Seminars and Colloquia by Series

Complexity, Pattern Formation and Chaos in the heart; a combined experimental and applied math approach for the study of arrhythmias."

Series
Dynamical Systems Working Seminar
Time
Tuesday, February 26, 2013 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 06
Speaker
F. FentonGeorgia Tech (Physics)
The heart is an electro-mechanical system in which, under normal conditions, electrical waves propagate in a coordinated manner to initiate an efficient contraction. In pathologic states, propagation can destabilize and exhibit period-doubling bifurcations that can result in both quasiperiodic and spatiotemporally chaotic oscillations. In turn, these oscillations can lead to single or multiple rapidly rotating spiral or scroll waves that generate complex spatiotemporal patterns of activation that inhibit contraction and can be lethal if untreated. Despite much study, little is known about the actual mechanisms that initiate, perpetuate, and terminate reentrant waves in cardiac tissue. In this talk, I will discuss experimental and theoretical approaches to understanding the dynamics of cardiac arrhythmias. Then I will show how state-of-the-art voltage-sensitive fluorescent dyes can be used to image the electrical waves present in cardiac tissue, leading to new insights about their underlying dynamics. I will establish a relationship between the response of cardiac tissue to an electric field and the spatial distribution of heterogeneities in the scale-free coronary vascular structure. I will discuss how in response to a pulsed electric field E, these heterogeneities serve as nucleation sites for the generation of intramural electrical waves with a source density ?(E) and a characteristic time constant ? for tissue excitation that obeys a power law. These intramural wave sources permit targeting of electrical turbulence near the cores of the vortices of electrical activity that drive complex fibrillatory dynamics. Therefore, rapid synchronization of cardiac tissue and termination of fibrillation can be achieved with a series of low-energy pulses. I will finish with results showing the efficacy and clinical application of this novel low energy mechanism in vitro and in vivo. e

Research on elliptic operators and related function spaces

Series
PDE Seminar
Time
Tuesday, February 26, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Xu, MingJi'Nan University, Guangzhou, China
In the report, we give an introduction on our previous work mainly on elliptic operators and its related function spaces. Firstly we give the problem and its root, secondly we state the difficulties in such problems, at last we give some details about some of our recent work related to it.

Geometric combinatorics, graphs and hypergraphs

Series
Other Talks
Time
Monday, February 25, 2013 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Gil KalaiHebrew University and Yale University
In the lecture I will describe how several questions in geometric combinatorics translate into questions about graphs and hypergraphs. 1. Borsuk's problem. 2. Tverberg theorem and Tverberg's type problems. Tverberg's theorem asserts that (r-1)(d+1)+1 points in d-space can be divided into r parts whose convex hull intersect. I will discuss situations where less points admit such a partition and connections with graph theory. (For more background, look at this MO question Tverberg partitions with less than (r-1)(d+1)+1 points<http://mathoverflow.net/questions/88718/tverberg-partitions-with-less-than-r-1d11-points> ) 3. Helly type theorems and conditions on induced subgraphs and sub-hypergraphs. I will explain the origin to the following conjecture of Meshulam and me: There is an absolute upper bound for the chromatic number of graphs with no induced cycles of length divisible by 3. 4. Embedding of 2-dimensional complexes and high dimensional minors. I will discuss the following conjecture: A 2-dimensional simplicial complex with E edges and F 2-dimensional faces that can be embedded into 4-space satisfies F < 4e. (For more background see my post *F ≤ 4E*<http://gilkalai.wordpress.com/2013/02/01/f-4e/> )

Georgia Scientific Computing Symposium

Series
Other Talks
Time
Saturday, February 23, 2013 - 08:30 for 8 hours (full day)
Location
Georgia State University
Speaker
Georgia Scientific Computing SymposiumGeorgia State University
The purpose of the GSC Symposium is to provide an opportunity for professors, postdocs, and graduate students in the Atlanta area to meet in an informal setting, to exchange ideas, and to highlight local scientific computing research. Certainly, the symposium is open to whole mathematics and computer sciences communities. The previous meetings were held at Emory University (2009), Georgia Institute of Technology (2010), Emory University (2011) and University of Georgia (2012). The 2013 GSC Symposium will be held at the Georgia State University campus and is organized by Alexandra Smirnova and Vladimir Bondarenko in the Department of Mathematics and Statistics, Georgia State. The following researchers have agreed to give invited plenary lectures: Hao Gao, Department of Mathematics and Computer Science, Department of Radiology and Imaging Sciences, Emory University; Guillermo Goldsztein, School of Mathematics, Georgia Institute of Technology; Yi Jiang, Department of Mathematics and Statistics, Georgia State University; Caner Kazanci, Department of Mathematics, University of Georgia; Brani Vidakovic, College of Engineering, Georgia Institute of Technology. There will be poster sessions. Anyone attending this symposium may present a poster. We especially encourage graduate students and postdocs to use this opportunity displaying their research results. Please register at the Symposium website.

Long paths and cycles in random subgraphs of graphs with large minimum degree

Series
Combinatorics Seminar
Time
Friday, February 22, 2013 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Choongbum LeeM.I.T.
For a given finite graph G of minimum degree at least k, let G_{p} be a random subgraph of G obtained by taking each edge independently with probability p. We prove that (i) if p \ge \omega/k for a function \omega=\omega(k) that tends to infinity as k does, then G_p asymptotically almost surely contains a cycle (and thus a path) of length at least (1-o(1))k, and (ii) if p \ge (1+o(1))\ln k/k, then G_p asymptotically almost surely contains a path of length at least k. Our theorems extend classical results on paths and cycles in the binomial random graph, obtained by taking G to be the complete graph on k+1 vertices. Joint w/ Michael Krivelevich (Tel Aviv), Benny Sudakov (UCLA).

Resonances for manifolds with hyperbolic ends

Series
Math Physics Seminar
Time
Friday, February 22, 2013 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
David BorthwickEmory University
Abstract: In this talk we will survey some recent developments in the scattering theory of complete, infinite-volume manifolds with ends modeled on quotients of hyperbolic space. The theory of scattering resonances for such spaces is in many ways parallel to the classical case of eigenvalues on a compact Riemann surface. However, it is only relatively recently that progress has been made in understanding the distribution of these resonances. We will give some introduction to the theory of resonances in this context and try to sketch this recent progress. We will also discuss some interesting outstanding conjectures and present numerical evidence related to these.

The Riemann-Roch theorem for graphs and applications

Series
ACO Student Seminar
Time
Friday, February 22, 2013 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Matt BakerSchool of Mathematics, Georgia Tech
We will begin by formulating the Riemann-Roch theorem for graphs, due to the speaker and Norine. We will then describe some refinements and applications. Refinements include a Riemann-Roch theorem for tropical curves, proved by Gathmann-Kerber and Mikhalkin-Zharkov, and a Riemann-Roch theorem for metrized complexes of curves, proved by Amini and the speaker. Applications include a new proof by Cools-Draisma-Payne-Robeva of the Brill-Noether theorem in algebraic geometry, a generalization by Amini and the speaker of the Eisenbud-Harris theory of limit linear series, and a new Chabauty-Coleman style bound for the number of rational points on an algebraic curve over the rationals, proved recently by Katz and Zureick-Brown.

Conormals and contact homology VI

Series
Geometry Topology Working Seminar
Time
Friday, February 22, 2013 - 11:30 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
John EtnyreGa Tech
In this series of talks I will begin by discussing the idea of studying smooth manifolds and their submanifolds using the symplectic (and contact) geometry of their cotangent bundles. I will then discuss Legendrian contact homology, a powerful invariant of Legendrian submanifolds of contact manifolds. After discussing the theory of contact homology, examples and useful computational techniques, I will combine this with the conormal discussion to define Knot Contact Homology and discuss its many wonders properties and conjectures concerning its connection to other invariants of knots in S^3.

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