Seminars and Colloquia by Series

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.

Reaching L^1 via Extrapolation Theory

Series
Analysis Seminar
Time
Wednesday, April 8, 2015 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Carlos Domingo – University of Barcelona
The classical Rubio de Francia extrapolation allows you to obtain strong-type estimates for weights in A_p (and every p>1) if you can show that it holds for some p_0>1. However, the endpoint p=1 has to be treated separately. In this talk we will explain how to deduce weak-type (1,1) estimates for A_1 weights if we have a certain restricted weak-type inequality at some level p_0>1. We will then show how this approach can be applied to the Bochner-Riesz operator at the critical index and Fourier multipliers.

Complex-oriented cohomology theories and Quillen's theorem Part I

Series
Geometry Topology Student Seminar
Time
Wednesday, April 8, 2015 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Xander Flood – Georgia Tech –
Complex-oriented cohomology theories are a class of generalized cohomology theories with special properties with respect to orientations of complex vector bundles. Examples include all ordinary cohomology theories, complex K-theory, and (our main theory of interest) complex cobordism.In two talks on these cohomology theories, we'll construct and discuss some examples and study their properties. Our ultimate goal will be to state and understand Quillen's theorem, which at first glance describes a close relationship between complex cobordism and formal group laws. Upon closer inspection, we'll see that this is really a relationship between C-oriented cohomology theories and algebraic geometry.

The Euler-Maxwell system in 2D

Series
PDE Seminar
Time
Tuesday, April 7, 2015 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Benoit Pausader – Princeton University
The Euler-Maxwell system describes the interaction between a compressible fluid of electrons over a background of fixed ions and the self-consistent electromagnetic field created by the motion.We show that small irrotational perturbations of a constant equilibrium lead to solutions which remain globally smooth and return to equilibrium. This is in sharp contrast with the case of neutral fluids where shock creation happens even for very nice initial data.Mathematically, this is a quasilinear dispersive system and we show a small data-global solution result. The main challenge comes from the low dimension which leads to slow decay and from the fact that the nonlinearity has some badly resonant interactions which force a correction to the linear decay. This is joint work with Yu Deng and Alex Ionescu.

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