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Tuesday, October 13, 2009 - 15:00 ,
Location: Skiles 269 ,
Suzanne Lee ,
College of Management, Georgia Tech ,
Organizer: Christian Houdre

We propose a new two stage semi-parametric test and estimation procedure to
investigate predictability of stochastic jump arrivals in asset prices. It allows us
to search for conditional information that affects the likelihood of jump occurrences up
to the intra-day levels so that usual factor analysis for jump dynamics can be
achieved. Based on the new theory of inference, we find empirical evidence of jump clustering
in U.S. individual equity markets during normal trading hours. We also present other
intra-day jump predictors such as analysts recommendation updates and stock news
releases.

Series: Geometry Topology Seminar

The deformation variety is similar to the representation variety inthat it describes (generally incomplete) hyperbolic structures on3-manifolds with torus boundary components. However, the deformationvariety depends crucially on a triangulation of the manifold: theremay be entire components of the representation variety which can beobtained from the deformation variety with one triangulation but notanother, and it is unclear how to choose a "good" triangulation thatavoids these problems. I will describe the "extended deformationvariety", which deals with many situations that the deformationvariety cannot. In particular, given a manifold which admits someideal triangulation we can construct a triangulation such that we canrecover any irreducible representation (with some trivial exceptions)from the associated extended deformation variety.

Monday, October 12, 2009 - 13:00 ,
Location: Skiles 255 ,
Wei Zhu ,
University of Alabama (Department of Mathematics) ,
wzhu7@bama.ua.edu ,
Organizer: Sung Ha Kang

The Rudin-Osher-Fatemi (ROF) model is one of the most powerful and popular models in image denoising. Despite its simple form, the ROF functional has proved to be nontrivial to minimize by conventional methods. The difficulty is mainly due to the nonlinearity and poor conditioning of the related problem. In this talk, I will focus on the minimization of the ROF functional in the one-dimensional case. I will present a new algorithm that arrives at the minimizer of the ROF functional fast and exactly. The proposed algorithm will be compared with the standard and popular gradient projection method in accuracy, efficiency and other aspects.

Series: Combinatorics Seminar

In this talk I will discuss a new technique discovered by myself
and Olof Sisask which produces many new insights in additive combinatorics,
not to mention new
proofs of classical theorems previously proved only using harmonic
analysis. Among these new proofs is one for Roth's theorem on three-term
arithmetic progressions, which gives the best bounds so
far achieved by any combinatorial method. And another is a new proof
that positive density subsets of the integers mod p contain very
long arithmetic progressions, first proved by Bourgain, and improved
upon by Ben Green and Tom Sanders. If time permits, I will discuss
how the method can be applied to the 2D corners problem.

Friday, October 9, 2009 - 15:00 ,
Location: Skiles 269 ,
Igor Belegradek ,
Georgia Tech ,
Organizer:

This 2 hour talk is a gentle introduction to simply-connected sugery
theory (following classical work by Browder, Novikov, and Wall). The
emphasis will be on classification of high-dimensional manifolds and
understanding concrete examples.

Series: Stochastics Seminar

One of the most important stochastic partial differential equations,
known as the superprocess, arises as a limit in population dynamics.
There are several notions of uniqueness, but for many years only weak
uniqueness was known. For a certain range of parameters, Mytnik and
Perkins recently proved strong uniqueness. I will describe joint work
with Barlow, Mytnik and Perkins which proves nonuniqueness for the
parameters not included in Mytnik and Perkins' result. This
completely settles the question for strong uniqueness, but I will end
by giving some problems which are still open.

Series: SIAM Student Seminar

This talk is based on a paper by Medvedev and Scaillet which derives closed form
asymptotic expansions for option implied volatilities (and option prices).
The model is a two-factor jump-diffusion stochastic volatility one with short time to
maturity. The authors derive a power series expansion (in log-moneyness and time
to maturity) for the implied volatility of near-the-money options with small time to
maturity. In this talk, I will discuss their techniques and results.

Series: Graph Theory Seminar

A metric graph is a geometric realization of a finite graph by identifying each edge with a real interval. A divisor on a metric graph Gamma is an element of the free abelian group on Gamma. The rank of a divisor on a metric graph is a concept appearing in the Riemann-Roch theorem for metric graphs (or tropical curves) due to Gathmann and Kerber, and Mikhalkin and Zharkov. A rank-determining set of a metric graph Gamma is defined to be a subset A of Gamma such that the rank of a divisor D on Gamma is always equal to the rank of D restricted on A. I will present an algorithm to derive the reduced divisor from any effective divisor in the same linear system, and show constructively that there exist finite rank-determining sets. Based on this discovery, we can compute the rank of an arbitrary divisor on any metric graph. In addition, I will discuss the properties of rank-determining sets in general and formulate a criterion for rank-determining sets.

Series: School of Mathematics Colloquium

A classification of the dynamics of polynomials in one complex variable has remained elusive, even when considering only the simpler "structurally stable" polynomials. In this talk, I will describe the basics of polynomial iteration, leading up to recent results in the direction of a complete classification. In particular, I will describe a (singular) metric on the complex plane induced by the iteration of a polynomial. I will explain how this geometric structure relates to topological conjugacy classes within the moduli space of polynomials.

Series: Analysis Seminar

Modulation spaces are a class of Banach spaces which provide a quantitative time-frequency analysis of functions via the Short-Time Fourier Transform. The modulation spaces are the "right" spaces for time-frequency analysis andthey occur in many problems in the same way that Besov Spaces are attached to wavelet theory and issues of smoothness. In this seminar, I will talk about embeddings of modulation Spaces into BMO or VMO (the space of functions of bounded or vanishing mean oscillation, respectively ). Membership in VMO is central to the Balian-Low Theorem, which is a cornerstone of time-frequency analysis.