Seminars and Colloquia by Series

The universal quantum invariant and colored ideal triangulations

Series
Geometry Topology Seminar
Time
Friday, December 2, 2016 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
S. Suzuki – RIMS, Kyoto University
The Drinfeld double of a finite dimensional Hopf algebra is a quasi-triangular Hopf algebra with the canonical element as the universal R matrix, and we obtain a ribbon Hopf algebra by adding the ribbon element. The universal quantum invariant is an invariant of framed links, and is constructed diagrammatically using a ribbon Hopf algebra. In that construction, a copy of the universal R matrix is attached to each positive crossing, and invariance under the Reidemeister III move is shown by the quantum Yang-Baxter equation of the universal R matrix. On the other hand, R. Kashaev showed that the Heisenberg double has the canonical element (the universal S matrix) satisfying the pentagon relation. In this talk we reconstruct the universal quantum invariant using Heisenberg double, and extend it to an invariant of colored ideal triangulations of the complement. In this construction, a copy of the universal S matrix is attached to each tetrahedron and the invariance under the colored Pachner (2,3) move is shown by the pentagon equation of the universal S matrix

Lazifying Conditional Gradient Algorithms

Series
ACO Student Seminar
Time
Friday, December 2, 2016 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Daniel Zink – Georgia Tech
Conditional gradient algorithms (also often called Frank-Wolfe algorithms) are popular due to their simplicity of only requiring a linear optimization oracle and more recently they also gained significant traction for online learning. While simple in principle, in many cases the actual implementation of the linear optimization oracle is costly. We show a general method to lazify various conditional gradient algorithms, which in actual computations leads to several orders of magnitude of speedup in wall-clock time. This is achieved by using a faster separation oracle instead of a linear optimization oracle, relying only on few linear optimization oracle calls.

Asymptotic equivalence between density estimation and Gaussian white noise revisited

Series
Job Candidate Talk
Time
Thursday, December 1, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Kolyan Ray – Leiden Univ. –
Asymptotic equivalence between two statistical models means that they have the same asymptotic (large sample) properties with respect to all decision problems with bounded loss. In nonparametric (infinite-dimensional) statistical models, asymptotic equivalence has been found to be useful since it can allow one to derive certain results by studying simpler models. One of the key results in this area is Nussbaum’s theorem, which states that nonparametric density estimation is asymptotically equivalent to a Gaussian shift model, provided that the densities are smooth enough and uniformly bounded away from zero.We will review the notion of asymptotic equivalence and existing results, before presenting recent work on the extent to which one can relax the assumption of being bounded away from zero. We further derive the optimal (Le Cam) distance between these models, which quantifies how close they are for finite-samples. As an application, we also consider Poisson intensity estimation with low count data. This is joint work with Johannes Schmidt-Hieber.

From stochastic calculus to geometric inequalities

Series
School of Mathematics Colloquium
Time
Thursday, December 1, 2016 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ronen Eldan – Weizmann Institute of Science –
The probabilistic method, pioneered by P. Erdös, has been key in many proofs from asymptotic geometric analysis. This method allows one to take advantage of numerous tools and concepts from probability theory to prove theorems which are not necessarily a-priori related to probability. The objective of this talk is to demonstrate several recent results which take advantage of stochastic calculus to prove results of a geometric nature. We will mainly focus on a specific construction of a moment-generating process, which can be thought of as a stochastic version of the logarithmic Laplace transform. The method we introduce allows us to attain a different viewpoint on the method of semigroup proofs, namely a path-wise point of view. We will first discuss an application of this method to concentration inequalities on high dimensional convex sets. Then, we will briefly discuss an application to two new functional inequalities on Gaussian space; an L1 version of hypercontractivity of the convolution operator related to a conjecture of Talagrand (joint with J. Lee) and a robustness estimate for the Gaussian noise-stability inequality of C.Borell (improving a result of Mossel and Neeman).

The Homfly skein and elliptic Hall algebras

Series
Geometry Topology Seminar
Time
Wednesday, November 30, 2016 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Peter Samuelson – Edinburgh –
The Homfly skein algebra of a surface is defined using links in thickened surfaces modulo local "skein" relations. It was shown by Turaev that this quantizes the Goldman symplectic structure on the character varieties of the surface. In this talk we give a complete description of this algebra for the torus. We also show it is isomorphic to the elliptic Hall algebra of Burban and Schiffmann, which is an algebra whose elements are (formal sums of) sheaves on an elliptic curve, with multiplication defined by counting extensions of such sheaves. (Joint work with H. Morton.)

Probability Theory in SOM, a Personal Perspective

Series
Research Horizons Seminar
Time
Wednesday, November 30, 2016 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Christian Houdré – Georgia Institute of Technology
I will start with a brief presentation of the Probability activities in SOM. I will continue by presenting results obtained in SOM, over the past ten years, answering long standing questions insequences comparison.

The nonlinear Schroedinger equation and the evolution of wave packets in nonlinear dispersive equations

Series
CDSNS Colloquium
Time
Wednesday, November 30, 2016 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Eugene Wayne – Boston University
The nonlinear Schroedinger equation (NLS) can be derived as a formal approximating equation for the evolution of wave packets in a wide array of nonlinear dispersive PDE’s including the propagation of waves on the surface of an inviscid fluid. In this talk I will describe recent work that justifies this approximation by exploiting analogies with the theory of normal forms for ordinary differential equations.

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