Seminars and Colloquia by Series

Sparsity pattern aggregation in generalized linear models.

Series
Stochastics Seminar
Time
Thursday, September 3, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Philippe Rigollet – Princeton University
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.

Planar Graphs and Planar Posets II

Series
Graph Theory Seminar
Time
Thursday, September 3, 2009 - 12:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
William T. Trotter – School of Mathematics, Georgia Tech
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.

Sum-Product Inequalities

Series
ACO Student Seminar
Time
Wednesday, September 2, 2009 - 14:00 for 1 hour (actually 50 minutes)
Location
ISyE Executive Classroom
Speaker
Ernie Croot – School of Mathematics
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.

Two weight inequalities for singular integrals, Continued

Series
Analysis Seminar
Time
Wednesday, September 2, 2009 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Michael Lacey – Georgia Institute of Technology
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.

Introduction to Sheaf Theory

Series
Other Talks
Time
Wednesday, September 2, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
John Etnyre – Ga Tech
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.

Global Existence of a Free Boundary Problem with Non--Standard Sources

Series
PDE Seminar
Time
Tuesday, September 1, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Lincoln Chayes – UCLA
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.

The joint spectral radius of a set of matrices: theoretical and computational aspects.

Series
Applied and Computational Mathematics Seminar
Time
Monday, August 31, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Nicola Guglielmi – Università di L'Aquila –
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.

Penalized orthogonal-components regression for large p small n data

Series
Stochastics Seminar
Time
Thursday, August 27, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Dabao Zhang – Purdue University
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

Planar graphs and planar posets

Series
Graph Theory Seminar
Time
Thursday, August 27, 2009 - 12:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
William T. Trotter – Math, GT
Slightly modifying a quote of Paul Erdos: The problem for graphs we solve this week. The corresponding problem for posets will take longer. As one example, testing a graph to determine if it is planar is linear in the number of edges. Testing an order (Hasse) diagram to determine if it is planar is NP-complete. As a second example, it is NP-complete to determine whether a graph is a cover graph. With these remarks in mind, we present some results, mostly new but some classic, regarding posets with planar cover graphs and planar diagrams. The most recent result is that for every h, there is a constant c_h so that if P is a poset of height h and the cover graph of P is planar, then the dimension of P is at most c_h.

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