Seminars and Colloquia by Series

Where to place a hole to achieve fastest escape (What are the best sink and source in a network)

Series
School of Mathematics Colloquium
Time
Thursday, February 24, 2011 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Leonid Bunimovich – Georgia Institute of Technology
Consider any dynamical system with the phase space (set of all states) M. One gets an open dynamical system if M has a subset H (hole) such that any orbit escapes ("disappears") after hitting H. The question in the title naturally appears in dealing with some experiments in physics, in some problems in bioinformatics, in coding theory, etc. However this question was essentially ignored in the dynamical systems theory. It occurred that it has a simple and counter intuitive answer. It also brings about a new characterization of periodic orbits in chaotic dynamical systems. Besides, a duality with Dynamical Networks allows to introduce dynamical characterization of the nodes (or edges) of Networks, which complements such static characterizations as centrality, betweenness, etc. Surprisingly this approach allows to obtain new results about such classical objects as Markov chains and introduce a hierarchy in the set of their states in regard of their ability to absorb or transmit an "information". Most of the results come from a finding that one can make finite (rather than traditional large) time predictions on behavior of dynamical systems even if they do not contain any small parameter. It looks plausible that a variety of problems in dynamical systems, probability, coding, imaging ... could be attacked now. No preliminary knowledge is required. The talk will be accessible to students.

Convergence to equilibrium for a thin-film equation

Series
Math Physics Seminar
Time
Wednesday, February 23, 2011 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Professor Almut Burchard – Department of Mathematics, University of Toronto
I will describe recent work with Marina Chugunovaand Ben Stephens on the evolution of a thin-filmequation that models a "coating flow" on a horizontalcylinder. Formally, the equation defines a gradientflow with respect to an energy that controls theH^1-norm.We show that for each given mass there exists aunique steady state, given by a droplet hanging from thebottom of the cylinder that meets the dry region withzero contact angle. The droplet minimizes the energy andattracts all strong solutions that satisfy certain energyand entropy inequalities. (Such solutions exist for arbitraryinitial values of finite energy and entropy, but it is notknown if they are unique.) The distance of any solutionfrom the steady state decays no faster than a power law.

Heat flow as gradient flow

Series
PDE Seminar
Time
Tuesday, February 22, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Nicola Gigli – University of Nice –
Aim of the talk is to make a survey on some recent results concerning analysis over spaces with Ricci curvature bounded from below. I will show that the heat flow in such setting can be equivalently built either as gradient flow of the natural Dirichlet energy in L^2 or as gradient flow if the relative entropy in the Wasserstein space. I will also show how such identification can lead to interesting analytic and geometric insights on the structures of the spaces themselves. From a collaboration with L.Ambrosio and G.Savare

Lecture series on the disjoint paths algorithm

Series
Graph Theory Seminar
Time
Monday, February 21, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 168
Speaker
Paul Wollan – Math, GT 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.

Chemotaxis in active suspensions

Series
Applied and Computational Mathematics Seminar
Time
Monday, February 21, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Enkeleida Lushi – NYU Math Dept.
Micro-organisms are known to respond to certain dissolved chemicalsubstances in their environment by moving preferentially away or towardtheir source in a process called chemotaxis. We study such chemotacticresponses at the population level when the micro-swimmers arehydrodynamically coupled to each-other as well as the chemicalconcentration. We include a chemotactic bias based on the known bacteriarun-and-tumble phenomenon in a kinetic model of motile suspension dynamicsdeveloped recently to study hydrodynamic interactions. The chemicalsubstance can be produced or consumed by the swimmers themselves, as wellas be advected by the fluid flows created by their movement. The linearstability analysis of the system will be discussed, as well as the entropyanalysis. Nonlinear dynamics are investigated using numerical simulationin two dimensions of the full system of equations. We show examples ofaggregation in suspensions of pullers (front-actuated swimmers) anddiscuss how chemotaxis affects the mixing flows in suspensions of pushers(rear-actuated swimmers). Last, I will discuss recent work on numericalsimulations of discrete particle/swimmer suspensions that have achemotactic bias.

Spinal Open Books and Symplectic Fillings

Series
Geometry Topology Seminar
Time
Monday, February 21, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jeremy Van Horn-Morris – AIM
A theorem of Chris Wendl allows you to completely characterize symplectic fillings of certain open book decompositions by factorizations of their monodromy into Dehn twists. Olga Plamenevskaya and I use this to generalize results of Eliashberg, McDuff and Lisca to classify the fillings of certain Lens spaces. I'll discuss this and a newer version of Wendl's theorem, joint with Wendl and Sam Lisi, this time for spinal open books, and discuss a few more applications.

Tail Risk: heuristics, definitions, some new results

Series
Mathematical Finance/Financial Engineering Seminar
Time
Friday, February 18, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 002
Speaker
Roger Cooke – Resources for the Future

Please Note: Hosted by Christian Houdre and Liang Peng

"Tail risk" refers to an 'unholy trinity' Fat Tails, Micro Correlations, and Tail Dependence, that confound traditional risk analysis and are very much under-appreciated. The talk illustrates this with some punchy data. Of great interest is the question: when does aggregation amplify tail dependence? I'll show some data and new results. Tail obesity is not well defined mathematically, we have at least three definitions, leptokurtic, regularly varying and subexponential. A measure of tail obesity for finite data sets is proposed, and some theoretical properties explored.

Long Arithmetic Progressions in Sumsets

Series
Combinatorics Seminar
Time
Friday, February 18, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ernie Croot – School of Math. Georgia Tech.
Fix a subset A of the group of integers mod N. In this talkI will discuss joint work with Izabella Laba, Olof Sisask and myselfon the length of the longest arithmetic progression in the sumset A+Ain terms of the density of the set A. The bounds we develop improve uponthe best that was previously known, due to Ben Green.

Nash Equilibria for a simple model of market with commodity money.

Series
Math Physics Seminar
Time
Wednesday, February 16, 2011 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Federico Bonetto – Georgia Tech
I'll present a simple model of market where the use of (commodity) money naturally arisefrom the agents interaction. I'll introduce the relevant notion of (Nash) equilibrium and discuss itsexistence and properties.

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