Seminars and Colloquia by Series

Train tracks and entropy

Series
Research Horizons Seminar
Time
Wednesday, February 8, 2012 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dan Margalit – Georgia Tech
To any self-map of a surface we can associate a real number, called the entropy. This number measures, among other things, the amount of mixing being effected on the surface. As one example, you can think about a taffy pulling machine, and ask how efficiently the machine is stretching the taffy. Using Thurston's notion of a train track, it is actually possible to compute these entropies, and in fact, this is quite easy in practice. We will start from the basic definitions and proceed to give an overview of Thurston's theory. This talk will be accessible to graduate students and advanced undergraduates.

CANCELLED!

Series
School of Mathematics Colloquium
Time
Wednesday, February 8, 2012 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jeff Kahn – Mathematics, Rutgers University
Pardon the inconvenience. We plan to reschedule later...

The surface quasi-geostrophic equation and its generalizations.

Series
PDE Seminar
Time
Tuesday, February 7, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jiahong Wu – Oklahoma State University
Fundamental issues such as the global regularity problem concerning the surface quasi-geostrophic (SQG) and related equations have attracted a lot of attention recently. Significant progress has been made in the last few years. This talk summarizes some current results on the critical and supercritical SQG equations and presents very recent work on the generalized SQG equations. These generalized equations are active scalar equations with the velocity fields determined by the scalars through general Fourier multiplier operators. The SQG equation is a special case of these general models and it corresponds to the Riesz transform. We obtain global regularity for equations with velocity fields logarithmically singular than the 2D Euler and local regularity for equations with velocity fields more singular than those corresponding to the Riesz transform. The results are from recent papers in collaboration with D. Chae and P. Constantin, and with D. Chae, P. Constantin, D. Cordoba and F. Gancedo.

Integral Closure Presentations and Membership

Series
Algebra Seminar
Time
Tuesday, February 7, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Douglas A. Leonard – Auburn University
Let I be an ideal in a polynomial ring R := F[x_n,...,x_1] Let A := R/I be the corresponding quotient ring, and let Q(A) be its field of fractions. The integral closure C(A, Q(A)) of A in Q(A) is a subring of the latter. But it is often given as a separate quotient ring, a presentation.Surprisingly, different computer algebra systems (Magma, Macaulay2, and Singular) choose to produce very different presentations. Some of these opt for presentations that have seductive forms, but miss the most important, namely a form that allows for determining when elements of Q(A) are in C(A,Q(A)). This is called membership and is directly related to determining isomorphism.

Positive commutator methods for unitary operators

Series
Math Physics Seminar
Time
Monday, February 6, 2012 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Rafael Tiedra de Aldecoa – Catholic University of Chile
We present an improved version of commutator methods for unitary operators under a weak regularity condition. Once applied to a unitary operator, the method typically leads to the absence of singularly continuous spectrum and to the local finiteness of point spectrum. Some applications for Floquet operators and for cocycles over irrational rotations will be presented.

Unified bijections for planar maps

Series
Combinatorics Seminar
Time
Friday, February 3, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Olivier Bernardi – Math, MIT –
Planar maps are embeddings of connected planar graphs in the plane considered up to continuous deformation. We will present a ``master bijection'' for planar maps and show that it can be specialized in various ways in order to count several families of maps. More precisely, for each integer d we obtain a bijection between the family of maps of girth d and a family of decorated plane trees. This gives new counting results for maps of girth d counted according to the degree distribution of their faces. Our approach unifies and extends many known bijections. This is joint work with Eric Fusy.

On the Integer Width of Lattice Free Sets

Series
ACO Student Seminar
Time
Friday, February 3, 2012 - 13:00 for 1 hour (actually 50 minutes)
Location
Executive classroom, ISyE Main Building
Speaker
Daniel Dadush – Georgia Tech, School of Industrial and Systems Engineering
A fundamental result in the geometry of numbers states that any lattice free convex set in R^n has integer width bounded by a function of dimension, i.e. the so called Flatness Theorem for Convex Bodies. This result provides the theoretical basis for the polynomial solvability of Integer Programs with a fixed number of (general) integer variables. In this work, we provide a simplified proof of the Flatness Theorem with tighter constants. Our main technical contribution is a new tight bound on the smoothing parameter of a lattice, a concept developed within lattice based cryptography which enables comparisons between certain discrete distributions over integer points with associated continuous Gaussian distributions. Based on joint work with Kai-Min Chung, Feng Hao Liu, and Christopher Peikert.

Two Weight inequality for the Hilbert transform

Series
Analysis Seminar
Time
Wednesday, February 1, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Michael Lacey – Georgia Tech
We continue with the proof of a real variable characterization of the two weight inequality for the Hilbert transform, focusing on a function theory in relevant for weights which are not doubling.

Adaptation in Irregular Regression Models

Series
Job Candidate Talk
Time
Tuesday, January 31, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Michael Chichignoud – ETH Zurich
We study the nonparametric regression model (X1 , Y1 ), ...(Xn , Yn ) , where (Xi )i≥1 is the deterministic design and (Yi )i≥1 is a sequence of real random variables. Assume that the density of Yi is known and can be written as g (., f (Xi )) , which depends on a regression function f at the point Xi . The function f is assumed smooth, i.e. belonging to a Hoelder ball or a Nikol’ski ball. The aim is to estimate the regression function from the observations for two error risks (pointwise and global estimations) and to find the optimal estimator (in the sense of rates of convergence) for each density g . We are particularly interested in the study of irregular models, i.e. when the Fisher information does not exist (for example, when the density g is discontinuous like the uniform density). In this case, the rate of convergence can be improved with the use of nolinear estimators like Maximum likelihood or bayesian estimators. We use the locally parametric approach to construct a new local version of bayesian estimators. Under some conditions on the likelihood of the model, we propose an adaptive procedure based on the so-called Lepski’s method (adaptive selection of the bandwidth) which allows us to construct an optimal adaptive bayesian estimator. We apply this theory to several models like multiplicative uniform model, shifted exponential model, alpha model, inhomogeous Poisson model and Gaussian model

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