Department of Mathematical Sciences

Colloquium Series, 2017 - 2018

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, October 13

3:00-4:00pm

The MAC

Prof. Emmanuele DiBenedetto

Department of Mathematics & Department of Molecular Physiology and Biophysics

Vanderbilt University

Title: A Wiener-type condition for the boundary continuity of Quasi-Minima of Variational Integrals

Abstract: A Wiener-type condition for the continuity at the boundary points of Q-minima, is established, in terms of the divergence of a suitable Wiener integral.

Friday, October 13

4:30-5:30pm

The MAC

Prof. Emmanuele DiBenedetto

Department of Mathematics & Department of Molecular Physiology and Biophysics

Vanderbilt University

Title: Phototransduction: Informing Biology with Mathematics

Abstract: Visual transduction is the process by which photons of light are converted into electrical signals by diffusion of the second messengers Calcium and cGMP (cyclic guanosine monophosphate) in the cytoplasm of the Rod Outer Segment (ROS). A mathematical model of such a transduction is presented, that accounts for the layered geometry of the Rod Outer Segments and the incisures born by the discs. The model provides an explanation for the role of incisures, believed as evolutionary residues. The model also explains the biological/structural reasons for the high filelity of the photoresponse, despite the fact that reception of photons of light is a process with several random components.

Friday, November 3

3:00-4:00pm

The MAC

Dr. Hugh Thompson

Chief Technology Officer

Symantec

Title: Radical Innovation: The Future of Cybersecurity

Abstract: With cyber threats such as the Wannacry ransomware outbreak and large-scale weaponization of IoT devices, the young discipline of cyber security is being forced to mature quickly. In this talk, we look at the threat landscape and its evolution. We will also explore how the field of cyber security is harnessing innovation and learning from other rapidly evolving disciplines.

Friday, November 17

3:00-4:00pm

The MAC

Prof. Irene Lasiecka

Department of Mathematical Sciences

University of Memphis

Title: Mathematical theory of evolutions arising in flow-structure interactions

Abstract: Fluid-structure interactions and flow-structure interactions are ubiquitous in nature. Problems such as attenuation of turbulence or flutter in an oscillating structure are prime examples of relevant applications. Mathematically, the models are represented by nonlinear Partial Differential Equations (Navier Stokes-Euler equations and nonlinear elasticity ) displaying strong boundary-type coupling at the interface between the two media. Moreover, in most models, the dynamical character of the two PDEs evolving on their corresponding domains is different and the overall system displays a parabolic/hyperbolic coupling, separated by the interface. This provides for a rich mathematical structure opening the door to several unresolved problems in the area of non-linear PDEs, dynamical systems and related harmonic analysis and geometry. This talk aims at providing a brief overview of recent developments in the area along with a presentation of the most recent advances addressing the issues of wellposedness and long time behavior of the corresponding evolutionary systems.

Friday, January 19

11:00am-12:00pm

The MAC

Prof. Richard H. Rand

Departments of Mathematics & Mechanical and Aerospace Engineering

Cornell University

Title: The Infinite Limit Cycle Bifurcation in Delay-Differential Equations

Abstract: The differential equation x(t)'' + x(t) + x(t)^3 = 0 is conservative and admits no limit cycles. If the linear term x(t) is replaced by a delayed term x(t-T), where T is the delay, the resulting delay-differential equation exhibits an infinite number of limit cycles for positive values of T in the neighborhood of T=0, their amplitudes going to infinity in the limit as T approaches zero. This newly-discovered bifurcation will be illustrated through the use of a variety of tools from nonlinear dynamics: harmonic balance, Melnikov's integral and numerical integration. The talk will include an introduction to delay-differential equations. This work is based on a 2017 paper with graduate students M. Davidow and B. Shayak.

Friday, January 26

3:00pm-4:00pm

The MAC

Martin E. Glicksman, Ph.D., NAE

Allen Henry Chair and Distinguished Professor of Engineering

Florida Institute of Technology

Title: Metals to Morphos, Snowflakes to Superalloys: The mathematics of pattern formation

Abstract: Complex patterns are encountered throughout nature, technology, and even society. The tropical blue morpho retenor butterfly exhibits brilliant bio-iridescence controlled by a chiten/air dendritic nanostructure in the insect's wing that interacts with incident white light and efficiently reflects blue without the need for any pigments. Branched crystals, called dendrites, form superalloys needed for modern jet engines, and also appear during electro-deposition and casting of metals and alloys. The question of how ubiquitous complex patterns arise, such as snowflakes, when freezing 'simple' fluids, such as water vapor, or molten metals, remains an active area of research in materials science, fluid dynamics, and biology.
The Leibniz-Reynolds transport theorem provides an omnimetric interface energy balance, i.e., one valid over all continuum length scales. The transport theorem indicates that solid-liquid interfaces support capillary-mediated redistribution of energy capable of modulating an interface's motion on mesoscopic scales---a thermodynamic phenomenon not captured by conventional Stefan balances that exclude capillarity. These energy fields were studied using entropy density multiphase-field simulations. Interfacial energy rate distributions were exposed and measured by equilibrating solid-liquid interfaces configured as variational grain boundary grooves (GBGs). The rates of interfacial cooling so revealed confirm independent predictions based on sharp-interface thermodynamics, variational calculus, and field theory. This study helps answer the long-standing question: How do diffusion-limited patterns initiate in nature and technology?

Friday, February 2

3:00pm-4:00pm

The MAC

Prof. Richard Wood

Department of Mathematics and Statistics

Dalhousie University

Title: An Introduction to Categories, in General, and Complete Distributivity, in Particular

Abstract: The talk is intended to be accessible to senior undergraduates and will introduce the main definitions of Category Theory, beginning with an emphasis on the subject's utility in mapping problems from one area of Mathematics to another. In addition to the examples of categories that comprise collections of mathematical structures, like spaces and groups, and their mappings, pursuit of some familiar mathematical objects as categories in their own right has led to surprising results. We will show that when a complete lattice is regarded as a category, complete distributivity admits a novel formulation that simplifies some classical results and leads to many new ideas.

Friday, February 9

3:00pm-4:00pm

The MAC

Prof. Eduardo V. Teixeira

Department of Mathematics

University of Central Florida

Title: Nonlinear diffusive processes: geometric insights and beyond

Abstract: Diffusion is a phenomenon which accounts average, spread or balance of quantities in a given process. These constitute innate trends in several fields of natural sciences, which in turn justify why diffusion is such a popular concept among scientists across disciplines. In the realm of mathematics, the study of diffusion is often related to second order differential operators of parabolic type --- or else their stationary versions, the so called elliptic operators. Current literature on the general theory of second order elliptic and parabolic differential operators is vast, dense, and regarded as rather challenging, specially when it comes to understanding regularizing effects of diffusion. In this talk, however, I will discuss a geometric alternative approach to elliptic regularity theory; the so termed Geometric Tangential Analysis. The roots of this idea go back to the foundation of De Giorgi's geometric measure theory of minimal surfaces, and accordingly, it is present in the development of the contemporary theory of free boundary problems. In recent years, however, geometric tangential methods have been significantly enhanced, amplifying their range of applications and providing a more user-friendly platform for advancing these endeavors. I will discuss some fundamental ideias supporting (modern) geometric tangential methods and will exemplify their power through select examples.

Friday, April 27

3:00pm-4:00pm

The MAC

Prof. Roberto Triggiani

Department of Mathematical Sciences

The University of Memphis

Title: Boundary control, stabilization and inverse problems for Schrodinger equations on a multi-dimensional bounded domain

Abstract: The study of control theoretic questions for, say, even linear Schrodinger equations defined over a bounded multidimensional domain and subject to the action of boundary control was long hampered by the lack of knowledge of even the most basic mathematical question: optimal regularity theory from the boundary, say in L2, to the interior. Starting from the solution of this issue in 1990, at least in the case of Dirichlet boundary control, we shall review a series of subsequent results on: (i) the classical Quadratic Optimal Control problem and related Riccati equations; (ii) boundary exact controllability or boundary feedback uniform stabilization in the space of optimal regularity, till (iii) recent inverse theory progress on the recovery (uniqueness and stability) of the potential coefficient in the equation with boundary Dirichlet- control, via just one Neumann-boundary measurement. Carleman-type estimates (since about 2004) will play a critical role in obtaining results for very general models, as to include magnetic potential terms. Open problems will also be noted.

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