Monday, December 13, 2010 - 08:30 , Location: University of Tennessee Knoxville , Southeast Geometry Seminar , University of Tennessee Knoxville , Organizer: John McCuan
The Southeast Geometry Seminar is a series of semiannual one-day events focusing on geometric analysis. These events are hosted in rotation by the following institutions: The University of Alabama at Birmingham; The Georgia Institute of Technology; Emory University; The University of Tennessee Knoxville. The following five speakers will give presentations on topics that include geometric analysis, and related fields, such as partial differential equations, general relativity, and geometric topology. Catherine Williams (Columbia U); Hugh Bray (Duke U); Simon Brendle (Stanford U); Spyros Alexakis (U of Toronto); Alessio Figalli (U of Texas at Austin). There will also be an evening public lecture by plenary speaker Hugh Bray (Duke U) entitled From Black Holes and the Big Bang to Dark Energy and Dark Matter: Successes of Einstein's Theory of Relativity.
Wednesday, December 8, 2010 - 15:00 , Location: Physics Howey L5 , Wendy W. Zhang , Physics Department and the James Franck Institute, University of Chicago , Organizer:
In school, we learned that fluid flow becomes simple in two limits. Over long lengthscales and at high speeds, inertia dominates and the motion can approach that of a perfect fluid with zero viscosity. On short lengthscales and at slow speeds, viscous dissipation is important. Fluid flows that correspond to the formation of a finite-time singularity in the continuum description involve both a vanishing characteristic lengthscale and a diverging velocity scale. These flows can therefore evolve into final limits that defy expectations derived from properties of their initial states. This talk focuses on 3 familiar processes that belong in this category: the formation of a splash after a liquid drop collides with a dry solid surface, the emergence of a highly-collimated sheet from the impact of a jet of densely-packed, dry grains, and the pinch-off of an underwater bubble. In all three cases, the motion is dominated by inertia but a small amount of dissipation is also present. Our works show that dissipation is important for the onset of splash, plays a minor role in the ejecta sheet formation after jet impact, but becomes irrelevant in the break-up of an underwater bubble. An important consequence of this evolution towards perfect-fluid flow is that deviations from cylindrical symmetry in the initial stages of pinch-off are not erased by the dynamics. Theory, simulation and experiment show detailed memories of initial imperfections remain encoded, eventually controlling the mode of break-up. In short, the final outcome is not controlled by a single universal singularity but instead displays an infinite variety.
Monday, December 6, 2010 - 10:00 , Location: Physics Howey 501 , Chris Scheper , Center for Applied Mathematics, Cornell University , Organizer:
Dynamical systems with multiple time scales have invariant geometric objects that organize the dynamics in phase space. The slow-fast structure of the dynamical system leads to phenomena such as canards, mixed-mode oscillations, and bifurcation delay. We'll discuss two projects involving chemical oscillators. The first is the analysis of a simple chemical model that exhibits complex oscillations. Its bifurcations are studied using a geometric reduction of the system to a one-dimensional induced map. The second investigates the slow-fast mechanisms generating mixed-mode oscillations in a model of the Belousov-Zhabotinsky (BZ) reaction. A mechanism called dynamic Hopf bifurcation is responsible for shaping the dynamics of the system. This webminar will be broadcast on evo.caltech.edu (register, start EVO, webminar link is evo.caltech.edu/evoNext/koala.jnlp?meeting=MMMeMn2e2sDDDD9v9nD29M )
Friday, November 12, 2010 - 14:00 , Location: Klaus 1447 , Eric de Sturler , Department of Mathematics, Virginia Tech , firstname.lastname@example.org , Organizer:
In a wide range of applications, we deal with long sequences of slowly changing matrices or large collections of related matrices and corresponding linear algebra problems. Such applications range from the optimal design of structures to acoustics and other parameterized systems, to inverse and parameter estimation problems in tomography and systems biology, to parameterization problems in computer graphics, and to the electronic structure of condensed matter. In many cases, we can reduce the total runtime significantly by taking into account how the problem changes and recycling judiciously selected results from previous computations. In this presentation, I will focus on solving linear systems, which is often the basis of other algorithms. I will introduce the basics of linear solvers and discuss relevant theory for the fast solution of sequences or collections of linear systems. I will demonstrate the results on several applications and discuss future research directions.
Wednesday, October 27, 2010 - 12:00 , Location: Skiles 269 , Meredith Casey , School of Mathematics, Georgia Tech , Organizer:
This talk will be the oral examination for Meredith Casey.
I will first discuss the motivation and background information necessary to study the subjects of branched covers and of contact geometry. In particular we will give some examples and constructions of topological branched covers as well as present the fundamental theorems in this area. But little is understood about the general constructions, and even less about how branched covers behave in the setting of contact geometry, which is the focus of my research. The remainder of the talk will focus on the results I have thus far and current projects.
Thursday, October 21, 2010 - 11:00 , Location: Klaus 1456 , Colm Mulcahy , Spelman College , Organizer: Matt Baker
Martin Gardner (1914-2010) "brought more mathematics to more millions than anyone else," according to Elwyn R. Berlekamp, John H. Conway & Richard K. Guy. Who was this man, how was he so influential, and will his legacy matter in the 22nd century? We'll try to answer these questions.This event is part of a one-day global celebration of the life of Martin Gardner. See www.g4g-com.org for information on Atlanta's Celebration of Mind party.
Tuesday, October 12, 2010 - 11:00 , Location: Executive classroom - Main Building , Egon Balas , Carnegie Mellon University , Organizer:
Hosted by Renato DC Monteiro, ISyE.
Intersection cuts are generated from a polyhedral cone and a convex set S whose interior contains no feasible integer point. We generalize these cuts by replacing the cone with a more general polyhedron C. The resulting generalized intersection cuts dominate the original ones. This leads to a new cutting plane paradigm under which one generates and stores the intersection points of the extreme rays of C with the boundary of S rather than the cuts themselves. These intersection points can then be used to generate deeper cuts in a non-recursive fashion. (This talk is based on joint work with Francois Margot.)
Monday, September 27, 2010 - 16:30 , Location: Skiles 311 , Christian Houdre , School of Mathematics, Georgia Tech , Organizer:
Tuesday, September 14, 2010 - 11:00 , Location: ISyE Executive Classroom , Dimitris Bertsimas , Operations Research/Statistics, Sloan School of Management, MIT , Organizer:
In this presentation, we show a significant role that symmetry, a fundamental concept in convex geometry, plays in determining the power of robust and finitely adaptable solutions in multi-stage stochastic and adaptive optimization problems. We consider a fairly general class of multi-stage mixed integer stochastic and adaptive optimization problems and propose a good approximate solution policy with performance guarantees that depend on the geometric properties such as symmetry of the uncertainty sets. In particular, we show that a class of finitely adaptable solutions is a good approximation for both the multi-stage stochastic as well as the adaptive optimization problem. A finitely adaptable solution specifies a small set of solutions for each stage and the solution policy implements the best solution from the given set depending on the realization of the uncertain parameters in the past stages. To the best of our knowledge, these are the first approximation results for the multi-stage problem in such generality. (Joint work with Vineet Goyal, Columbia University and Andy Sun, MIT.)
Monday, September 13, 2010 - 16:30 , Location: Skiles 269 , Michael Lacey , GT , Organizer: Michael Lacey
The why and how of applying to graduate school, with examples of different opportunities drawn from the past 10 years of undergraduate mathematics majors that have gone on to programs in EE, Physics, Applied Math, Statistics, Math, and even Public Policy. Useful for all undergraduate math majors. This is part of the regular Club Math meetings.