Seminars and Colloquia by Series

Stochastic Discrete Dynamical Systems

Series
Mathematical Biology Seminar
Time
Wednesday, April 18, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
David Murrugarra – Virginia Tech
Modeling stochasticity in gene regulation is an important and complex problem in molecular systems biology. This talk will introduce a stochastic modeling framework for gene regulatory networks. This framework incorporates propensity parameters for activation and degradation and is able to capture the cell-to-cell variability. It will be presented in the context of finite dynamical systems, where each gene can take on a finite number of states and where time is a discrete variable. One of the new features of this framework is that it allows a finer analysis of discrete models and the possibility to simulate cell populations. A background to stochastic modeling will be given and applications will use two of the best known stochastic regulatory networks, the outcome of lambda phage infection of bacteria and the p53-mdm2 complex.

Cellular Cuts, Flows, Critical Groups, and Cocritical Groups

Series
Algebra Seminar
Time
Tuesday, April 17, 2012 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jeremy Martin – University of Kansas –
The critical group of a graph G is an abelian group K(G) whose order is the number of spanning forests of G. As shown by Bacher, de la Harpe and Nagnibeda, the group K(G) has several equivalent presentations in terms of the lattices of integer cuts and flows on G. The motivation for this talk is to generalize this theory from graphs to CW-complexes, building on our earlier work on cellular spanning forests. A feature of the higher-dimensional case is the breaking of symmetry between cuts and flows. Accordingly, we introduce and study two invariants of X: the critical group K(X) and the cocritical group K^*(X), As in the graph case, these are defined in terms of combinatorial Laplacian operators, but they are no longer isomorphic; rather, the relationship between them is expressed in terms of short exact sequences involving torsion homology. In the special case that X is a graph, torsion vanishes and all group invariants are isomorphic, recovering the theorem of Bacher, de la Harpe and Nagnibeda. This is joint work with Art Duval (University of Texas, El Paso) and Caroline Klivans (Brown University).

Introduction to Synthetic-Aperture Radar Imaging

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 16, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Margaret Cheney – Rensselaer Polytechnic Institute
Radar imaging is a technology that has been developed, verysuccessfully, within the engineering community during the last 50years. Radar systems on satellites now make beautiful images ofregions of our earth and of other planets such as Venus. One of thekey components of this impressive technology is mathematics, and manyof the open problems are mathematical ones.This lecture will explain, from first principles, some of the basicsof radar and the mathematics involved in producing high-resolutionradar images.

Grid Movie Moves and Combinatorial Knot Floer Homology

Series
Geometry Topology Seminar
Time
Monday, April 16, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Matt Graham – Brandeis University
Recently, Sarkar showed that a smooth marked cobordism between two knots K_1 , K_2 induces a map between the knot Floer homology groups of the two knots HFK(K_1 ), HFK(K_2 ). It has been conjectured that this map is well defined (with respect to smooth marked cobordisms). After outlining what needs to be shown to prove this conjecture, I will present my current progress towards showing this result for the combinatorial version of HFK. Specifically, I will present a generalization of Carter and Saito's movie move theorem to grid diagrams, give a very brief introduction to combinatorial knot Floer homology and then present a couple of the required chain homotopies needed for the proof of the conjecture.

Wave run-up on random and deterministic beaches

Series
Math Physics Seminar
Time
Monday, April 16, 2012 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Denis Dukyth – CNRS/Univ. of Savoie
The phenomenon of wave run-up has the capital importance for the beach erosion, coastal protection and flood hazard estimation. In the present talk we will discuss two particular aspects of the wave run-up problem. In this talk we focus on the wave run-up phenomena on a sloping beach. In the first part of the talk we present a simple stochastic model of the bottom roughness. Then, we quantify the roughness effect onto the maximal run-up height using Monte-Carlo simulations. A critical comparison with more conventional approaches is also performed.In the second part of the talk we study the run-up of simple wave groups on beaches of various geometries. Some resonant amplification phenomena are unveiled. The maximal run-up height in resonant cases can be 20 times higher than in regular situations. Thus, this work can provide a possible mechanism of extreme tsunami run-up conventionally ascribed to "local site effects".References:Dutykh, D., Labart, C., & Mitsotakis, D. (2011). Long wave run-up on random beaches. Phys. Rev. Lett, 107, 184504.Stefanakis, T., Dias, F., & Dutykh, D. (2011). Local Runup Amplification by Resonant Wave Interactions. Phys. Rev. Lett., 107, 124502.

Circle homeomorphisms with singularity points.

Series
CDSNS Colloquium
Time
Monday, April 16, 2012 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Akhtam Djalilov – Univ. of Samarkand and CUNY Stony Brook
An important question in circle dynamics is regarding the absolute continuity of an invariant measure. We will consider orientation preserving circle homeomorphisms with break points, that is, maps that are smooth everywhere except for several singular points at which the first derivative has a jump. It is well known that the invariant measures of sufficiently smooth circle dieomorphisms are absolutely continuous w.r.t. Lebesgue measure. But in the case of homeomorphisms with break points the results are quite dierent. We will discuss conjugacies between two circle homeomorphisms with break points. Consider the class of circle homeomorphisms with one break point b and satisfying the Katznelson-Ornsteins smoothness condition i.e. Df is absolutely continuous on [b; b + 1] and D2f 2 Lp(S1; dl); p > 1: We will formulate some results concerning the renormaliza- tion behavior of such circle maps.

Discrete Mathematical Biology Working Seminar

Series
Other Talks
Time
Monday, April 16, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Svetlana Poznanovik – Georgia Tech
A discussion of the paper "Evaluation of the information content of RNA structure mapping data for secondary structure prediction" by Quarrier et al (RNA, 2010).

The size of a hypergraph and its matching number

Series
Combinatorics Seminar
Time
Friday, April 13, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Huang Hao – Math, UCLA
More than 40 years ago, Erdos asked to determine the maximum possible number of edges in a k-uniform hypergraph on n vertices with no matching of size t (i.e., with no t disjoint edges). Although this is one of the most basic problem on hypergraphs, progress on Erdos' question remained elusive. In addition to being important in its own right, this problem has several interesting applications. In this talk we present a solution of Erdos' question for t

Plane fields on 3-manifolds III

Series
Geometry Topology Working Seminar
Time
Friday, April 13, 2012 - 14:00 for 2 hours
Location
Skiles 006
Speaker
John Etnyre – Ga Tech

Please Note: Note this is a 2 hour talk.

In this series of talks I will discuss various special plane fields on 3-manifold. Specifically we will consider folaitions and contact structures and the relationship between them. We will begin by sketching a proof of Eliashberg and Thurston's famous theorem from the 1990's that says any sufficiently smooth foliation can be approximated by a contact structure. In the remaining talks I will discuss ongoing research that sharpens our understanding of the relation between foliations and contact structures.

Variational problems and PDEs arising in congested transport models

Series
PDE Seminar
Time
Thursday, April 12, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Guillaume Carlier – Universite de Paris IX (Paris-Dauphine)
In this talk, I will describe several models arising in congested transport problems. I will first describe static models which lead to some highly degenerate elliptic PDEs. In the second part of the talk, I will address dynamic models which can be seen as a generalization of the Benamou-Brenier formulation of the quadratic optimal transport problem and will discuss the existence and regularity of the adjoint state. The talk will be based on several joint works with Lorenzo Brasco, Pierre Cardaliaguet, Bruno Nazaret and Filippo Santambrogio.

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