Colloquia scheduled for Tuesdays and Thursdays take place at 4:30-5:30 pm in LN 2205 with refreshments served from 4:00-4:25 pm in the Anderson Memorial Reading Room, while colloquia scheduled for Mondays, Wednesdays and Fridays normally take place at 4:40-5:40 pm in LN 2205 with refreshments served from 4:10-4:35 pm in the Anderson Memorial Reading Room.
Unless stated otherwise, colloquia are scheduled for Thursdays.
Here you find some directions to Binghamton University and the Department of Mathematical Sciences.
Thursday, November 3, 2011
Speaker:
Anatole Katok, Pennsylvania State University
Title:
ACTIONS OF HIGHER RANK ABELIAN GROUPS: FROM MEASURE RIGIDITY TO ARITHMETICITY TO
TOPOLOGY
Time:
4:30 - 5:30 pm
Room: LN-2205
Abstract: While topology of a compact manifold allows to make inferences about periodic
points of maps and, to a lesser extent, closed orbit of vector fields supported by
the manifold, there is notoriously little relation between topology of a
manifold and ergodic properties of diffeomorphisms and smooth flows supported by
it.
A somewhat related fact is that ergodic properties of such dynamical systems
tell little about their geometric structure.
All this changes in a dramatic way when one considers dynamical systems with
multi-dimensional time, i.e. actions of higher rank abelian groups by
diffeomorphisms of compact manifolds. Here is a representative case that will be
discussed in the talk.
Assume that k>1. Consider k commuting diffeomorphisms of a (k+1)- dimensional
manifold M and assume that they preserve a measure that is sufficiently ``rich''
or ``stochastic''. This assumption will be explained in the talk, but for a
person with some dynamical background one form of it states that all non-zero
elements of the suspension action have positive entropy with respect to the
measure.
A striking topological conclusion is that the manifold is a ``slightly modified''
(finite factor of the) torus:
there is homeomorphism from an open subset in finite cover of M that contains
support of the lifted measure to the( k+1)-dimensional torus with a finite set
removed. In particular
the fundamental group of a finite cover of M contains a free abelian subgroup or
rank (k+1).
On the ergodic side we obtain precise information about the structure of the
action.
It is fully ``arithmetic'', i.e. exactly the same as an action by commuting
hyperbolic
matrices with integer entries and determinant 1 or -1 on the torus or its finite
factor.
Moreover, the correspondence is smooth the sense of Whithey
on a set whose complement has arbitrary small measure.
This is a recent joint work with Federico Rodriguez Hertz based on earlier
published work joint with him and with Boris Kalinin.
Thursday, November 10, 2011
Speaker:
Lizhen Ji, University of Michigan, Ann Arbor
Title:
Geometry and Analysis of moduli spaces of Riemann surfaces
Time:
4:30 - 5:30 pm
Room: LN-2205
Abstract: Riemann surfaces are basic objects in mathematics, and their moduli spaces have also played a fundamental role in mathematics. Moduli spaces of Riemann surfaces are quotients of Teichmuller spaces by mapping class groups of surfaces, and they have been extensively studied from various different points of view. It is known that the Teichmuller spaces and hence the moduli spaces admit several natural metrics. In this talk, I will discuss several results on the spectral theory of the Laplacian with respect to these metrics and some topological invariants of moduli spaces such as the simplicial volume.
Tuesday, November 29, 2011, Recruitment Talk
Speaker:
Sebastian Kurtek, Florida State University
Title:
Riemannian Shape Analysis of Functions, Curves and Surfaces
Time:
4:30 - 5:30 pm
Room: LN-2205
Abstract: In this talk we will consider the problems of shape analysis of parameterized curves and surfaces without sampling into finite point sets. Our main interest lies in comparing shapes of these objects. Traditional methods that use point sets for shape comparisons remove variability due to similarity transformations, but we additionally need invariance to re-parameterizations. This requires metrics and representations that lead to the desired invariances. In the case of real-valued functions, we use the Fisher-Rao Riemannian metric and the square-root velocity function (SRVF) representation. In the case of Euclidean curves, we have developed an elastic Riemannian metric and a mathematical representation that facilitates elastic shape analysis of curves. In the case of 3D objects, we introduced a novel mathematical representation that allows parameterization-invariant shape analysis of surfaces. These distances are then used to compute sample statistics and Gaussian probability models on shape manifolds. I will demonstrate these ideas using multiple applications including medical image analysis, analysis of protein backbones, handwriting analysis and others.
Friday, December 2, 2011, Recruitment Talk
Speaker:
Aleksey S. Polunchenko
Title:
State-of-the-Art in Sequential Change-Point Detection
Time:
4:40 - 5:40 pm
Room: LN-2205
Abstract: We consider the problem of sequential change-point detection. This problem is concerned with the design
and analysis of fastest ways to detect a change in the statistical profile of a random time process, given a
tolerable risk of making false detection. The subject finds applications, e.g., in quality control, anomaly
detection, failure detection, surveillance, process control, intrusion detection, boundary tracking, etc. We
provide an overview of the state-of-the-art in the field. The overview spans over all major formulations of the
underlying optimization problem, namely, Bayesian, generalized Bayesian, and minimax. We pay particular
attention to the latest advances made in each. Also, we link together the generalized Bayesian problem with
multi-cyclic disorder detection in a stationary regime when the change occurs at a distant time horizon. We
conclude with a case study to show the field's best detection procedures at work.
Remark. This is joint work with Alexander G. Tartakovsky, Department of Mathematics and Center for
Applied Mathematical Sciences, University of Southern California.
Monday, December 5, 2011, Recruitment Talk
Speaker:
Linglong Kong
Title:
Multivariate Varying Coefficient Model and its Application to
Neuroimaging Data
Time:
5 - 6 pm
Room: LN-2205
Abstract: Motivated by recent work studying massive imaging data in the neuroimaging literature, we propose multivariate varying coefficient models (MVCM) for modeling the relation between multiple functional responses and a set of covariates. We develop several statistical inference procedures for MVCM and systematically study their theoretical properties. We first establish the weak convergence of the local linear estimate of coefficient functions, as well as its asymptotic bias and variance, and then we derive asymptotic bias and mean integrated squared error of smoothed individual functions and their uniform convergence rate. We establish the uniform convergence rate of the estimated covariance function of the individual functions and its associated eigenvalue and eigenfunctions. We propose a global test for linear hypotheses of varying coefficient functions, and derive its asymptotic distribution under the null hypothesis. We also propose a simultaneous confidence band for each individual effect curve. We conduct Monte Carlo simulation to examine the finite-sample performance of the proposed procedures. We also illustrate a real data analysis on the attention deficit hyperactivity disorder (ADHD) data at NYU site from the ADHD-200 sample.
Friday, December 9, 2011, Recruitment Talk
Speaker:
Kobi Abayomi, Georgia Tech
Title:
Statistics for re-identification in networked data models
Time:
4:40 - 5:40 pm
Room: LH 10
Abstract: Re-identification in networked data models involves testing procedures for the identification of similar observations. We consider this testing problem from first principles: we derive probability distributions for a version of a similarity score for three well known network data models. Our method is unique in that it suggests a sufficiency property for (at least) these distributions, an unexplored area of network/graphical modeling.
Thursday, February 23, 2012
Speaker:
Dinesh Thakur, University of Arizona
Title:
TBA
Time:
4:30 - 5:30 pm
Room: LN-2205
Abstract: TBA
Thursday, April 12, 2012
Speaker:
Cristian Popescu, UC San Diego
Title:
TBA
Time:
4:30 - 5:30 pm
Room: LN-2205
Abstract: TBA