Seminars and Colloquia by Series

Series: PDE Seminar
Tuesday, September 8, 2009 - 15:05 , Location: Skiles 255 , Konstantina Trivisa , University of Maryland, College Park , Organizer:
Multicomponent reactive flows arise in many practical applicationssuch as combustion, atmospheric modelling, astrophysics, chemicalreactions, mathematical biology etc. The objective of this work isto develop a rigorous mathematical theory based on the principles ofcontinuum mechanics. Results on existence, stability, asymptotics as wellas singular limits will be discussed.
Monday, September 7, 2009 - 14:00 , Location: - , - , - , Organizer: John Etnyre
Friday, September 4, 2009 - 15:00 , Location: Skiles 255 , Karthekeyan Chandrasekaran , College of Computing , Organizer: Prasad Tetali
Lovasz Local Lemma (LLL) is a powerful result in probability theory that states that the probability that none of a set of bad events happens is nonzero if the probability of each event is small compared to the number of events that depend on it. It is often used in combination with the probabilistic method for non-constructive existence proofs. A prominent application of LLL is to k-CNF formulas, where LLL implies that, if every clause in the formula shares variables with at most d \le 2^k/e other clauses then such a formula has a satisfying assignment. Recently, a randomized algorithm to efficiently construct a satisfying assignment was given by Moser. Subsequently Moser and Tardos gave a randomized algorithm to construct the structures guaranteed by the LLL in a very general algorithmic framework. We will address the main problem left open by Moser and Tardos of derandomizing their algorithm efficiently when the number of other events that any bad event depends on is possibly unbounded. An interesting special case of the open problem is the k-CNF problem when k = \omega(1), that is, when k is more than a constant.
Friday, September 4, 2009 - 13:00 , Location: Skiles 255 , Maria Reguera Rodriguez , Georgia Tech , , Organizer:
In this talk we will review some of the classical weighted theory for singular integral operators, and discuss some recent progress on finding sharp bounds in terms of the A_p constant associated with the weight
Thursday, September 3, 2009 - 16:00 , Location: Skiles 269 , Lincoln Chayes , UCLA , , Organizer: Michael Loss
The McK--V system is a non--linear diffusion equation with a non--local non--linearity provided by convolution.  Recently popular in a variety of applications, it enjoys an ancient heritage as a basis for understanding equilibrium and near equilibrium fluids.  The model is discussed in finite volume where, on the basis of the physical considerations, the correct scaling (for the model itself) is identified.  For dimension two and above and in large volume, the phase structure of the model is completely elucidated in (somewhat disturbing) contrast to dynamical results.  This seminar represents joint work with V. Panferov.
Thursday, September 3, 2009 - 15:00 , Location: Skiles 269 , Philippe Rigollet , Princeton University , Organizer:
The goal of this talk is to present a new method for sparse estimation which does not use standard techniques such as $\ell_1$ penalization. First, we introduce a new setup for aggregation which bears strong links with generalized linear models and thus encompasses various response models such as Gaussian regression and binary classification. Second, by combining maximum likelihood estimators using exponential weights we derive a new procedure for sparse estimations which satisfies exact oracle inequalities with the desired remainder term. Even though the procedure is simple, its implementation is not straightforward but it can be approximated using the Metropolis algorithm which results in a stochastic greedy algorithm and performs surprisingly well in a simulated problem of sparse recovery.
Thursday, September 3, 2009 - 12:05 , Location: Skiles 255 , William T. Trotter , School of Mathematics, Georgia Tech , Organizer: Robin Thomas
We will discuss the classic theorem of Walter Schnyder: a graph G is planar if and only if the dimension of its incidence poset is at most 3. This result has been extended by Brightwell and Trotter to show that the dimension of the vertex-edge-face poset of a planar 3-connected graph is 4 and the removal of any vertex (or by duality, any face) reduces the dimension to 3. Recently, this result and its extension to planar multigraphs was key to resolving the question of the dimension of the adjacency poset of a planar bipartite graph. It also serves to motivate questions about the dimension of posets with planar cover graphs.
Wednesday, September 2, 2009 - 14:00 , Location: Skiles 269 , Michael Lacey , Georgia Institute of Technology , Organizer:
We will survey recent developments in the area of two weight inequalities, especially those relevant for singular integrals.  In the second lecture, we will go into some details of recent characterizations of maximal singular integrals of the speaker, Eric Sawyer, and Ignacio Uriate-Tuero.
Wednesday, September 2, 2009 - 14:00 , Location: ISyE Executive Classroom , Ernie Croot , School of Mathematics , Organizer: Annette Rohrs
Sum-Product inequalities originated in the early 80's with the work of Erdos and Szemeredi, who showed that there exists a constant c such that if A is a set of n integers, n sufficiently large, then either the sumset A+A = {a+b : a,b in A} or the product set A.A = {ab : a,b in A}, must exceed n^(1+c) in size. Since that time the subject has exploded with a vast number of generalizations and extensions of the basic result, which has led to many very interesting unsolved problems (that would make great thesis topics). In this talk I will survey some of the developments in this fast-growing area.
Series: Other Talks
Wednesday, September 2, 2009 - 13:00 , Location: Skiles 255 , John Etnyre , Ga Tech , Organizer: John Etnyre
In these talks we will introduced the basic definitions and examples of presheaves, sheaves and sheaf spaces. We will also explore various constructions and properties of these objects.