Seminars and Colloquia by Series

A proof of the sharp Sobolev inequality

Series
SIAM Student Seminar
Time
Thursday, September 18, 2014 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Rohan GhantaSchool of Mathematics, Georgia Tech
By showing a duality relation between the Sobolev and Hardy-Littlewood-Sobolev inequalities, I discuss a proof of the sharp Sobolev inequality. The duality relation between these two inequalities is known since 1983 and has led to interesting recent work on the inequalities (which may be the topic of future talks).

Mark Kac's Master Equation and Propagation of Chaos

Series
SIAM Student Seminar
Time
Thursday, March 6, 2014 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Hagop TossounianSchool of Mathematics, Georgia Tech
In 1956 Mark Kac introduced an equation governing the evolution of the velocity distribution of n particles. In his derivation, he assumed a stochastic model based on binary collisions which preserves energy but not momentum. In this talk I will describe Kac's model and the main theorem of Kac's paper : that solutions with chaotic initial data can be related to the solutions Boltzmann type equation.

New model for cell phone signal problem

Series
SIAM Student Seminar
Time
Friday, January 24, 2014 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Li WuchenSchool of Mathematics, Georgia Tech
We introduce a new model for cell phone signal problem, which is stochastic van der Pol oscillator with condition that ensures global boundedness in phase space and keeps unboundedness for frequency. Also we give a new definition for stochastic Poincare map and find a new approximation to return time and point. The new definition is based on the numerical observation. Also we develop a new approach by using dynamic tools, such as method of averaging and relaxation method, to estimate the return time and return point. Thus we can show that the return time is always not Gaussian and return point's distribution is not symmetric under certain section.

TBA by Albert Bush

Series
SIAM Student Seminar
Time
Wednesday, October 9, 2013 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Albert Bush School of Mathematics, Georgia Tech
Erdos and Szemeredi conjectured that if one has a set of n numbers, one must have either the sumset or product set be of nearly maximal size, cn^2/log(n). In this talk, he will introduce the sum-product problem in the reals, show previous, beautiful geometric proofs by Solymosi and Elekes, and discuss some recent progress by Amirkhanyan, Croot, Pryby and Bush.

A characterization of 4-ordered cycle in planar graphs

Series
SIAM Student Seminar
Time
Friday, April 29, 2011 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 246
Speaker
Jie MaSchool of Mathematics, Georgia Tech
Fix k vertices in a graph G, say a_1,...,a_k, if there exists a cycle that visits these vertices with this specified order, we say such a cycle is (a_1,a_2,...,a_k)-ordered. It is shown by Thomas and Wollan that any 10k-connected graph is k-linked, therefore any 10k-connected graph has an (a_1,a_2,...,a_k)-ordered for any a_1,...,a_k. However, it is possible that we can improve this bound when k is small. It is shown by W. Goddard that any 4-connected maximal planar graph has an (a_1,...,a_4)-ordered cycle for any choice of 4 vertices. We will present a complete characterization of 4-ordered cycle in planar graphs. Namely, for any four vertices a,b,c,d in planar graph G, if there is no (a,b,c,d)-ordered cycle in G, then one of the follows holds: (1) there is a cut S separating {a,c} from {b,d} with |S|\leq 3; (2) roughly speaking, a,b,d,c "stay" in a face of G with this order.

Khovanov Homology and Slice Genus

Series
SIAM Student Seminar
Time
Friday, April 22, 2011 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 246
Speaker
Amey KalotiSchool of Mathematics, Georgia Tech

Please Note: Hosted also by Ben Webb

We will try to define what Khovanov homology for a link in a S^3 is. We will then try to give a proof figuring out unknotting number of certain kinds of knots in S^3.

Metropolis Light Transport and Spherical Harmonics in Computer Graphics Rendering

Series
SIAM Student Seminar
Time
Friday, April 8, 2011 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 246
Speaker
Nathan ParrishSchool of Electrical and Computer Engineering, Georgia Tech
The discussion will focus on some recent advances in improving performance of rendering 3D scenes. First, a Monte Carlo method based upon the Metropolis algorithm is described. Then a method of using spherical harmonics to generate vectors and matrices which allow efficient high-quality rendering in real time will be described. Finally, a discussion will be made of possible future areas for improving the efficiency of such algorithms.

On the Steinberg's Conjecture: 3-coloring of planar graphs

Series
SIAM Student Seminar
Time
Friday, April 1, 2011 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 246
Speaker
Peter WhalenSchool of Mathematics, Georgia Tech
Steinberg's Conjecture states that any planar graph without cycles of length four or five is three colorable. Borodin, Glebov, Montassier, and Raspaud showed that planar graphs without cycles of length four, five, or seven are three colorable and Borodin and Glebov showed that planar graphs without five cycles or triangles at distance at most two apart are three colorable. We prove a statement similar to both of these results: that any planar graph with no cycles of length four through six or cycles of length seven with incident triangles distance exactly two apart are three colorable. Special thanks to Robin Thomas for substantial contributions in the development of the proof.

A one-dimensional dynamical system with random switching

Series
SIAM Student Seminar
Time
Friday, March 18, 2011 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 246
Speaker
Tobias HurthSchool of Mathematics, Georgia Tech
We will study a simple dynamical system with two driving vector fields on the unit interval. The driving vector fields point to opposite directions, and we will follow the trajectory induced by one vector field for a random, exponentially distributed, amount of time before switching to the regime of the other one. Thanks to the simplicity of the system, we obtain an explicit formula for its invariant density. Basically exploiting analytic properties of this density, we derive versions of the law of large numbers, the central limit theorem and the large deviations principle for our system. If time permits, we will also discuss some ideas on how to prove existence of invariant densities, both in our one-dimensional setting and for more general systems with random switching. The talk will rely to a large extent on my Master's thesis I wrote last year under the guidance and supervision of Yuri Bakhtin.

Invariant Manifolds in Dynamical Systems

Series
SIAM Student Seminar
Time
Friday, December 3, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Nan LuSchool of Mathematics, Georgia Tech
In this talk, I am going to give a elementary introduction of invariant manifold theory in dynamical systems. I will start with the motivation and definition of invariant manifolds. Then I will discuss how to construct various invariant manifolds of maps and flows. Finally, I will discuss some applications. If time is permitted, I will also discuss a little about invariant foliation.

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