Seminars and Colloquia by Series

State Transitions and Feedback Loops in the Immune Response

Series
Job Candidate Talk
Time
Tuesday, February 1, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Peter Kim – University of Utah –
The immune system is a complex, multi-layered biological system, making it difficult to characterize dynamically. Perhaps, we can better understand the system’s construction by isolating critical, functional motifs. From this perspective, we will investigate two simple, yet ubiquitous motifs:state transitions and feedback regulation.Numerous immune cells exhibit transitions from inactive to activated states. We focus on the T cell response and develop a model of activation, expansion, and contraction. Our study suggests that state transitions enable T cells to detect change and respond effectively to changes in antigen levels, rather than simply the presence or absence of antigen. A key component of the system that gives rise to this change detector is initial activation of naive T cells. The activation step creates a barrier that separates the slow dynamics of naive T cells from the fast dynamics of effector T cells, allowing the T cell population to compare short-term changes in antigen levels to long-term levels. As a result, the T cell population responds to sudden shifts in antigen levels, even if the antigen were already present prior to the change. This feature provides a mechanism for T cells to react to rapidly expandingsources of antigen, such as viruses, while maintaining tolerance to constant or slowly fluctuating sources of stimulation, such as healthy tissue during growth.For our second functional motif, we investigate the potential role of negative feedback in regulating a primary T cell response. Several theories exist concerning the regulation of primary T cell responses, the most prevalent being that T cells follow developmental programs. We propose an alternative hypothesis that the response is governed by a feedback loop between conventional and adaptive regulatory T cells. By developing a mathematical model, we show that the regulated response is robust to a variety of parameters and propose that T cell responses may be governed by a simple feedback loop rather than by autonomous cellular programs.

PDE Methods for Cardiovascular Treatment

Series
PDE Seminar
Time
Tuesday, February 1, 2011 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Suncica Canic – Department of Mathematics, University of Houston –
Mathematical modeling, analysis and numerical simulation, combined with imagingand experimental validation, provide a powerful tool for studying various aspects ofcardiovascular treatment and diagnosis. At the same time, problems motivated bycardiovascular applications give rise to mathematical problems whose studyrequires the development of sophisticated mathematical techniques. This talk willaddress two examples where such a synergy led to novel mathematical results anddirections. The first example concerns a mathematical study of the benchmarkproblem of fluid‐structure interaction (FSI) in blood flow. The resulting problem is anonlinear moving‐boundary problem coupling the flow of a viscous, incompressiblefluid with the motion of a linearly viscoelastic membrane/shell. An existence resultfor an effective, reduced model will be presented.The second example concerns a novel dimension reduction/multi‐scale approach tomodeling of endovascular stents as 3D meshes of 1D curved rods. The resultingmodel is in the form of a nonlinear hyperbolic network, for which no generalexistence results are available. The modeling background and the challenges relatedto the analysis of the solutions will be presented. An application to the study of themechanical properties of the currently available coronary stents on the US marketwill be shown.This talk will be accessible to a wide scientific audience.Collaborators include: Josip Tambaca (University of Zagreb, Croatia), Ando Mikelic(University of Lyon 1, France), Dr. David Paniagua (Texas Heart Institute), and Dr.Stephen Little (Methodist Hospital in Houston).

Lecture series on the disjoint paths algorithm

Series
Graph Theory Seminar
Time
Monday, January 31, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 168
Speaker
Paul Wollan – GT, Math and University of Rome
The k-disjoint paths problem takes as input a graph G and k pairs of vertices (s_1, t_1),..., (s_k, t_k) and determines if there exist internally disjoint paths P_1,..., P_k such that the endpoints of P_i are s_i and t_i for all i=1,2,...,k. While the problem is NP-complete when k is allowed to be part of the input, Robertson and Seymour showed that there exists a polynomial time algorithm for fixed values of k. The existence of such an algorithm is the major algorithmic result of the Graph Minors series. The original proof of Robertson and Seymour relies on the whole theory of graph minors, and consequently is both quite technical and involved. Recent results have dramatically simplified the proof to the point where it is now feasible to present the proof in its entirety. This seminar series will do just that, with the level of detail aimed at a graduate student level.

Decomposing an infinite matroid into its 3-connected minors

Series
Combinatorics Seminar
Time
Friday, January 28, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Luke Postle – School of Math. Georgia Tech.
We extend the theory of infinite matroids recently developed by Bruhn et al to a well-known classical result in finite matroids while using the theory of connectivity for infinitematroids of Bruhn and Wollan. We prove that every infinite connected matroid M determines a graph-theoretic decomposition tree whose vertices correspond to minors of M that are3-connected, circuits, or cocircuits, and whose edges correspond to 2-separations of M. Tutte and many other authors proved such a decomposition for finite graphs; Cunningham andEdmonds proved this for finite matroids and showed that this decomposition is unique if circuits and cocircuits are also allowed. We do the same for infinite matroids. The knownproofs of these results, which use rank and induction arguments, do not extend to infinite matroids. Our proof avoids such arguments, thus giving a more first principles proof ofthe finite result. Furthermore, we overcome a number of complications arising from the infinite nature of the problem, ranging from the very existence of 2-sums to proving the treeis actually graph-theoretic.

Gromov's knot distortion

Series
Geometry Topology Seminar
Time
Friday, January 28, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
John Pardon – Princeton University –
Gromov defined the distortion of an embedding of S^1 into R^3 and asked whether every knot could be embedded with distortion less than 100. There are (many) wild embeddings of S^1 into R^3 with finite distortion, and this is one reason why bounding the distortion of a given knot class is hard. I will show how to give a nontrivial lower bound on the distortion of torus knots, which is sharp in the case of (p,p+1) torus knots. I will also mention some natural conjectures about the distortion, for example that the distortion of the (2,p)-torus knots is unbounded.

Generalized Fiducial Inference and Its Application to Wavelet Regression

Series
Stochastics Seminar
Time
Thursday, January 27, 2011 - 16:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Thomas Lee – University of California, Davis
In this talk we re-visit Fisher's controversial fiducial technique for conducting statistical inference. In particular, a generalization of Fisher's technique, termed generalized fiducial inference, is introduced. We illustrate its use with wavelet regression. Current and future work for generalized fiducial inference will also be discussed. Joint work with Jan Hannig and Hari Iyer

Global Testing under Sparse Alternatives: ANOVA, Multiple Comparisons and the Higher Criticism

Series
Stochastics Seminar
Time
Thursday, January 27, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ery Arias-Castro – University of California, San Diego
We study the problem of testing for the significance of a subset of regression coefficients in a linear model under the assumption that the coefficient vector is sparse, a common situation in modern high-dimensional settings.  Assume there are p variables and let S be the number of nonzero coefficients.  Under moderate sparsity levels, when we may have S > p^(1/2), we show that the analysis of variance F-test is essentially optimal.  This is no longer the case under the sparsity constraint S < p^(1/2).  In such settings, a multiple comparison procedure is often preferred and we establish its optimality under the stronger assumption S < p^(1/4).  However, these two very popular methods are suboptimal, and sometimes powerless, when p^(1/4) < S < p^(1/2).  We suggest a method based on the Higher Criticism that is essentially optimal in the whole range S < p^(1/2).  We establish these results under a variety of designs, including the classical (balanced) multi-way designs and more modern `p > n' designs arising in genetics and signal processing. (Joint work with Emmanuel Candès and Yaniv Plan.)

Evolution problem in General Relativity

Series
School of Mathematics Colloquium
Time
Thursday, January 27, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Igor Rodnianski – Princeton University
The talk will introduce basic mathematical concepts of General Relativity and review the progress, main challenges and open problems, viewed through the prism of the evolution problem. I will illustrate interaction of Geometry and PDE methods in the context of General Relativity on examples ranging from incompleteness theorems and formation of trapped surfaces to geometric properties of black holes and their stability.

A diagrammatic categorification of quantum groups

Series
Job Candidate Talk
Time
Wednesday, January 26, 2011 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Aaron Lauda – Columbia University
The Jones polynomial is a link invariant that can be understood in terms of the representation theory of the quantum group associated to sl2. This description facilitated a vast generalization of the Jones polynomial to other quantum link and tangle invariants called Reshetikhin-Turaev invariants. These invariants, which arise from representations of quantum groups associated to simple Lie algebras, subsequently led to the definition of quantum 3-manifold invariants. In this talk we categorify quantum groups using a simple diagrammatic calculus that requires no previous knowledge of quantum groups. These diagrammatically categorified quantum groups not only lead to a representation theoretic explanation of Khovanov homology but also inspired Webster's recent work categorifying all Reshetikhin-Turaev invariants of tangles.

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