Seminars and Colloquia by Series

Knot invariants and their categorifications via Howe duality

Series
Geometry Topology Seminar
Time
Monday, April 13, 2015 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Aaron Lauda – USC –
It is a well understood story that one can extract linkinvariants associated to simple Lie algebras. These invariants arecalled Reshetikhin-Turaev invariants and the famous Jones polynomialis the simplest example. Kauffman showed that the Jones polynomialcould be described very simply by replacing crossings in a knotdiagram by various smoothings. In this talk we will explainCautis-Kamnitzer-Licata's simple new approach to understanding theseinvariants using basic representation theory and the quantum Weylgroup action. Their approach is based on a version of Howe duality forexterior algebras called skew-Howe duality. Even the graphical (orskein theory) description of these invariants can be recovered in anelementary way from this data. The advantage of this approach isthat it suggests a `categorification' where knot homology theoriesarise in an elementary way from higher representation theory and thestructure of categorified quantum groups. Joint work with David Rose and Hoel Queffelec

Parareal methods for highly oscillatory ordinary differential equations

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 13, 2015 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Seong Jun Kim – Georgia Tech –
We introduce a new parallel in time (parareal) algorithm which couples multiscale integrators with fully resolved fine scale integration and computes highly oscillatory solutions for a class of ordinary differential equations in parallel. The algorithm computes a low-cost approximation of all slow variables in the system. Then, fast phase-like variables are obtained using the parareal iterative methodology and an alignment algorithm. The method may be used either to enhance the accuracy and range of applicability of the multiscale method in approximating only the slow variables, or to resolve all the state variables. The numerical scheme does not require that the system is split into slow and fast coordinates. Moreover, the dynamics may involve hidden slow variables, for example, due to resonances.

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.

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