Seminars and Colloquia by Series

Factorial moments of point processes

Series
Stochastics Seminar
Time
Wednesday, April 29, 2015 - 16:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
J.-C. Breton – University of Rennes
In this talk, we propose moment identities for point processes. After revisiting the case of Poisson point processes, we propose a direct approach to derive (joint factorial) moment identities for point processes admitting Papangelou intensities. Applications of such identities are given to random transformations of point processes and to their distribution invariance properties.

The dual Steenrod algebra

Series
Geometry Topology Student Seminar
Time
Wednesday, April 29, 2015 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Robert Krone – Georgia Tech –

Please Note: For Prof. Wickelgren's Stable Homotopy Theory class

The Steenrod algebra consists of all natural transformations of cohomology over a prime field. I will present work of Milnor showing that the Steenrod algebra also has a natural coalgebra structure and giving an explicit description of the dual algebra.

Computer assisted proof for coexistence of stationary hexagons and rolls in a spatial pattern formation problem.

Series
CDSNS Colloquium
Time
Wednesday, April 29, 2015 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jason Mireles-James – University of Florida Atlantic
I will discuss a two dimensional spatial pattern formation problem proposed by Doelman, Sandstede, Scheel, and Schneider in 2003 as a phenomenological model of convective fluid flow . In the same work the authors just mentioned use geometric singular perturbation theory to show that the coexistence of certain spatial patterns is equivalent to the existence of some heteroclinic orbits between equilibrium solutions in a four dimensional vector field. More recently Andrea Deschenes, Jean-Philippe Lessard, Jan Bouwe van den Berg and the speaker have shown, via a computer assisted argument, that these heteroclinic orbits exist. Taken together these arguments provide mathematical proof of the existence of some non-trivial patterns in the original planar PDE. I will present some of the ingredients of this computer assisted proof.

Global Classical Solution to the Two-dimensional Compressible Navier-Stokes Equations with Density-dependent Viscosity

Series
PDE Seminar
Time
Tuesday, April 28, 2015 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Quansen Jiu – Capital Normal University, China
In this talk, we will present some results on global classical solution to the two-dimensional compressible Navier-Stokes equations with density-dependent of viscosity, which is the shear viscosity is a positive constant and the bulk viscosity is of the type $\r^\b$ with $\b>\frac43$. This model was first studied by Kazhikhov and Vaigant who proved the global well-posedness of the classical solution in periodic case with $\b> 3$ and the initial data is away from vacuum. Here we consider the Cauchy problem and the initial data may be large and vacuum is permmited. Weighted stimates are applied to prove the main results.

Orderings of the Braid Groups

Series
Geometry Topology Student Seminar
Time
Friday, April 24, 2015 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Andrew McCullough – Georgia Institute of Technology
We will give a description of the Dehornoy order on the full braid group Bn, and if time permits mention a few facts about a bi-ordering associated to the pure braid group Pn.

Minimization Problems Involving Policonvex Integrands

Series
Dissertation Defense
Time
Friday, April 24, 2015 - 13:30 for 1 hour (actually 50 minutes)
Location
Skiles 249
Speaker
Romeo Awi – School of Mathematics, Georgia Tech
This thesis is mainly concerned with problems in the areas of the Calculus of Variations and Partial Differential Equations (PDEs). The properties of the functional to minimize play an important role in the existence of minimizers of integral problems. We will introduce the important concepts of quasiconvexity and polyconvexity. Inspired by finite element methods from Numerical Analysis, we introduce a perturbed problem which has some surprising uniqueness properties.

Semicircular limits and transfer principles on the free Poisson chaos

Series
Stochastics Seminar
Time
Thursday, April 23, 2015 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Solesne Bourguin – Carnegie Mellon University
Motivated by understanding the intricate combinatorial structure of the Poisson chaos in order to see whether or not a fourth moment type theorem may hold on that space, we define, construct and study the free Poisson chaos, a non-commutative counterpart of the classical Poisson space, on which we prove the free counter part of the fourth moment theorem. This is joint work with Giovanni Peccati.

Heavily burdened deformable bodies: Asymptotics and attractors

Series
CDSNS Colloquium
Time
Thursday, April 23, 2015 - 13:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Stuart S. Antman – University of Maryland

Please Note: This is the 3rd Jorge Ize Memorial lecture, at IIMAS, Mexico City. We will join a videoconference of the event.

The equations governing the motion of a system consisting of a deformable body attached to a rigid body are the partial differential equations for the deformable body subject to boundary conditions that are the equations of motion for the rigid body. (For the ostensibly elementary problem of a mass point on a light spring, the dynamics of the spring itself is typically ignored: The spring is reckoned merely as a feedback device to transmit force to the mass point.) If the inertia of a deformable body is small with respect to that of a rigid body to which it is attached, then the governing equations admit an asymptotic expansion in a small inertia parameter. Even for the simple problem of the spring considered as a continuum, the asymptotics is tricky: The leading term of the regular expansion is not the usual equation for a mass on a massless spring, but is a curious evolution equation with memory. Under very special physical circumstances, an elementary but not obvious process shows that the solution of this equation has an attractor governed by a second-order ordinary differential equation. (This survey of background material is based upon joint work with Michael Wiegner, J. Patrick Wilber, and Shui Cheung Yip.) This lecture describes the rigorous asymptotics and the dimensions of attractors for the motion in space of light nonlinearly viscoelastic rods carrying heavy rigid bodies and subjected to interesting loads. (The motion of the rod is governed by an 18th-order quasilinear parabolic-hyperbolic system.) The justification of the full expansion and the determination of the dimensions of attractors, which gives meaning to these curious equations, employ some simple techniques, which are briefly described (together with some complicated techniques, which are not described). These results come from work with Suleyman Ulusoy.

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