Seminars and Colloquia by Series

A Filtration of the Magnus Representation

Series
Geometry Topology Working Seminar
Time
Friday, March 4, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Taylor McNeill – Rice University
While orientable surfaces have been classified, the structure of their homeomorphism groups is not well understood. I will give a short introduction to mapping class groups, including a description of a crucial representation for these groups, the Magnus representation. In addition I will talk about some current work in which I use Johnson-type homomorphisms to define an infinite filtration of the kernel of the Magnus representation.

Discussion of Gender Issues and Authority in Academics

Series
Other Talks
Time
Friday, March 4, 2011 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 257
Speaker
Open Discussions – School of Mathematics, Georgia Tech
Are there gender differences in authority in mathematics? For instance, do students treat male and female professors differently and what can we do to overcome any negative consequences? Also, what might some positive differences be? We may also discuss issues surrounding respect and authority in research. All are welcome, but if possible, please let Becca Winarski rwinarski@math.gatech.edu know if you plan on attending, so she can get an approximate head count.

String Reconstruction from Substring Compositions

Series
ACO Colloquium
Time
Thursday, March 3, 2011 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alon Orlitsky – Professor, UCSD –
Motivated by mass-spectrometry protein sequencing, we consider the simple problem of reconstructing a string from its substring compositions. Relating the question to the long-standing turnpike problem, polynomial factorization, and cyclotomic polynomials, we cleanly characterize the lengths of reconstructable strings and the structure of non-reconstructable ones. The talk is elementary and self contained and covers work with Jayadev Acharya, Hirakendu Das, Olgica Milenkovic, and Shengjun Pan.

Plug-in Approach to Active Learning

Series
Stochastics Seminar
Time
Thursday, March 3, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Stas Minsker – Georgia Tech
 Let (X,Y) be a random couple with unknown distribution P, X being an observation and Y - a binary label to be predicted. In practice, distribution P remains unknown but the learning algorithm has access to the training data - the sample from P. It often happens that the cost of obtaining the training data is associated with labeling the observations while the pool of observations itself is almost unlimited. This suggests to measure the performance of a learning algorithm in terms of its label complexity, the number of labels required to obtain a classifier with the desired accuracy. Active Learning theory explores the possible advantages of this modified framework.We will present a new active learning algorithm based on nonparametric estimators of the regression function and explain main improvements over the previous work.Our investigation provides upper and lower bounds for the performance of proposed method over a broad class of underlying distributions. 

Beyond Calderon's algebra

Series
Analysis Seminar
Time
Wednesday, March 2, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Camil Muscalu – Cornell
Calderon's algebra can be thought of as a world whichincludes singular integral operators and operators of multiplicationwith functions which grow at most linearly (more precisely, whose firstderivatives are bounded).The goal of the talk is to address and discuss in detail the followingnatural question: "Can one meaningfully extend it to include operatorsof multiplication with functions having polynomial growth as well ?".

Elliptic curves with many points

Series
Research Horizons Seminar
Time
Wednesday, March 2, 2011 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Doug Ulmer – School of Mathematics - Georgia Institute of Technology
An elliptic curve is the set of solutions to a cubic equation in two variables and it has a natural group structure---you can add two points to get another. I'll explain why this is so, give some examples of the different types of groups that can arise (depending on the ground field), and mention some recent results on curves with many points. The are some nice thesis problems in this area which will be discussed in a follow-up talk later this semester in the algebra seminar.

Souls of Some Convex Surfaces

Series
Geometry Topology Student Seminar
Time
Wednesday, March 2, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Eric Choi – Emory
The soul of a complete, noncompact, connected Riemannian manifold (M; g) of non-negative sectional curvature is a compact, totally convex, totally geodesic submanifold such that M is diffeomorphic to the normal bundle of the soul. Hence, understanding of the souls of M can reduce the study of M to the study of a compact set. Also, souls are metric invariants, so understanding how they behave under deformations of the metric is useful to analyzing the space of metrics on M. In particular, little is understood about the case when M = R2 . Convex surfaces of revolution in R3 are one class of two-dimensional Riemannian manifolds of nonnegative sectional curvature, and I will discuss some results regarding the sets of souls for some of such convex surfaces.

Exact results for percolation thresholds, enclosed-area distribution functions and correlation functions in percolation

Series
Stochastics Seminar
Time
Tuesday, March 1, 2011 - 16:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Robert Ziff – Michigan Center for Theoretical Physics, Department of Chemical Engineering, University of Michigan
Various exact results in two-dimensional percolation are presented. A method for finding exact thresholds for a wide variety of systems, which greatly expands previously known exactly solvable systems to such new lattices as "martini" and generalized "bowtie" lattices, is given. The size distribution is written in a Zipf's-law form in terms of the enclosed- area distribution, and the coefficient can be written in terms of the the number of hulls crossing a cylinder. Additional properties of hull walks (equivalent to some kinds of trajectories) are given. Finally, some ratios of correlation functions are shown to be universal, with a functional form that can be found exactly from conformal field theory.

Stability of planar diffusion waves for bipolar hydrodynamic model of semiconductors in multi-dimensional space

Series
PDE Seminar
Time
Tuesday, March 1, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Ming Mei – Champlain College and McGill University –
In this talk, we consider the n-dimensional bipolar hydrodynamic model for semiconductors in the form of Euler-Poisson equations. In 1-D case, when the difference between the initial electron mass and the initial hole mass is non-zero (switch-on case), the stability of nonlinear diffusion wave has been open for a long time. In order to overcome this difficulty, we ingeniously construct some new correction functions to delete the gaps between the original solutions and the diffusion waves in L^2-space, so that we can deal with the one dimensional case for general perturbations, and prove the L^\infty-stability of diffusion waves in 1-D case. The optimal convergence rates are also obtained. Furthermore, based on the results of one-dimension, we establish some crucial energy estimates and apply a new but key inequality to prove the stability of planar diffusion waves in n-D case, which is the first result for the multi-dimensional bipolar hydrodynamic model of semiconductors, as we know. This is a joint work with Feimin Huang and Yong Wang.

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