Seminars and Colloquia by Series

A parametrization method for invariant manifolds of periodic orbits, with applications to the restricted three body problem.

Series
CDSNS Colloquium
Time
Monday, January 28, 2013 - 16:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Maciej Capinski – Georgia Tech and AGH Univ. Krakow –
We present a method for the detection of stable and unstable fibers of invariant manifolds of periodic orbits. We show how to propagate the fibers to prove transversal intersections of invariant manifolds. The method can be applied using interval arithmetic to produce rigorous, computer assisted estimates for the manifolds. We apply the method to prove transversal intersections of stable and unstable manifolds of Lyapunov orbits in the restricted three body problem.

Symplectic structures on cotangent bundles of open 4-manifolds

Series
Geometry Topology Seminar
Time
Monday, January 28, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Adam Knapp – Columbia University
Given any smooth manifold, there is a canonical symplectic structure on its cotangent bundle. A long standing idea of Arnol'd suggests that the symplectic topology of the cotangent bundle should contain a great deal of information about the smooth topology of its base. As a contrast, I show that when X is an open 4-manifold, this symplectic structure on T^*X does not depend on the choice of smooth structure on X. I will also discuss the particular cases of smooth structures on R^4 and once-punctured compact 4-manifolds.

An algebraic proof of the Szemeredi-Trotter Theorem

Series
Combinatorics Seminar
Time
Friday, January 25, 2013 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Ernie Croot – Georgia Tech
This talk will be on an algebraic proof of theSzemeredi-Trotter theorem, as given by Kaplan, Matousek and Sharir.The lecture assumes no prior knowledge of advanced algebra.

Coordinate Gradient Descent Method and Incremental Gradient Method for Nonsmooth Optimization

Series
Applied and Computational Mathematics Seminar
Time
Friday, January 25, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Sangwoon Yun – Sung Kyun Kwan Univ. (Korea) –
In this talk, we introduce coordinate gradient descent methods for nonsmooth separable minimization whose objective function is the sum of a smooth function and a convex separable function and for linearly constrained smooth minimization. We also introduce incremental gradient methods for nonsmooth minimization whose objective function is the sum of smooth functions and a convex function.

Conormals and contact homology II

Series
Geometry Topology Working Seminar
Time
Friday, January 25, 2013 - 11:30 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
John Etnyre – Ga 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.

Lincoln and Atlanta

Series
Other Talks
Time
Thursday, January 24, 2013 - 16:30 for 1 hour (actually 50 minutes)
Location
Clough Commons Auditorium
Speaker
Charlie Crawford – School of Mathematics, Alumnus

Please Note: Mr. Crawford grew up near Philadelphia and has a B.S. in Applied Mathematics from Georgia Tech. He served as an Air Force officer, retiring as a colonel in 1996. In addition to being a member of Georgia Battlefields Association and the Civil War Round Table of Atlanta, Charlie is a life member of the Civil War Trust.

Charlie Crawford, president of Georgia Battlefields Association, explores the significance of the fall of Atlanta to Lincoln's re-election as President and examines George Barnard's photographic documentation of the battlefields around Atlanta. Crawford will discuss how land that is now a part of Georgia Tech's campus was once the site of Confederate and Federal fortifications. As president of Georgia Battlefields Association, a non-profit battlefield preservation group, Mr. Crawford has made over 95 presentations and led over 35 tours relating to the Civil War in Georgia.

Clique Number of Random Geometric Graphs in High Dimension

Series
Stochastics Seminar
Time
Thursday, January 24, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skyles 006
Speaker
Sebastien Bubeck – Princeton University
In small dimension a random geometric graph behaves very differently from a standard Erdös-Rényi random graph. On the other hand when the dimension tends to infinity (with the number of vertices being fixed) both models coincides. In this talk we study the behavior of the clique number of random geometric graphs when the dimension grows with the number of vertices.

Mixing in fluid flow

Series
Job Candidate Talk
Time
Thursday, January 24, 2013 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alexander Kiselev – University of Wisconsin, Madison
Mixing by fluid flow is important in a variety of situations in nature and technology. One effect fluid motion can have is to strongly enhance diffusion. The extent of diffusion enhancement depends on the properties of the flow. I will give an overview of the area, and will discuss a sharp criterion describing a class of incompressible flows that are especially effective mixers. The criterion uses spectral properties of the dynamical system associated with the flow, and is derived from a general result on decay rates for dissipative semigroups of certain structure. The proofs rely on methods developed in studies of wavepacket spreading in mathematical quantum mechanics.

Knots and Dynamics II

Series
Geometry Topology Student Seminar
Time
Wednesday, January 23, 2013 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 006.
Speaker
Amey Kaloti – Georgia Tech
This is continuation of talk from last week. Periodic orbits of flows on $3$ manifolds show very rich structure. In this talk we will try to prove a theorem of Ghrist, which states that, there exists vector fields on $S^3$ whose set of periodic orbits contains every possible knot and link in $S^3$. The proof relies on template theory.

Supersingular curves

Series
Research Horizons Seminar
Time
Wednesday, January 23, 2013 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Doug Ulmer – Georgia Tech, School of Math
I will review a little bit of the theory of algebric curves, which essentialy amounts to studying the zero set of a two-variable polynomial. There are several amazing facts about the number of points on a curve when the ground field is finite. (This particular case has many applications to cryptography and coding theory.) An open problem in this area is whether there exist "supersingular" curves of every genus. (I'll explain the terminology, which has something to do with having many points or few points.) A new project I have just started should go some way toward resolving this question.

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