Seminars and Colloquia by Series

Valuations on convex sets and integral geometry

Series
Analysis Seminar
Time
Wednesday, January 23, 2019 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Semyon AleskerTel Aviv University
Valuations are finitely additive measures on convex compact subsets of a finite dimensional vector space. The theory of valuations originates in convex geometry. Valuations continuous in the Hausdorff metric play a special role, and we will concentrate in the talk on this class of valuations. In recent years there was a considerable progress in the theory and its applications. We will describe some of the progress with particular focus on the multiplicative structure on valuations and its applications to kinematic formulas of integral geometry.

On the relationship between the thin film equation and Tanner's law

Series
PDE Seminar
Time
Tuesday, January 22, 2019 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Matias DelgadinoImperial College
In this talk we will introduce two models for the movement of a small droplet over a substrate: the thin film equation and the quasi static approximation. By tracking the motion of the apparent support of solutions to the thin film equation, we connect these two models. This connection was expected from Tanner's law: the edge velocity of a spreading thin film on a pre-wetted solid is approximately proportional to the cube of the slope at the inflection. This is joint work with Prof. Antoine Mellet.

Fast sampling of sparse contingency tables

Series
Combinatorics Seminar
Time
Friday, January 18, 2019 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 169 (*Unusual room*)
Speaker
Samuel DittmerMathematics, UCLA
We present a new algorithm for sampling contingency tables with fixed margins. This algorithm runs in polynomial time for certain broad classes of sparse tables. We compare the performance of our algorithm theoretically and experimentally to existing methods, including the Diaconis-Gangolli Markov chain and sequential importance sampling. Joint work with Igor Pak.

Chaotic regimes for random dynamical systems

Series
Job Candidate Talk
Time
Friday, January 18, 2019 - 11:15 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alex BlumenthalUniv. of Maryland

It is anticipated that chaotic regimes (characterized by, e.g., sensitivity with respect to initial conditions and loss of memory) arise in a wide variety of dynamical systems, including those arising from the study of ensembles of gas particles and fluid mechanics. However, in most cases the problem of rigorously verifying asymptotic chaotic regimes is notoriously difficult. For volume-preserving systems (e.g., incompressible fluid flow or Hamiltonian systems), these issues are exemplified by coexistence phenomena: even in quite simple models which should be chaotic, e.g. the Chirikov standard map, completely opposite dynamical regimes (elliptic islands vs. hyperbolic sets) can be tangled together in phase space in a convoluted way.

Recent developments have indicated, however, that verifying chaos is tractable for systems subjected to a small amount of noise— from the perspective of modeling, this is not so unnatural, as the real world is inherently noisy. In this talk, I will discuss two recent results: (1) a large positive Lyapunov exponent for (extremely small) random perturbations of the Chirikov standard map, and (2) a positive Lyapunov exponent for the Lagrangian flow corresponding to various incompressible stochastic fluids models, including stochastic 2D Navier-Stokes and 3D hyperviscous Navier-Stokes on the periodic box. The work in this talk is joint with Jacob Bedrossian, Samuel Punshon-Smith, Jinxin Xue and Lai-Sang Young.

Stein's Method for Infinitely Divisible Laws With Finite First Moment

Series
Stochastics Seminar
Time
Thursday, January 17, 2019 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Benjamin ArrasUniversity of Lille
Stein's method is a powerful technique to quantify proximity between probability measures, which has been mainly developed in the Gaussian and the Poisson settings. It is based on a covariance representation which completely characterizes the target probability measure. In this talk, I will present some recent unifying results regarding Stein's method for infinitely divisible laws with finite first moment. In particular, I will present new quantitative results regarding Compound Poisson approximation of infinitely divisible laws, approximation of self-decomposable distributions by sums of independent summands and stability results for self-decomposable laws which satisfy a second moment assumption together with an appropriate Poincaré inequality. This is based on joint works with Christian Houdré.

A tale of models for random graphs

Series
Combinatorics Seminar
Time
Thursday, January 17, 2019 - 12:00 for 1.5 hours (actually 80 minutes)
Location
Skiles 005
Speaker
Jeong Han KimKorea Institute for Advanced Study (KIAS)
Since Erdős–Rényi introduced random graphs in 1959, two closely related models for random graphs have been extensively studied. In the G(n,m) model, a graph is chosen uniformly at random from the collection of all graphs that have n vertices and m edges. In the G(n,p) model, a graph is constructed by connecting each pair of two vertices randomly. Each edge is included in the graph G(n,p) with probability p independently of all other edges. Researchers have studied when the random graph G(n,m) (or G(n,p), resp.) satisfies certain properties in terms of n and m (or n and p, resp.). If G(n,m) (or G(n,p), resp.) satisfies a property with probability close to 1, then one may say that a `typical graph’ with m edges (or expected edge density p, resp.) on n vertices has the property. Random graphs and their variants are also widely used to prove the existence of graphs with certain properties. In this talk, two problems for these categories will be discussed. First, a new approach will be introduced for the problem of the emergence of a giant component of G(n,p), which was first considered by Erdős–Rényi in 1960. Second, a variant of the graph process G(n,1), G(n,2), …, G(n,m), … will be considered to find a tight lower bound for Ramsey number R(3,t) up to a constant factor. (No prior knowledge of graph theory is needed in this talk.)

Matrix Estimation with Latent Permutations

Series
Job Candidate Talk
Time
Thursday, January 17, 2019 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Cheng MaoYale University
A wide variety of applied tasks, such as ranking, clustering, graph matching and network reconstruction, can be formulated as a matrix estimation problem where the rows and columns of the matrix are shuffled by a latent permutation. The combinatorial nature of the unknown permutation and the non-convexity of the parameter space result in both statistical and algorithmic challenges. I will present recent developments of average-case models and efficient algorithms, primarily for the problems of ranking from comparisons and statistical seriation. On the statistical side, imposing shape constraints on the underlying matrix extends traditional parametric approaches, allowing for more robust and adaptive estimation. On the algorithmic front, I discuss efficient local algorithms with provable guarantees, one of which tightens a conjectured statistical-computational gap for a stochastically transitive ranking model.

Fluctuation of ergodic sums over periodic orbits

Series
CDSNS Colloquium
Time
Thursday, January 17, 2019 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Manfred DenkerPenn State University
The fluctuations of ergodic sums by the means of global and local specifications on periodic points will be discussed. Results include a Lindeberg-type central limit theorems in both setups of specification. As an application, it is shown that averaging over randomly chosen periodic orbits converges to the integral with respect to the measure of maximal entropy as the period approaches infinity. The results also suggest to decompose the variances of ergodic sums according to global and local sources.

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