Seminars and Colloquia by Series

On an endpoint mapping property for certain bilinear pseudodifferential operators

Series
Analysis Seminar
Time
Wednesday, April 1, 2015 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Virginia Naibo – Kansas State University
The main result to be discussed will be the boundedness from $L^\infty \times L^\infty$ into $BMO$ of bilinear pseudodifferential operators with symbols in a range of bilinear H\"ormander classes of critical order. Such boundedness property is achieved by means of new continuity results for bilinear operators with symbols in certain classes and a new pointwise inequality relating bilinear operators and maximal functions. The role played by these estimates within the general theory will be addressed.

Stability of periodic waves for 1D NLS

Series
PDE Seminar
Time
Tuesday, March 31, 2015 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Stephen Gustafson – UBC
Cubic focusing and defocusing Nonlinear Schroedinger Equations admit spatially (and temporally) periodic standing wave solutions given explicitly by elliptic functions. A natural question to ask is: are they stable in some sense (spectrally/linearly, orbitally, asymptotically,...), against some class of perturbations (same-period, multiple-period, general...)? Recent efforts have slightly enlarged our understanding of such issues. I'll give a short survey, and describe an elementary proof of the linear stability of some of these waves. Partly joint work in progress with S. Le Coz and T.-P. Tsai.

Proof of the middle levels conjecture

Series
Combinatorics Seminar
Time
Tuesday, March 31, 2015 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Torsten Muetze – ETH (Zurich) and Georgia Tech –
Define the middle layer graph as the graph whose vertex set consists of all bitstrings of length 2n+1 that have exactly n or n+1 entries equal to 1, with an edge between any two vertices for which the corresponding bitstrings differ in exactly one bit. The middle levels conjecture asserts that this graph has a Hamilton cycle for every n>=1. This conjecture originated probably with Havel, Buck and Wiedemann, but has also been (mis)attributed to Dejter, Erdos, Trotter and various others, and despite considerable efforts it remained open during the last 30 years. In this talk I present a proof of the middle levels conjecture. In fact, I show that the middle layer graph has 2^{2^{\Omega(n)}} different Hamilton cycles, which is best possible. http://www.openproblemgarden.org/op/middle_levels_problem and http://www.math.uiuc.edu/~west/openp/revolving.html

Do polynomials dream of symmetric curves?

Series
Job Candidate Talk
Time
Tuesday, March 31, 2015 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Andrei Martinez-Finkelshtein – Universidad de Almeria, Spain
Polynomials defined either by some type of orthogonality or satisfying differential equations are pervasive in approximation theory, random matrix theory, special functions, harmonic analysis, scientific computing and applications. Numerical simulations show that their zeros exhibit a common feature: they align themselves along certain curves on the plane. What are these curves? In some cases we can answer this question, at least asymptotically. The answer connects fascinating mathematical objects, such as extremal problems in electrostatics, Riemann surfaces, trajectories of quadratic differentials, algebraic functions; this list is not complete. This talk is a brief survey of some ideas related to this problem, from the breakthrough developments in the 1980-ies to nowadays, finishing with some recent results and open problems.

Deterministic diffusion on periodic lattices

Series
Other Talks
Time
Monday, March 30, 2015 - 15:15 for 1 hour (actually 50 minutes)
Location
Howey W505
Speaker
Carl Dettmann – University of Bristol

Please Note: Hosted by Predrag Cvitanovic, School of Physics

A brief presentation, followed by an informal discussion.

Sparse sum-of-squares certificates on finite abelian groups

Series
Algebra Seminar
Time
Monday, March 30, 2015 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Hamza Fawzi – MIT
We consider functions on finite abelian groups that are nonnegative and also sparse in the Fourier basis. We investigate conditions under which such functions admit sparse sum-of-certificates certificates of nonnegativity, i.e., certificates where the functions in the sum of squares decomposition have a small common sparsity pattern. Our conditions are purely combinatorial in nature, and are based on finding particularly nice chordal covers of a certain Cayley graph. These techniques allow us to show that any nonnegative quadratic function in binary variables is a sum of squares of functions of degree at mostceil(n/2), resolving a conjecture of Laurent. After discussing the connection with semidefinite programming lifts of polytopes, we also see how our techniques provide an example of separation between sizes ofsemidefinite programming lifts and linear programming lifts. This is joint work with James Saunderson and Pablo Parrilo.

A method of computation of 2D Fourier transforms and diffraction integrals with applications in vision science

Series
Applied and Computational Mathematics Seminar
Time
Monday, March 30, 2015 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Professor Andrei Martinez-Finkelshtein – University of Almería
The importance of the 2D Fourier transform in mathematical imaging and vision is difficult to overestimate. For instance, the impulse response of an optical system can be defined in terms of diffraction integrals, that are in turn Fourier transforms of a function on a disk. There are several popular competing approaches used to calculate diffraction integrals, such as the extended Nijboer-Zernike (ENZ) theory. In this talk, an alternative efficient method of computation of two dimensional Fourier-type integrals based on approximation of the integrand by Gaussian radial basis functions is discussed. Its outcome is a rapidly converging series expansion for the integrals, allowing for their accurate calculation. The proposed method yields a reliable and fast scheme for simultaneous evaluation of such kind of integrals for several values of the defocus parameter, as required in the characterization of the through-focus optics.

Independence of Whitehead Doubles of Torus Knots in the Smooth Concordance Group

Series
Geometry Topology Seminar
Time
Monday, March 30, 2015 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Juanita Pinzon-Caicedo – University of Georgia
In the 1980’s Furuta and Fintushel-Stern applied the theory of instantons and Chern-Simons invariants to develop a criterion for a collection of Seifert fibred homology spheres to be independent in the homology cobordism group of oriented homology 3-spheres. In turn, using the fact that the 2-fold cover of S^3 branched over the Whitehead double of a positive torus knot is negatively cobordant to a Seifert fibred homology sphere, Hedden-Kirk establish conditions under which an infinite family of Whitehead doubles of positive torus knots are independent in the smooth concordance group. In the talk, I will review some of the definitions and constructions involved in the proof by Hedden and Kirk and I will introduce some topological constructions that greatly simplify their argument. Time permiting I will mention some ways in which the result could be generalized to include a larger set of knots.

Seifert conjecture in the even convex case

Series
CDSNS Colloquium
Time
Monday, March 30, 2015 - 11:00 for 1 hour (actually 50 minutes)
Location
Slikes 005
Speaker
Chungen Liu – Nankai University, China
The iteration theory for Lagrangian Maslov index is a very useful tool in studying the multiplicity of brake orbits of Hamiltonian systems. In this talk, we show how to use this theory to prove that there exist at least $n$ geometrically distinct brake orbits on every $C^2$ compact convex symmetric hypersurface in $\R^{2n}$ satisfying the reversible condition. As a consequence, we show that if the Hamiltonian function is convex and even, then Seifert conjecture of 1948 on the multiplicity of brake orbits holds for any positive integer $n$.

Furstenberg sets and Furstenberg schemes over finite fields

Series
Algebra Seminar
Time
Friday, March 27, 2015 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jordan Ellenberg – University of Wisconsin, Madison

Please Note: Useful background:The paper I’m discussing: http://arxiv.org/abs/1502.03736Terry Tao’s blog post on Dvir’s theorem: https://terrytao.wordpress.com/2008/03/24/dvirs-proof-of-the-finite-fiel...My earlier paper with Terry and Richard Oberlin about Kakeya restriction over finite fields: http://arxiv.org/abs/0903.1879

The study of extremal configurations of points and subspaces sits at the boundary between combinatorics, harmonic analysis, and number theory; since Dvir’s 2008 resolution of the Kakeya conjecture over finite fields, it has been clear that algebraic geometry is also part of the story.We prove a theorem of Kakeya type for the intersection of subsets of n-space over a finite field with k-planes. Let S be a subset of F_q^n with the "k-plane Furstenberg property": for every k-plane V, there is a k-plane W parallel to V which intersects S in at least q^c points. We prove that such a set has size at least a constant multiple of q^{cn/k}. The novelty is the method; we prove that the theorem holds, not only for subsets of the plane, but arbitrary 0-dimensional subschemes, and reduce the problem by Grobner methods to a simpler one about G_m-invariant non-reduced subschemes supported at a point. The talk will not assume that everyone in the room is an algebraic geometer. It will, however, try to convince everyone in the room that it can be useful to be an algebraic geometer.This is joint work with Daniel Erman.

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