## Seminars and Colloquia by Series

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.
Series: PDE Seminar
Tuesday, September 1, 2009 - 15:00 , Location: Skiles 255 , Lincoln Chayes , UCLA , Organizer: Zhiwu Lin
This seminar concerns the analysis of a PDE, invented by J.M. Lasry and P.L. Lions whose applications need not concern us. Notwithstanding, the focus of the application is the behavior of a free boundary in a diffusion equation which has dynamically evolving, non--standard sources.  Global existence and uniqueness are established for this system.  The work to be discussed represents a collaborative effort with Maria del Mar Gonzalez, Maria Pia Gualdani and Inwon Kim.
Monday, August 31, 2009 - 14:01 , Location: Skiles 269 , , Section de Mathématiques Université de Genève , , Organizer: Stavros Garoufalidis
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Monday, August 31, 2009 - 13:00 , Location: Skiles 255 , , Università di L'Aquila , , Organizer: Sung Ha Kang
In this talk I will address the problem of the computation of the jointspectral radius (j.s.r.) of a set of matrices.This tool is useful to determine uniform stability properties of non-autonomous discrete linear systems. After explaining how to extend the spectral radius from a single matrixto a set of matrices and illustrate some applications where such conceptplays an important role I will consider the problem of the computation ofthe j.s.r. and illustrate some possible strategies.  A basic tool I willuse to this purpose consists of polytope norms, both real and complex.I will illustrate a possible algorithm for the computation of the j.s.r. ofa family of matrices which is based on the use of these classes of norms.Some examples will be shown to illustrate the behaviour of the algorithm.Finally I will address the problem of the finite computability of the j.s.r.and state some recent results, open problems and conjectures connected withthis issue.
Thursday, August 27, 2009 - 15:00 , Location: Skiles 269 , Dabao Zhang , Purdue University , Organizer:
We propose a penalized orthogonal-components regression (POCRE) for large p small n data. Orthogonal components are sequentially constructed to maximize, upon standardization, their correlation to the response residuals. A new penalization framework, implemented via empirical Bayes thresholding, is presented to effectively identify sparse predictors of each component. POCRE is computationally efficient owing to its sequential construction of leading sparse principal components. In addition, such construction offers other properties such as grouping highly correlated predictors and allowing for collinear or nearly collinear predictors. With multivariate responses, POCRE can construct common components and thus build up latent-variable models for large p small n data. This is an joint work with Yanzhu Lin and Min Zhang