Seminars and Colloquia by Series

From the "slicing problem" to "KLS Conjecture": The concentration of measure phenomenon in log-concave measures

Series
Joint ACO and ARC Colloquium
Time
Monday, March 7, 2011 - 13:30 for 1 hour (actually 50 minutes)
Location
Klaus 1116W
Speaker
Grigoris PaourisTexas A &M University

Please Note: Tea and light refreshments 2:30 p.m.  in Room 2222

We will discuss several open questions on the concentration of measure on log-concave measures and we will present the main ideas of some recent positive results.

Ramified optimal transportation in geodesic metric spaces

Series
CDSNS Colloquium
Time
Monday, March 7, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Qinglan XiaUniversity of California Davis
An optimal transport path may be viewed as a geodesic in the space of probability measures under a suitable family of metrics. This geodesic may exhibit a tree-shaped branching structure in many applications such as trees, blood vessels, draining and irrigation systems. Here, we extend the study of ramified optimal transportation between probability measures from Euclidean spaces to a geodesic metric space. We investigate the existence as well as the behavior of optimal transport paths under various properties of the metric such as completeness, doubling, or curvature upper boundedness. We also introduce the transport dimension of a probability measure on a complete geodesic metric space, and show that the transport dimension of a probability measure is bounded above by the Minkowski dimension and below by the Hausdorff dimension of the measure. Moreover, we introduce a metric, called "the dimensional distance", on the space of probability measures. This metric gives a geometric meaning to the transport dimension: with respect to this metric, the transport dimension of a probability measure equals to the distance from it to any finite atomic probability measure.

Complexity and criticality of the Ising problem

Series
Combinatorics Seminar
Time
Friday, March 4, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Martin LoeblCharles University, Prague, Czech Republic
The Ising problem on finite graphs is usually treated by a reduction to the dimer problem. Is this a wise thing to do? I will show two (if time allows) recent results indicating that the Ising problem allows better mathematical analysis than the dimer problem. Joint partly with Gregor Masbaum and partly with Petr Somberg.

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 McNeillRice 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 DiscussionsSchool 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 MinskerGeorgia 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 MuscaluCornell
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 UlmerSchool 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 ChoiEmory
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.

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