Seminars and Colloquia by Series

On the Potential of Potential Theory

Series
Research Horizons Seminar
Time
Wednesday, April 6, 2016 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Prof. Doron LubinskySchool of Mathematics, Georgia Institute of Technology

Please Note: Food and Drinks will be provided before the seminar.

Abstract: If P(z) is a polynomial, then log|P(z)| is a potential. We discuss some facets of this observation, and some gems in classical potential theory. A special topics course on potential theory will be offered in the fall.

On Dilated Covering Number of a Convex Body

Series
Research Horizons Seminar
Time
Wednesday, March 30, 2016 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Prof. Galyna LivshytsSchool of Mathematics, Georgia Institute of Technology

Please Note: Food and Drinks will be provided before the seminar.

We shall introduce and discuss several notions from classical Convex geometry. In particular, covering number, separation number and illumination number shall be defined and explored. Another parameter, which has been studied in the recent years, the dilated covering number of a convex set shall be introduced. We shall present best known estimate on this number, which is a part of a joint work with K. Tikhomirov.

étale and Motivic Homotopy Theory

Series
Research Horizons Seminar
Time
Wednesday, February 24, 2016 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Prof. Kirsten WickelgrenSchool of Mathematics, Georgia Institute of Technology

Please Note: Food and Drinks will be provided before the seminar.

Abstract: It is not necessary to know what étale, motivic, or homotopy mean for this talk. The talk is intended to advertise motivic homotopy theory, and introduce it a little too. To do this, we'll give an example of an elementary problem the field can be used to solve, and then describe some aspects of the field itself which make this possible. The part of this talk which is original is joint with Jesse Kass.

How Geometry plays a role in Industry

Series
Research Horizons Seminar
Time
Wednesday, November 18, 2015 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Dr. Jesse JohnsonGoogle Company

Please Note: Food and Drinks will be provided before the seminar.

In this talk, we will discuss: (1) How geometry plays a role in machine learning/data science? (2) What it's like being a mathematician at a software company.

Weak Galerkin Finite Element Methods for PDEs

Series
Research Horizons Seminar
Time
Wednesday, November 4, 2015 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Chunmei WangDepartment of Mathematics, Georgia Institute of Technology

Please Note: Food and Drinks will be provided before the seminar.

Weak Galerkin (WG) is a new finite element method for partial differential equations where the differential operators (e.g., gradient, divergence, curl, Laplacian etc) in the variational forms are approximated by weak forms as generalized distributions. The WG discretization procedure often involves the solution of inexpensive problems defined locally on each element. The solution from the local problems can be regarded as a reconstruction of the corresponding differential operators. The fundamental difference between the weak Galerkin finite element method and other existing methods is the use of weak functions and weak derivatives (i.e., locally reconstructed differential operators) in the design of numerical schemes based on existing variational forms for the underlying PDE problems. Weak Galerkin is, therefore, a natural extension of the conforming Galerkin finite element method. Due to its great structural flexibility, the weak Galerkin finite element method is well suited to most partial differential equations by providing the needed stability and accuracy in approximation. In this talk, the speaker will introduce a general framework for WG methods by using the second order elliptic problem as an example. Furthermore, the speaker will present WG finite element methods for several model PDEs, including the linear elasticity problem, a fourth order problem arising from fluorescence tomography, and the second order problem in nondivergence form. The talk should be accessible to graduate students with adequate training in computational mathematics.

Mechanisms of Chaos

Series
Research Horizons Seminar
Time
Wednesday, October 28, 2015 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Leonid BunimovichSchool of Mathematics, Georgia Institute of Technology

Please Note: Food and Drinks will be provided before the seminar

In this seminar,we will explain why and how unpredictable (chaotic) dynamics arises in deterministic systems. Some open problems in dynamical systems, probability, statistical mechanics, optics, (differential) geometry and number theory will be formulated.

Scaling limits of Polynomials are fairly universal

Series
Research Horizons Seminar
Time
Wednesday, October 21, 2015 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Prof. Doron LubinskySchool of Mathematics, Georgia Institute of Technology

Please Note: Food and Drinks will be provided before the seminar.

In elementary calculus, we learn that (1+z/n)^n has limit exp(z) as n approaches infinity. This type of scaling limit arises in many contexts - from approximation theory to universality limits in random matrices. We discuss some examples.

Walkers Induced Wobbling of Pedestrian Bridges

Series
Research Horizons Seminar
Time
Wednesday, October 14, 2015 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Prof. Guillermo GoldszteinSchool of Mathematics, Georgia Institute of Technology

Please Note: Food and Drinks will be provided before the seminar.

We will discussing the wobbling of some pedestrian bridges induced by walkers when crowded and show how this discussion leads to several problems that can be studied with the help of mathematical modeling, analysis and simulations.

Wind-driven Waves and Fluid Instabilities

Series
Research Horizons Seminar
Time
Wednesday, October 7, 2015 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Prof. Chongchun ZengSchool of Mathematics, Georgia Institute of Technology

Please Note: Food and Drinks will be provided before the seminar.

In this talk, we start with the mathematical modeling of air-water interaction in the framework of the interface problem between two incompressible inviscid fluids under the influence of gravity/surface tension. This is a nonlinear PDE system involving free boundary. It is generally accepted that wind generates surface waves due to the instability of shear flows in this context. Based on the linearized equations about shear flow solutions, we will discuss the classical Kelvin--Helmholtz instability etc. before we illustrate Miles' critical layer theory.

Spatial epidemic models: lattice differential equation analysis of wave behavior

Series
Research Horizons Seminar
Time
Wednesday, September 23, 2015 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Chi-Jen, WangSchool of Mathematics, Georgia Institute of Technology

Please Note: Food and Drinks will be provided before the seminar.

Spatially discrete stochastic models have been implemented to analyze cooperative behavior in a variety of biological, ecological, sociological, physical, and chemical systems. In these models, species of different types, or individuals in different states, reside at the sites of a periodic spatial grid. These sites change or switch state according to specific rules (reflecting birth or death, migration, infection, etc.) In this talk, we consider a spatial epidemic model where a population of sick or healthy individual resides on an infinite square lattice. Sick individuals spontaneously recover at rate *p*, and healthy individual become infected at rate O(1) if they have two or more sick neighbors. As *p* increases, the model exhibits a discontinuous transition from an infected to an all healthy state. Relative stability of the two states is assessed by exploring the propagation of planar interfaces separating them (i.e., planar waves of infection or recovery). We find that the condition for equistability or coexistence of the two states (i.e., stationarity of the interface) depends on orientation of the interface. We analyze this stochastic model by applying truncation approximations to the exact master equations describing the evolution of spatially non-uniform states. We thereby obtain a set of discrete (or lattice) reaction-diffusion type equations amenable to numerical analysis.

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