Wednesday, April 22, 2015 - 12:05 , Location: Skiles 006 , Zhiwu Lin , Georgia Tech , Organizer: Benjamin Ide
Many physical models without dissipation can be written in a Hamiltonian form. For example, nonlinear Schrodinger equation for superfluids and Bose-Einstein condensate, water waves and their model equations (KDV, BBM, KP, Boussinesq systems...), Euler equations for inviscid fluids, ideal MHD for plasmas in fusion devices, Vlasov models for collisionless plasmas and galaxies, Yang-Mills equation in gauge field theory etc. There exist coherent structures (solitons, steady states, traveling waves, standing waves etc) which play an important role on the long time dynamics of these models. First, I will describe a general framework to study linear stability (instability) when the energy functional is bounded from below. For the models with indefinite energy functional (such as full water waves), approaches to find instability criteria will be mentioned. The implication of linear instability (stability) for nonlinear dynamics will be also briefly discussed.
Wednesday, January 28, 2015 - 12:15 , Location: Skiles 005 , Dr. Molei Tao , Georgia Tech Math Department , Organizer: Alexander Hoyer
Please note the delayed start for this week only.
The main focus of this talk is a class of asymptotic methods called averaging. These methods approximate complicated differential equations that contain multiple scales by much simpler equations. Such approximations oftentimes facilitate both analysis and computation. The discussion will be motivated by simple examples such as bridge and swing, and it will remain intuitive rather than fully rigorous. If time permits, I will also mention some related projects of mine, possibly including circuits, molecules, and planets.
Wednesday, January 7, 2015 - 12:00 , Location: Skiles 005 , Allen Hoffmeyer , JP Morgan , firstname.lastname@example.org , Organizer: Allen Hoffmeyer
In this talk, we will discuss what entails being a front-office quant at JP Morgan in the Emerging Markets group. We discuss why Emerging Markets is viewed as its own asset class and what there is to model. We also give practical examples of things we look at on a daily basis. This talk aims to be informal and to appeal to a wide audience.
Wednesday, November 12, 2014 - 12:00 , Location: Skiles 005 , Dr. Kirsten Wickelgren , Georgia Tech Math Department , Organizer: Alexander Hoyer
We will discuss methods for solving polynomial equations with integer solutions using the loops on the space of all complex solutions to the same equations. We will then state generalizations of this method due to A. Grothendieck.
Wednesday, October 29, 2014 - 12:05 , Location: Skiles 005 , Dr. John Etnyre , Georgia Tech Math Department , Organizer: Alexander Hoyer
There is a beautiful idea that one can study spaces by studying associated geometric objects. More specifically one can associate to a manifold (that is some space) a symplectic or contact manifold (that is the geometric object). The question is how useful is this idea. We will discuss this idea and related questions for subspaces (that is immersions and embeddings) with a focus on curves in the plane and knots in three space. If time permits we will discuss powerful new tools from contact geometry that allow one use this idea to construct invariants of knots and more generally embeddings and immersions in any space.
Wednesday, October 1, 2014 - 12:00 , Location: Skiles 005 , Ionel Popescu , Georgia Tech Math Department , Organizer: Alexander Hoyer
This talk is intended to be a cocktail of many things. I will start with standard random matrices (called GUE in the slang) and formal computations which leads one to the main problem of counting planar diagrams. This was done by physicists, though the main computation of generating functions for such planar diagrams go through an analytic tools. Here I will change the topic to analysis, and get through with the help of Chebyshev polynomials and how these can be used to solve a minimization problem and then from there to compute several generating functions of planar diagrams. Then I will talk about tridiagonalization which is a main tool in matrix analysis and point out an interesting potential view on this subject.
Wednesday, September 17, 2014 - 12:00 , Location: Skiles 005 , D. Lubinsky , Georgia Tech Math Department , Organizer: Alexander Hoyer
There is a long standing asymptotic relationship in several areas of analysis, between polynomials and entire functions of exponential type. Many extremal problems for polynomials of degree n turn into analogous extremal problems for entire functions of exponential type, as the degree n approaches infinity. We discuss some of the old such as Bernstein's constant on approximation of |x|, and recent work on Plancherel-Polya and Nikolskii inequalities.
Wednesday, September 3, 2014 - 12:00 , Location: Skiles 005 , Dr. Dan Margalit , Georgia Tech Math Department , Organizer: Alexander Hoyer
Here is a classical theorem. Consider a bijection (just a set map!) from the Euclidean plane to itself that takes 0 to 0 and takes the points on an arbitrary line to the points on a (possibly different line). The theorem is that such a bijection always comes from a linear map. I'll discuss various generalizations of this theorem in geometry, topology, and algebra, ending with a discussion of some recent, related research on the topology of surfaces.
Wednesday, August 27, 2014 - 12:00 , Location: Skiles 005 , Dr. Matthew Clark , Northrop Grumman, Future Technical Leaders (FTL) Program , Organizer: Alexander Hoyer
Have you heard the urban legend that an experienced college recruiter can make an initial decision on whether or not to read your resume in less than six seconds? Would you like to see if your current resume can survive the six-second glance? Would you like to improve your chances of surviving the initial cut? Do you know what happens to your resume once you hand it to the recruiter? Should you have different resumes for online submission and handing to decision makers? How many different resumes should you prepare before you go to the career fair? Does it really take 30 revisions of your resume before it is ready to be submitted? Dr. Matthew Clark has supported college recruiting efforts for a variety of large corporations and is a master at sorting resumes in six seconds or under. Join us for a discussion of how most industry companies handle resumes, what types of follow up activities are worth-while, and, how to improve your chances of having your resume pass the “six second glance”.
Thursday, May 1, 2014 - 13:00 , Location: Skiles 006 , Dr. Gunnar Carlsson , Stanford University , Organizer:
Note: This is a special time for Research Horizons.
Special seminar title: The idea of studying the geometry and topology of finite metric spaces has arisen due to the fact that almost all kinds of data sets arising in science or the commercial world are equipped with a metric. This has led to the development of cohomology theories applicable to finite metric spaces, which allow one to construct "measurements" of the shape of the data sets. We will define these theories and discuss their properties. We will also describe their applications, and suggest directions of future research on them.