Mathematics Homepage

Department Colloquia

Spring 2014 and Fall 2013



 

Driving directions.

Past talks.

Time and place: 3:45pm--4:45pm, Fridays at MSC 459; Cookies available in the lounge at 3:30pm.



April 25, 2014

Dr. Marie Snipes, Kenyon College

Title: Euclidean Embeddings of Snowflake Metric Spaces

Abstract: Metric spaces are useful tools for modeling sets of objects where there is a natural notion of distance; examples include geographical data, genetic data, and signals (like sound waves or images).  We often seek to classify metric spaces by how Euclidean they look: specifically, we want to know if some metric space can be embedded in Euclidean space.  In this talk we will use examples to introduce the general embedding problem.  We will then discuss a theorem by Assouad guaranteeing bi-Lipschitz embeddings of so-called snowflake metric spaces into Euclidean space and some recent related work by Naor-Nieman and David-Snipes.




April 18, 2014

Dr.  Alan Nathan, University of Illinois

Title: The Physics of Baseball: "You Can Observe A Lot By Watching"

Abstract: Following Yogi Berra's words of wisdom, I will use high-speed video clips to highlight some of the interesting physics underlying the game of baseball.  The talk will focus on the subtleties of the baseball-bat collision, the intricacies of the flight of a baseball, and many other things. I will investigate some very practical questions and show how a physicist goes about trying to answer these questions. Some examples:

What is the"sweet spot" of a bat?
How does the batter's grip affect the batted ball?
Why is a knunckleball so erratic?
How does spin affect the flight of a batted ball?
Why does aluminum outperform wood?
What's the deal with the humidor?

The talk should have something for everybody, whether your interest is baseball, physics, or the connection between them.



April 11, 2014

Dr.  Alessandro Ottazzi, Fondazione Bruno Kessler

Title: Special maps on stratified Lie groups

Abstract: In this talk I discuss some new results concerning the study of special maps on Carnot-Carathéodory spaces, obtained in different collaborations. I shall begin with the definition of Carnot-Carathéodory space and that of Carnot group. Then I describe the classes of maps in which I am interested: isometries, conformal maps, quasiconformal maps. Finally, I will briefly comment on the techniques that are used in the proofs and discuss the open problems.




March 28, 2014

Dr.  Rui Feng, University of Pennsylvania

Title: Borrowing and Renewing Phase Information in Genetic Studies

Abstract: The majority of current genetic studies have been focused on finding disease-associated polymorphisms. However, how multiple polymorphisms jointly function is more important to truly understand gene functions and causes of diseases. Such valuable information, partially contained in the combination of alleles on a single chromosome, has been largely neglected. In this talk, I will show how the phase or haplotype inferencecanbe effective for identifying disease-causing loci and introduce our proposed methods in three completely different studies. The performance and utility of these methods have been evaluated in simulations and real studies. Our innovative methods have demonstrated additional population information and power gain, improving our ability to determine the role of genomic variations in human diseases.




March 21, 2014

Dr.  Sharon Senk, Michigan State University

Title: Mathematics Teacher Education: Lessons learned from cross-national and national surveys

Abstract: In this talk I will share data from two recent surveys of mathematics teacher preparation that provide an opportunity to understand how teacher education varies within the U.S. and how it compares to the preparation of mathematics teachers in 16 other countries.

 

About the speaker: Dr. Sharon Senk, Mathematics Education Professor Michigan State University (PhD, University of Chicago)
Sharon Senk is a Professor in the Mathematics Department and the Program in Mathematics Education. Her primary research interests are the learning and teaching of secondary school mathematics, the nature of assessment in high school mathematics classrooms, and the mathematical preparation of elementary and secondary teachers. She currently is the Principal Investigator (PI) of a Collaborative Research Project with Yukiko Maeda and Jill Newton at Purdue University called Preparing to Teach Algebra: A Study of Teacher Education. She also serves as Co-PI of the Teacher Education Study in Mathematics (TEDS-M) and as a Consultant on Evaluation to the Secondary Component of the University of Chicago School Mathematics Project (UCSMP).




March 7, 2014

Dr. Miodrag C Iovanov, University of Iowa

Title: On invariants in representation theory

Abstract: We discuss and recall several classical invariants in representation theory. The representations of an algebra A provide a good tool to gain insight on the structure of A. For group algebras, Lie algebras, algebraic groups, Hopf algebras, the representations have ring structures that make for a stronger invariant, but which can still fail to distinguish even between some small groups. Frobenius-Schur (FS) indicators are very good invariants of group representations that have the advantage that they can be generalized to any nice enough tensor category. For groups, these indicators are always integers, and it was believed they should be so for braided categories - that is, in situations when the tensor product of representations is "commutative". We give an overview if some recent results on indicators for Drinfeld doubles of groups D(G); this is important since D(G) are in some sense the algebras closest to group algebras and which have braided categories, and on the other hand they cover a generic braided situation. We show that integrality of the FS indicators is false in general, but it is however true for D(G) of symmetric groups, certain classes of p-groups, simple groups, etc.; we mention some open questions that arise here and could offer insights on the representation theory and combinatorial properties of some classes of groups.




February 28, 2014

Dr.  Dilum P De Silva, Bowling Green State University at Firelands

Title: The Lind-Lehmer constant for groups of the form Z_p^2

Abstract: click here

 




January 31, 2014

Dr.  Xiu Ye, University of Arkansas at Little Rock

Title: A New Class of Finite Element Methods: Weak Galerkin Methods

Abstract: When the classic continuous finite element methods cannot meet the needs of modern computational techniques such as hp adaptive and hybrid meshes, discontinuous piecewise polynomials are used in the finite element procedures. This presentation will study the finite element methods that use totally discontinuous approximation functions. Discontinuous Galerkin (DG) methods are such kind methods including IPDG methods, LDG methods and HDG methods. DG methods enforce the continuity of the approximation solutions cross elements by either tuning the penalty parameters or introducing additional equations. The weak Galerkin (WG) finite element method provides a framework for handling discontinuous functions. This general framework will provide a platform for  deriving new methods and simplifying the existing methods.

 




November 15, 2013

Dr.  Sean Li, University of Chicago

Title: Coarse differentiation of Lipschitz functions

Abstract: Bates, Johnson, Lindenstrauss, Preiss, and Schechtman introduced a notion of large scale differentiation.  We discuss an extension of this to the nonabelian setting of Lipschitz maps between Carnot groups and it's application in quantitative nonembeddability.




November 8, 2013

Dr. Dan Burghelea, Ohio State University

Title: Data Analysis, Persistent Homology and Computational Morse Theory

Abstract: I will explain how topology/geometry, via ideas from Morse theory, proposes to  bring some light in  often very unstructured and large amount of data we get addicted to collect. I will also indicate how this process suggests  new mathematics



November 1, 2013

Dr. Deane Arganbright, Divine Word University (Papua New Guinea)

Title: Creative Mathematical Visualization, Modeling, and Interdisciplinary Applications via Spreadsheets

Abstract: A spreadsheet, such as Microsoft Excel, is a creative instrument for the mathematical disciplines. In the classroom, it closely fits the way in which we typically do mathematics, while giving students experience with the principal mathematical tool of the workplace. We can implement many mathematical concepts and algorithms in Excel in a natural manner. This talk presents a diverse range of animated modeling and visualization applications developed during 30 years of experience in universities around the world. We also provide creative interdisciplinary and multicultural uses, such as using mathematics to create pictorial alphabet books for the national languages of Papua New Guinea. While the talk will provide new ideas for mathematicians, others will also find it readily accessible.

(Additional information: Dr. Arganbright is a 1962 B.S. graduate of BGSU, with a 1967 PhD in finite groups from the U. of Washington. He has held positions at Iowa State U., Whitworth U., and U. of Tennessee at Martin, as well as overseas positions at the U. of Papua New Guinea, Bendigo CAE (Australia), U. of Vienna, KAIST (South Korea), and Divine Word U. (PNG). He has been a pioneer in developing mathematical uses of spreadsheets, and has given presentations in over 25 counties, including 2 MAA Invited hour addresses. Additionally, he has published books and journal articles in this area.)



October 25, 2013

Dr.  John P. Nolan, Math/Stat Department, American University, Washongton, D.C.

Title: Stable distributions: models for heavy tailed data

Abstract: Stable distributions are a class of heavy tailed probability distributions that generalize the Gaussian distribution and that can be used to model a variety of problems. An overview of univariate stable laws is given, with emphasis on the practical aspects of working with stable distributions. Then a range of statistical applications will be explored. If there is time, a brief introduction to multivariate stable distributions will be given.




October 18, 2013

Dr.  Daniel Farley, Department of Mathematics, Miami University

Title: The lower algebraic K-theory of Hilbert modular groups

Abstract:

We will describe the lower algebraic K-theory of the Hilbert modular groups; that is, the groups PSL_{2}(O_d), where O_d is the ring of integers in a totally real number field. We will concentrate on the case of quadratic extensions of the rationals. The lower algebraic K-groups include the Whitehead group, which is especially important in topological applications.

Our calculation uses fundamental work of Farrell and Jones, who show that the lower algebraic K-theory of a group G is isomorphic to certain generalized homology groups of the classifying space of G with isotropy in the virtually cyclic subgroups.

A large part of the talk should be accessible to a general mathematical audience. It will involve studying the action of the Hilbert modular groups on the upper-half plane model of hyperbolic space. This is joint work with Ivonne Ortiz.





October 4, 2013

Dr.  Kaibo Wang, Tsing Hua University

Title: Engineering Knowledge Driven Statistical Modeling for Spatial Data

Abstract: In certain complex manufacturing systems, the quality of a product is adequately characterized by a high-dimensional data map rather than by single or multiple variables. Such data maps also preserve unique spatial structures. Therefore, variation pattern analysis and statistical modeling based on the data map become very important for enhanced process understanding and quality improvement.
Using a real wafer example from semiconductor manufacturing and a carbon nano tube example from nano-manufacturing, we demonstrate how statistical models can be developed by incorporating engineering knowledge. In the wafer example, a three-stage hierarchical model is proposed. The wafer surface variation is decomposed into the macro- and micro-scale variations, which are modeled as a cubic curve and a first-order intrinsic Gaussian Markov random field, respectively. In the carbon nano tube example, a piece-wise polynomial model with spatial auto-regressive disturbance is developed. These examples show that engineering knowledge driven statistical modeling can play an important role in quality control of complex systems, and is also a promising area for statistical research.



September 27, 2013

Dr. Martin Mohlenkamp, Department of Mathematics, Ohio University

Title: If the Multiparticle Schrodinger Equation were easy to solve, then Chemistry would be too boring to support life.

Abstract: The multiparticle Schrodinger equation is the basic governing equation in quantum mechanics. Many person-centuries and cpu-millennia have been spent constructing approximate solutions to it. We should be glad it is so hard to solve because its subtle behavior allows the rich Chemistry upon which life depends.

I will describe the multiparticle Schrodinger equation and explain (some of) the reasons it is difficult to solve:
high-dimensionality, antisymmetry, scaling to large systems, inter-particle cusps, singular potentials and nuclear cusps, odd function spaces, etc. I will also describe our efforts to overcome these difficulties.




September 13, 2013

Dr. Artem Zvavitch, Department of Mathematical Sciences, Kent State University

Title: Mahler's conjecture for convex bodies

Abstract: The volume product (Mahler volume) of  origin symmetric convex body K is just a product of  volume of K and its dual/polar body. It turned out to be quite a useful object in Functional Analysis and Convex Geometry. Santalo inequality tell us that the volume product takes its maximal value at the Euclidean Ball.  Mahler conjectured that the volume product  is minimized by a cube. Despite many important partial results, the conjecture is still open in dimensions 3 and higher. In this talk we will discuss some recent progress and ideas concerning this conjecture. 

September 6, 2013

Dr. Robert Gramacy, School of Business, University of Chicago

Title: Estimating Player Contribution in Hockey with Regularized Logistic Regression

Abstract: We present a regularized logistic regression model for evaluating player contributions in hockey. The traditional metric for this purpose is the plus-minus statistic, which allocates a single unit of credit (for or against) to each player on the ice for a goal. However, plus-minus scores measure only the marginal effect of players, do not account for sample size, and provide a very noisy estimate of performance. We investigate a related regression problem: what does each player on the ice contribute, beyond aggregate team performance and other factors, to the odds that a given goal was scored by their team? Due to the large-p (number of players) and imbalanced design setting of hockey analysis, a major part of our contribution is a careful treatment of prior shrinkage in model estimation. We showcase two recently developed techniques -- for posterior maximization or simulation -- that make such analysis feasible. Each approach is accompanied with publicly available software and we include the simple commands used in our analysis. Our results show that most players do not stand out as measurably strong (positive or negative) contributors. This allows the stars to really shine, reveals diamonds in the rough overlooked by earlier analyses, and argues that some of the highest paid players in the league are not making contributions worth their expense.