenon, an extension phenomenon for holomorphic functions of several variables which has no analog in one variable.

Speaker: Ben Salisbury

Title: Introduction to Crystals and an Application

Abstract: In this short talk, we will quickly introduce crystal bases in a combinatorial way, and overview a very recent application of the theory of crystal bases to the field of automorphic forms.

Speaker: Pin-Hung Kao (Central Michigan University) March 18, 2014
Title: Small Gaps Between Primes
Abstract: Gaps between the prime numbers are of great interest to the number theorists. One of the most well-known example of such is the twin prime conjecture. Although it remains one of the most elusive problems in number theory, significant progress in bounded prime gaps has been made within the recent decade. In 2005, Goldston, Pintz, and Yוldוrוm proved, while assuming the Elliot--Halberstam conjecture, that \[ \liminf_{n \to \infty} (p_{n+1} - p_n) \le 16. \] In May of 2013, Yitang Zhang surprised the mathematics community with a proof showing unconditionally that \[ \liminf_{n \to \infty} (p_{n+1} - p_n) < 7 \times 10^7. \] Shortly after, James Maynard announced in November of 2013 a proof that \[ \liminf_{n \to \infty} (p_{n+1} - p_n) \le 600 \] unconditionally. Throughout the development of the bounded gaps between primes, sieve methods continually prove to be indispensable. In this talk, we will present some principle sieve theoretic techniques that made the above results possible. More specifically, we will introduce the Selberg sieve, the Goldston--Pintz--Yוldוrוm sieve, and Maynard's generalization of GPY sieve. Lastly, we will show how these sieves were employed in the proofs of the above results.
Speaker: Mohamed Amezziane & Mingan Yang (Central Michigan University) April 8, 2014
Title: Statistics & Actuarial Sciences Area Spotlight
Abstract: In this seminar we will have the following two 20-minute presentations.

Speaker: Mohamed Amezziane

Title: Function Estimation Using Shrinkage Techniques

Abstract: This talk introduces the concept of estimating a function (as opposed to estimating a function's parameters) and its connection to the problem of estimating the means of several Normal random variables. This connection enables the use of shrinkage techniques to obtain several types of function estimators with nice asymptotic optimality properties. These types of estimators, like any other nonparametric estimators, are plagued by the curse of dimensionality, i.e., the degradation of the estimator's accuracy as the dimension of the data increases. To curb the effect of this curse, shrinkage techniques are used to propose new classes of semiparametric estimators.

Speaker: Mingan Yang

Title: Bayesian Variable Selection For Mixed Effects Models

Abstract: Recently, variable selection has drawn great attention and a vast number of penalized regression approaches with shrinkage estimation have been developed for general linear models. Correspondingly, the Bayesian alternative approaches have also been proposed. However, it gains little attention for the linear mixed effects model.

For linear mixed effects model, generally, it is a common practice to assume that the random effects follow a parametric distribution, for example, a normal distribution. However, substantial violation of the normality assumption might potentially impact the subset selection of variables in the models. Potentially, one might propose a nonparametric random effect model. The challenge is that the random effects generally have a none-zero mean, which causes identifiability and complicates interpretation for variable selection, in the nonparametric random effect model. I propose a shrinkage approach on a nonparametric centered random effects models and consider some possible extensions.

Speaker: Panel Discussion (C. Cheng, S. Cooper (moderator), Y. Kim, D. Lapp, B. Safnuk) April 22, 2014
Title: What I Wish I Knew...
Abstract: It is natural to reflect on one's decisions. For example, have you ever wondered if you will be happy with your career of choice in 20 years? Are there any secrets to success that you may not know of yet? As the saying goes, hindsight is certainly 20-20. This seminar will be a panel discussion with faculty members who will share what they wished they knew during graduate school now that they can look back on their experiences. Participants can ask questions regarding the graduate program, the rewards of teaching, possible career paths, balancing one's personal life and work, and more. The discussion will be moderated by Dr. Cooper.

We hope to see you there!

Graduate Student Seminar - Fall 2013
Speaker: Cleland Loszewski (Central Michigan University) October 1, 2013
Title: Symplectic Vector Spaces
Abstract: A symplectic vector space is a vector space V equipped with a bilinear, skew-symmetric, non-degenerate form Ω. In this talk I will give an introduction to symplectic vector spaces. I will give a proof of the canonical basis for a symplectic vector space, also called the Darboux basis, and introduce the block form matrix of Ω. In the end we will see that every 2n-dimensional symplectic vector space is symplectomorphic to R2n equipped with a 'natural' symplectic form. If time permits, I'll go on to discuss symplectic manifolds and the symplectic volume of a manifold.

This talk will be accessible to all graduate students.

Speaker: Olaseni Fadipe (Central Michigan University) October 22, 2013
Title: Inverse Problems
Abstract: Inverse Problems abound today in science, engineering, technology, medicine, finance, econometrics and statistics. Many of these problems are often ill-posed in the sense that they violate at least one of Hadamard's (1923) conditions -- existence, uniqueness, and stability -- for well-posed problems. These ill-posed problems need regularization before being amenable to methods for solutions of Inverse Problems. We will examine Linear Inverse Problems and illustrate inversion theory with two or three examples from the physical sciences.
Speaker: Dr. John Daniels (Central Michigan University) October 29, 2013
Title: The 20/30 Game Winner ... An Endangered/Extinct Species?
Abstract: It is October and for many American Baseball Fans that means the World Series. This talk is intended to introduce some of you to the game of American Baseball. Although not as globally popular as soccer, baseball has been played in this country for over 150 years and had over 74,000,000 fans in attendance in 2013. In this talk, I will discuss the basic rules of baseball, how statistical analysis of baseball is done as academic research, and then summarize an article appearing in the Baseball Research Journal Nov 1. Some of the information for this article came from a Plan B paper done by Steve Kuehl, a CMU Masters Degree (Mathematics) student and co-author. So, yes, it is possible to be published before you complete a dissertation.
Speaker: Jason Pode (Central Michigan University) November 5, 2013
Title: Finding Algebraic Forms of Graph Invariants
Abstract: Numerous connections can be made between the fields of commutative algebra, combinatorics and graph theory. In particular, there is a correspondence between edge and cover ideals in algebra to various graph invariants such as the chromatic and clique numbers. In this talk we will explore this correspondence and investigate exactly how these special monomial ideals can be used to translate certain graph invariants into an algebraic form.
Speaker: Pin-Hung Kao (Central Michigan University) November 12, 2013
Title: An Overview of the Langlands Program
Abstract: In the late 1960's, Robert Langlands conjectured a relationship between algebraic objects (Galois representations) and analytic ones (automorphic forms). Often considered as one of the most important problems of contemporary mathematics, the Langlands program has far-reaching consequences. We will give an overview of the Langlands program with Artin’s reciprocity law as a motivation. The recent works of Peter Scholze will also be discussed briefly in this presentation.
Speaker: Drew Lazar (Central Michigan University) November 19, 2013
Title: Dimension Reduction in Spaces of Positive Definite Matrices
Abstract: Principal component analysis (PCA) is an important approach to reduce the dimension and explore the variance structure of unconstrained vector space valued data. For data under constraints that can be modeled as non-linear Riemannian manifolds, a generalization of PCA, known as principal geodesic analysis (PGA), has been proposed. Finding solutions to PGA, however, can be difficult and computationally intensive and first-order approximations are often used. In this talk I will consider such approximations as well as propose a novel, recursive approach to produce faster and more accurate approximations to PGA.

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