Seminars and Colloquia by Series

Singularity theory for nontwist tori: from rigorous results to computations

Series
CDSNS Colloquium
Time
Monday, April 13, 2015 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Alex Haro – Univ. of Barcelona
We present a method to find KAM tori with fixed frequency in degenerate cases, in which the Birkhoff normal form is singular. The method provides a natural classification of KAM tori which is based on Singularity Theory. The method also leads to effective algorithms of computation, and we present some numerical results up to the verge of breakdown. This is a joint work with Alejandra Gonzalez and Rafael de la Llave.

Atlanta Lecture Series in Combinatorics and Graph Theory XV

Series
Other Talks
Time
Saturday, April 11, 2015 - 13:00 for 4 hours (half day)
Location
Skiles 006
Speaker
David Conlon – University of Oxford
Emory University, Georgia Tech and Georgia State University, with support from the National Science Foundation, will continue the series of mini-conferences and host a series of 9 new mini-conferences from 2014-2017. The 15th of these mini-conferences will be held at Georgia Tech during April 11-12, 2015. The conferences will stress a variety of areas and feature one prominent researcher giving 2 fifty minute lectures and 4 outstanding researchers each giving one fifty minute lecture. There will also be several 25 minute lecturers by younger researchers or graduate students. For more details, see the schedule

Introduction to regularity theory of second order Hamilton-Jacobi-Bellman equations

Series
PDE Working Seminar
Time
Friday, April 10, 2015 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 202
Speaker
Andrzej Swiech – Georgia Tech
I will give a series of elementary lectures presenting basic regularity theory of second order HJB equations. I will introduce the notion of viscosity solution and I will discuss basic techniques, including probabilistic techniques and representation formulas. Regularity results will be discussed in three cases: degenerate elliptic/parabolic, weakly nondegenerate, and uniformly elliptic/parabolic.

Reciprocal linear spaces and their Chow forms

Series
Algebra Seminar
Time
Friday, April 10, 2015 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Cynthia Vinzant – North Carolina State
A reciprocal linear space is the image of a linear space under coordinate-wise inversion. This nice algebraic variety appears in many contexts and its structure is governed by the combinatorics of the underlying hyperplane arrangement. A reciprocal linear space is also an example of a hyperbolic variety, meaning that there is a family of linear spaces all of whose intersections with it are real. This special real structure is witnessed by a determinantal representation of its Chow form in the Grassmannian. In this talk, I will introduce reciprocal linear spaces and discuss the relation of their algebraic properties to their combinatorial and real structure.

Compactness on Multidimensional Steady Euler Equations

Series
PDE Seminar
Time
Thursday, April 9, 2015 - 15:05 for 1 hour (actually 50 minutes)
Location
Skile 005
Speaker
Tian-Yi Wang – The Chinese University of Hong Kong
This is a special PDE seminar in Skiles 005. In this talk, we will introduce the compactness framework for approximate solutions to sonic-subsonic flows governed by the irrotational steady compressible Euler equations in arbitrary dimension. After that, similar results will be presented for the isentropic case. As a direct application, we establish several existence theorems for multidimensional sonic-subsonic Euler flows. Also, we will show the recent progress on the incompressible limits.

Bipartite Kneser graphs are Hamiltonian

Series
Graph Theory Seminar
Time
Thursday, April 9, 2015 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Torsten Muetze – School of Mathematics, Georgia Tech and ETH Zurich
For integers k>=1 and n>=2k+1, the bipartite Kneser graph H(n,k) is defined as the graph that has as vertices all k-element and all (n-k)-element subsets of {1,2,...,n}, with an edge between any two vertices (=sets) where one is a subset of the other. It has long been conjectured that all bipartite Kneser graphs have a Hamilton cycle. The special case of this conjecture concerning the Hamiltonicity of the graph H(2k+1,k) became known as the 'middle levels conjecture' or 'revolving door conjecture', and has attracted particular attention over the last 30 years. One of the motivations for tackling these problems is an even more general conjecture due to Lovasz, which asserts that in fact every connected vertex-transitive graph (as e.g. H(n,k)) has a Hamilton cycle (apart from five exceptional graphs). Last week I presented a (rather technical) proof of the middle levels conjecture. In this talk I present a simple and short proof that all bipartite Kneser graphs H(n,k) have a Hamilton cycle (assuming that H(2k+1,k) has one). No prior knowledge will be assumed for this talk (having attended the first talk is not a prerequisite). This is joint work with Pascal Su (ETH Zurich).

Elliptic moduli in algebraic topology

Series
School of Mathematics Colloquium
Time
Thursday, April 9, 2015 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Haynes Miller – MIT
Much effort in the past several decades has gone into lifting various algebraic structures into a topological context. I will describe one such lifting: that of the arithmetic theory of elliptic curves. The result is a rich and highly structured family of cohomology theories collectively known as elliptic cohomology. By forming "global sections" one is led to a topological enrichment of the ring of modular forms. Geometric interpretations of these theories are enticing but still conjectural at best.

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