Colloquia
Backwards uniqueness for the Ricci flow and the non-expansion of the isometry group
Backwards uniqueness for the Ricci flow and the non-expansion of the isometry group.
Brett Kotschwar, Massachusetts Institute of Technology Department of Mathematics
January 19, 2010
Abstract: I will discuss some recent work on the problem of backwards uniqueness or unique-continuation for the Ricci flow, and show that two solutions of uniformly bounded curvature that agree at some non-initial time must agree identically at all previous times. A particular consequence is that the flow does not sponsor the generation of new isometries within the lifetime of a solution, nor permit a solution to become Einstein or self-similar in finite time.
On Evolution Equations
On Evolution Equations
Cristina Caputo, University of Texas at Austin
January 25, 2010
Abstract: This talk will be made accessible to a general audience of mathematicians (graduate students included). Existence, regularity, and other issues will be described for solutions of certain evolution equations. Similarities and differences of the behavior of such solutions will be discussed.
Rank and rank gradient of groups that split
Rank and rank gradient of groups that split
Jason DeBlois of the University of Illinois, Chicago
January 26, 2010
Abstract: "The rank of a finitely generated group G -- the minimal cardinality of a generating set -- provides a rough measure of the complexity of G. In particular, results like Grushko's theorem relate the ranks of groups that "split" to the objects involved in their decompositions. I will discuss applications of such theorems to questions about rank gradient, which measures the growth rate of rank in families of finite-index subgroups, and relate them to the "rank vs. Heegaard genus" question for 3-manifolds. Then I will describe how geometric methods can be used to improve estimates in some cases, and show why this matters for rank gradient."
Hierarchical spatial models for predicting forest variables over large heterogeneous domains
Hierarchical spatial models for predicting forest variables over large heterogeneous domains
Dr. Sudipto Banerjee, Associate Professor, Division of Biostatistics, School of Public Health, University of Minnesota
January 28, 2010
Abstract:
We are interested in predicting one or more continuous forest variables (e.g., biomass, volume, age) at a fine resolution (e.g., pixel-level) across a specified domain. Given a definition of forest/non-forest, this prediction is typically a two step process. The first step predicts which locations are forested. The second step predicts the value of the ariable for only those forested locations. Rarely is the forest/non-forest predicted without error. However, the uncertainty in this prediction is typically not propagated through to the subsequent prediction of the forest variable of interest. Failure to acknowledge this error can result in biased and perhaps falsely precise estimates. In response to this problem, we offer a modeling framework that will allow propagation of this uncertainty. Here we envision two latent processes generating the data. The first is a continuous spatial process while the second is a binary spatial process. We assume that the processes are independent of each other. The continuous spatial process controls the spatial association structure of the forest variable of interest, while a binary process indicates presence of a ``measurable'' quantity at a given location. Finally, we explore the use of a predictive process for both the continuous and binary processes to reduce the dimensionality of the data and ease the computational burden.The proposed models are motivated using georeferenced National Forest Inventory (NFI) data and coinciding remotely sensed predictor variables.
This is joint work with Andrew O. Finley (Department of Forestry and Geography, Michigan State University)
Embedded Surfaces in 3-Manifolds
Embedded Surfaces in 3-ManifoldsJesse Johnson, Oklahoma State University
February 11, 2010
Abstract:
I will give an overview of the current state of research
studying isotopy classes of surfaces in 3-dimensional manifolds, with a focus
on open problems and possible future directions.
Wavelets and Semigroups
Wavelets and Semigroups
Swanhild Bernstein, Institut für Angewandte Analysis, TU Bergakademie Freiberg, Germany
March 2, 2010
The Stretch Conjecture
The Stretch ConjectureAl Baernstein, Washington University in St. Louis
March 4, 2010
Click here to view the abstract.
The closed range property and boundary regularity for the Cauchy-Riemann equations
The closed range property and boundary regularity for the Cauchy-Riemann equations
Mei-Chi Shaw, University of Notre Dame
March 9, 2010
Abstract: In this talk we will study the closed range property and boundary regularity of the Cauchy-Riemann equations on domains in complex Euclidean spaces or complex manifolds. When the domain is pseudoconvex in the complex Euclidean space, one has the celebrated H\"ormander's $L^2$ existence theorems and Kohn's boundary regularity results. We will discuss the case for an annulus between two pseudoconvex domains in $C^n$ as well as the recent results on product domains (joint work with Debraj Chakrabarti). Some results and open problems on domains in complex projective spaces will also be discussed.
On-line inference in autoregressions, mixtures of autoregressions and state-space autoregressions with structured priors
On-line inference in autoregressions, mixtures of autoregressions and state-space autoregressions with structured priorsRaquel Prado, University of California, Santa Cruz
March 11, 2010
Abstract: This work is motivated by the analysis of multiple brain signals recorded during an experiment that aimed to characterize mental fatigue in subjects performing a cognitive task continuously for an extended period of time.
The recorded brain signals can be modeled via mixtures of autoregressive process with structured priors. More specifically, we follow a Bayesian approach that imposes structured prior distributions on the reciprocal roots of the characteristic polynomials that define the AR processes. Such prior structure allows modellers to include scientifically meaningful information related to various states of mental alertness. We focus on the implementation of sequential Monte Carlo methods for on-line parameter learning within the following model classes: structured AR models, mixtures of structured AR models and structured AR plus noise models.
Flipping Bridge Surfaces
Flipping Bridge SurfacesMaggy Tomova, University of Iowa
March 18, 2010
Abstract: Recently the "stabilization conjecture", an important question in 3-manifolds, was resolved. In a joint paper with Jesse Johnson we gave a generalization of this result by allowing knots in the manifold. I will present our results in the special case of a knot in the three sphere and give an idea of how this special case can be generalized to knots in any 3-manifold.