Department of Mathematical Sciences

Colloquium Series

Purpose: To discuss mathematical research and interdisciplinary problems in all areas of mathematics and applied mathematics. Talks are welcome from faculty, graduate students, and outside speakers from academia and industry. Talks should be at a level accessible to graduate students. Students and faculty at all levels and from all departments are welcome to attend.

Date/Time Speaker Title/Abstract
Friday, September 19

3-4pm Crawford 404

Dr. Ugur Abdulla

Department of Mathematical Sciences

Florida Institute of Technology

Title: The Wiener Type Test for the Removability of the Logarithmic Singularity for the Elliptic PDEs with Measurable Coefficients and its Consequences

Abstract: In this lecture I will formulate a new necessary and sufficient condition for the removability of the logarithmic singularity for the second order elliptic PDEs with bounded and measurable coefficients and discuss its measure-theoretical and topological consequences. New concepts of logarithmic capacity and log-regularity of the boundary points will be introduced.

Friday, October 10

3-4pm Crawford 404

Dr. Jian Du

Department of Mathematical Sciences

Florida Institute of Technology

Title: A Continuum Computational model for Intravascular Platelet Aggregation

Abstract: A computational model is introduced to describe the formation of platelet thrombi in blood vessels. It involves interactions among a viscous, incompressible fluid; populations of non-activated and activated platelets; activating chemicals; and the vessel walls. Adhesion of platelets to the injured wall and cohesion between activated platelets is modelled using distributions of elastic links which generate stresses that can influence the fluid motion. Computational methods are presented that meet the diverse challenges posed by the model equations.

Friday, October 31

3-4pm Crawford 404

Dr. Mukesh Kumar

Department of Mathematical Sciences

Norwegian University of Science and Technology

Title: Divergence-conforming LR B-Splines discretizations for Stokes problems

Abstract: To solve the incompressible flow problems, the use of compatible spaces for finite element approximations were originally introduced by Arnold et al., and more recently in a isogeometric context by Buffa et al. Compatible spaces are useful in developing computational methods for solving (partial) differential equations that fulfills certain important qualitative behavior. One important class of problems where this may be utilized is incompressible Stokes and Navier- Stokes flows. The incompressibility constraint will for these two cases imply requiring divergence free velocity fields. In this work, we construct div-compatible spline spaces with local refinement capability using Locally Refined (LR) B-splines. We argue that the splines spaces generated on locally refined meshes will satisfy compatibility provided they span the entire function spaces as governed by Mourrain dimension formula. We show that the locally structured refined LR B-splines, introduced by Johannessen et al., fulfills the necessary requirements for being div-compatible. Further, we consider these div-compatible LR B-spline spaces to approximate the velocity and pressure fields in mixed discretization for Stokes problem and a set of standard benchmark tests are performed to show the stability, efficiency and the conservation properties of the discrete velocity fields in adaptive isogeometric analysis.

Friday, November 14

3-4pm Crawford 404

Dr. Andrei Ludu

Mathematics Department

Embry-Riddle Aeronautical University

SIAM Speaker

Title: Nonlinear Surface Waves, and Hollow Patterns in Rotating Fluids

Abstract: There is experimental evidence of formation of regular polygonal rotating patterns in rotating liquids, Leidenfrost drops and hurricane eye wall. In this talk we will present these phenomena occurring at such different scales, and also present our recent experimental results concerning liquid nitrogen Leidenfrost drops. We will introduce a nonlinear 2-dimensional surface wave model which explains the formation of the rotating stable patterns, predicts the formation or limitation of other such patterns, and arguments in favor of the universality and scale-independence of this behavior.

Monday, December 1

1-2pm Skurla 120

Dr. Nathanael Berestycki

Department of Pure Mathematics and Mathematical Statistics

University of Cambridge

Title: Geometry of Random Surfaces

Abstract: What is a random surface? And what does it look like? In the last 10-15 years probabilists (and physicists) have been trying to answer these questions. I will explain two approaches. In the discrete approach, one studies the combinatorics of large random planar maps. In the continuous approach, one studies a universal object known as the Gaussian Free Field. I will outline some of the major achievements in this field and discuss some outstanding conjectures.

Wednesday, December 10

2-3pm MAC

Dr. Eugene Demidenko

Department of Biomedical Data Science

Dartmouth College

Title: Statistical Analysis of Biomedical Images

Abstract: One of the major task of the scientific application of images in biomedicine is to compare samples of images as we routinely do using the t-test. The existing Image Processing discipline does not serve this purpose because it deals with one image at a time. The goal of the talk is to urge the development of a new chapter of Image Science when two samples of images are compared by computing the p-value for images. The concept is illustrated with histology images, brain MRI, atomic force microscopy images of cancer cells for cancer detection, and Mona Lisa portrait enhancement.

Past Semesters

Summer 2014

Spring 2014

Fall 2013

Spring 2013

Fall 2012