The Department of Mathematics, Applied Mathematics and Statistics at Case Western Reserve University is an active center for mathematical research. Faculty members conduct research in algebra, analysis, applied mathematics, convexity, dynamical systems, geometry, imaging, inverse problems, life sciences applications, mathematical biology, modeling, numerical analysis, probability, scientific computing, stochastic systems and other areas.

The department offers a variety of programs leading to both undergraduate and graduate degrees in traditional and applied mathematics, and statistics. Undergraduate degrees are Bachelor of Arts or Bachelor of Science in mathematics, Bachelor of Science in applied mathematics, and Bachelor of Arts or Bachelor of Science in statistics. Graduate degrees are Master of Science and Doctor of Philosophy. The Integrated BS/MS program allows a student to earn a Bachelor of Science in either mathematics or applied mathematics and a master’s degree from the mathematics department or another department in five years. The department, in cooperation with the college’s teacher licensure program and John Carroll University, offers a program for individuals interested in pre-college teaching. Together with the Department of Physics, it offers a specialized joint Bachelor of Science in Mathematics and Physics.

Date posted: May 7th, 2015

Thursday, May 7, 2015 (2:00 p.m. in Yost 335)

**Title:** On the Perimeter of a Convex Set

**Speaker:** Galyna Livshyts (Ph.D. Student, Kent State University)

**Abstract:** The perimeter of a convex set in R^n with respect to a given measure is the measure’s density averaged against the surface measure of the set. It was proved by Ball in 1993 that the perimeter of a convex set in R^n with respect to the standard Gaussian measure is asymptotically bounded from above by n^{1/4}. […Read more]

Date posted: May 6th, 2015

Thursday, May 7, 2015 (12:30 p.m. in Yost 306)

**Title: **Parameter Determination for a Channelized Hotelling Detectability Experiment

**Speaker:** Zhengyi Liu (Case Western Reserve University)

**Advisor:** Steven Izen (Professor, Case Western Reserve University)

**Abstract: **In CT scanning it is desirable to quantify when an object can be detected among a noisy background. This problem is an application for signal detection theory. This theory attempts to quantify how easy is to discern signals from noisy backgrounds. […Read more]

Date posted: May 4th, 2015

Tuesday, May 5, 2015 (4:00 p.m. in Yost 306)

**Title: **Overdispersion of Regression Models

**Speaker:** Feng Jin (Case Western Reserve University)

**Advisor:** Danhong Song (Lecturer, Case Western Reserve University)

**Abstract: **Overdispersion in Poisson models occurs when the response variance is greater than the mean.

It may cause standard errors of the estimates to be deflated or underestimated. In this presentation, the data set contains information on smoking behavior and other variables for a random sample of single adults from the United States. […Read more]

Date posted: April 27th, 2015

Wednesday, April 29, 2015 (11:00 a.m. in Yost 306)

**Title: **Bregman Operator Splitting with Variable Step Size for TGV based Multi-Channel MRI Reconstruction

**Speaker:** Benjamin Cowen (Case Western Reserve University)

**Advisor:** Weihong Guo (Assistant Professor, Case Western Reserve University)

**Abstract: **We present fast algorithm for total generalized variation (TGV) based image reconstruction of magnetic resonance images collected by a technique known as partial parallel imaging (PPI). TGV is a generalization of the commonly employed total variation (TV) regularizer. […Read more]

Date posted: April 14th, 2015

Monday, April 27, 2015 (3:15 p.m. in Yost 306)

**Title: **Dynamics of Neurons and Field Potentials in the Auditory Brainstem

**Speaker:** Joshua Goldwyn (Visiting Assistant Professor, Ohio State University)

**Abstract: **Neurons in the medial superior olive (MSO) are temporally precise coincidence detectors that support our ability to localize sound sources. Questions persist regarding the precise workings of MSO neurons, in part because prominent sound-evoked extracellular field potentials hinder the acquisition of single cell in vivo data in the MSO. […Read more]

Date posted: April 14th, 2015

Monday, April 20, 2015 (3:15 p.m. in Yost 306)

**Title: **The Role of Long Range Coupling in the Crayfish Swimmeret System

**Speaker:** Lucy Spardy (Postdoctoral Fellow, Mathematical Biosciences Institute, Ohio State University)

**Abstract: **The crayfish swimmeret system provides an ideal model for studying coordinated limb activity. During forward swimming, four pairs of limbs move rhythmically in a back to front metachronal wave to propel the crayfish through the water. […Read more]

Date posted: April 6th, 2015

Monday, April 13, 2015 (3:15 p.m. in Yost 306)

**Title: **Data-Driven Modeling of Living Fluids

**Speaker:** M. Gregory Forest

Grant Dahlstrom Distinguished Professor

Departments of Mathematics & Biomedical Engineering

Director, Carolina Center for Interdisciplinary Applied Mathematics

University of North Carolina at Chapel Hill

**Abstract: **I will talk about mathematical modeling of three fluid systems: living yeast cells, living mammalian cells, and mucus. In each fluid system, we collaborate with experimentalists and let their data and their biological or medical questions drive our mathematical modeling effort. […Read more]

Date posted: April 6th, 2015

Monday, April 13, 2015 (3:15 p.m. in Yost 306)

**Title: **Data-Driven Modeling of Living Fluids

**Speaker:** M. Gregory Forest

Grant Dahlstrom Distinguished Professor

Departments of Mathematics & Biomedical Engineering

Director, Carolina Center for Interdisciplinary Applied Mathematics

University of North Carolina at Chapel Hill

**Abstract: **I will talk about mathematical modeling of three fluid systems: living yeast cells, living mammalian cells, and mucus. In each fluid system, we collaborate with experimentalists and let their data and their biological or medical questions drive our mathematical modeling effort. […Read more]

Date posted: April 6th, 2015

Friday, April 10, 2015 (1:00 p.m. in Yost 306)

**Title:** Banded Matrices and Fast Inverses

**Speaker:** Gilbert Strang (Professor of Mathematics, MIT)

**Abstract:** The inverse of a banded matrix A has a special form with low rank submatrices except at the main diagonal. That form comes directly from the Nullity Theorem. Then the inverse of that matrix A^-1 is the original A, which can be found by a remarkable “local” […Read more]

Date posted: April 2nd, 2015

Friday, April 10, 2015 (3:00 p.m. in Yost 306)

**Title: **From the Jones Polynomial to Khovanov Homotopy

**Speaker:** Robert Lipschitz (Associate Professor, Columbia University Department of Mathematics)

**Abstract: **We will start by introducing some basic questions in knot theory. We will then talk about the Jones polynomial, a knot invariant from the 1980’s, and how it lets you answer some of those questions (some of the time). We will then introduce two more refined knot invariants, […Read more]