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Series: Algebra Seminar

The "Exceptionally Simple Theory of Everything" has been the subject of

articles in The New Yorker (7/21/08), Le Monde (11/20/07), the

Financial Times (4/25/09), The Telegraph (11/10/09), an invited talk at

TED (2/08), etc. Despite positive descriptions of the theory in the

popular press, it doesn't work. I'll explain a little of the theory,

the mathematical reasons why it doesn't work, and a theorem (joint work

with Jacques Distler) that says that no similar theory can work. This

talk should be accessible to all graduate students in mathematics.

articles in The New Yorker (7/21/08), Le Monde (11/20/07), the

Financial Times (4/25/09), The Telegraph (11/10/09), an invited talk at

TED (2/08), etc. Despite positive descriptions of the theory in the

popular press, it doesn't work. I'll explain a little of the theory,

the mathematical reasons why it doesn't work, and a theorem (joint work

with Jacques Distler) that says that no similar theory can work. This

talk should be accessible to all graduate students in mathematics.

Series: Analysis Working Seminar

James Curry will finish the discussion of arXiv:0911.3437

Series: Other Talks

Refreshments in Room 2222, Klaus Building from 2-3 PM.

Simple, distributed and iterative algorithms, popularly known as the message passing algorithms, have emerged as the architecture of choice for engineered networks as well as cannonical behavioral model for societal and biological networks. Despite their simplicity, message passing algorithms have been surprisingly effective. In this talk, I will try to argue in favor of such algorithms by means of two results in the context of designing efficient medium access in wireless networks and modeling agent behavior in road transportation networks. See the

full abstract,

full abstract,

Friday, February 5, 2010 - 14:00 ,
Location: Skiles 269 ,
Meredith Casey ,
Georgia Tech ,
Organizer:

Exact Topic TBA. Talk will be a general survery of branched covers, possibly including covers from the algebraic geometry perspective. In addition we will look at branched coveres in higher dimensions, in the contact world, and my current research interests. This talk will be a general survery, so very little background is assumed.

Series: SIAM Student Seminar

We are dealing with the following minimization problem: inf {I(\mu): \mu

is a probability measure on R and \int f(x)=t_{0}}, where I(\mu) = \int

(x^2)/2 \mu(dx) + \int\int log|x-y|^{-1} \mu(dx)\mu(dy), f(x) is a bounded

continuous function and t is a given real number. Its motivation and its connection to radom matrices theory will be introduced. We will show that the solution is unique and has a compact support. The possible extension of the

class of f(x) will be discussed.

is a probability measure on R and \int f(x)=t_{0}}, where I(\mu) = \int

(x^2)/2 \mu(dx) + \int\int log|x-y|^{-1} \mu(dx)\mu(dy), f(x) is a bounded

continuous function and t is a given real number. Its motivation and its connection to radom matrices theory will be introduced. We will show that the solution is unique and has a compact support. The possible extension of the

class of f(x) will be discussed.

Series: Job Candidate Talk

We consider the statistical deconvolution problem where one observes $n$

replications from the model $Y=X+\epsilon$, where $X$ is the unobserved

random signal of interest and where $\epsilon$ is an independent random

error with distribution $\varphi$. Under weak assumptions on the decay of

the Fourier transform of $\varphi$ we derive upper bounds for the

finite-sample sup-norm risk of wavelet deconvolution density estimators

$f_n$ for the density $f$ of $X$, where $f: \mathbb R \to \mathbb R$ is

assumed to be bounded. We then derive lower bounds for the minimax sup-norm

risk over Besov balls in this estimation problem and show that wavelet

deconvolution density estimators attain these bounds. We further show that

linear estimators adapt to the unknown smoothness of $f$ if the Fourier

transform of $\varphi$ decays exponentially, and that a corresponding result

holds true for the hard thresholding wavelet estimator if $\varphi$ decays

polynomially. We also analyze the case where $f$ is a 'supersmooth'/analytic

density. We finally show how our results and recent techniques from

Rademacher processes can be applied to construct global nonasymptotic

confidence bands for the density $f$.

replications from the model $Y=X+\epsilon$, where $X$ is the unobserved

random signal of interest and where $\epsilon$ is an independent random

error with distribution $\varphi$. Under weak assumptions on the decay of

the Fourier transform of $\varphi$ we derive upper bounds for the

finite-sample sup-norm risk of wavelet deconvolution density estimators

$f_n$ for the density $f$ of $X$, where $f: \mathbb R \to \mathbb R$ is

assumed to be bounded. We then derive lower bounds for the minimax sup-norm

risk over Besov balls in this estimation problem and show that wavelet

deconvolution density estimators attain these bounds. We further show that

linear estimators adapt to the unknown smoothness of $f$ if the Fourier

transform of $\varphi$ decays exponentially, and that a corresponding result

holds true for the hard thresholding wavelet estimator if $\varphi$ decays

polynomially. We also analyze the case where $f$ is a 'supersmooth'/analytic

density. We finally show how our results and recent techniques from

Rademacher processes can be applied to construct global nonasymptotic

confidence bands for the density $f$.

Series: School of Mathematics Colloquium

Refreshments at 4PM in Skiles 236

The Pentagram map is a projectively natural iteration on

plane polygons. Computer experiments show that the Pentagram map has

quasi-periodic behavior. I shall explain that the Pentagram map is a

completely integrable system whose continuous limit is the Boussinesq

equation, a well known integrable system of soliton type. As a

by-product, I shall demonstrate new configuration theorems of

classical projective geometry.

plane polygons. Computer experiments show that the Pentagram map has

quasi-periodic behavior. I shall explain that the Pentagram map is a

completely integrable system whose continuous limit is the Boussinesq

equation, a well known integrable system of soliton type. As a

by-product, I shall demonstrate new configuration theorems of

classical projective geometry.

Series: Analysis Seminar

In this talk we will present some recent results about the matrix representation of the multiplication operator in terms of a basis of either orthogonal polynomials (OPUC) or orthogonal Laurent polynomials (OLPUC) with respect to a nontrivial probability measure supported on the unit circle. These are the so called GGT and CMV matrices.When spectral linear transformations of the measure are introduced, we will find the GGT and CMV matrices associated with the new sequences of OPUC and OLPUC, respectively. A connection with the QR factorization of such matrices will be stated. A conjecture about the generator system of such spectral transformations will be discussed.Finally, the Lax pair for the GGT and CMV matrices associated with some special time-depending deformations of the measure will be analyzed. In particular, we will study the Schur flow, which is characterized by a complex semidiscrete modified KdV equation and where a discrete analogue of the Miura transformation appears. Some open problems for time-depending deformations related to spectral linear transformations will be stated.This is a joint work with K. Castillo (Universidad Carlos III de Madrid) and L. Garza (Universidad Autonoma de Tamaulipas, Mexico).

Series: Mathematical Biology Seminar

Even the simplest biochemical networks often have more degrees of freedoms than one can (or

should!) analyze. Can we ever hope to do the physicists' favorite trick of coarse-graining,

simplifying the networks to a much smaller set of effective dynamical variables that still

capture the relevant aspects of the kinetics? I will argue then that methods of statistical

physics provide hints at the existence of rigorous coarse-grained methodologies in modeling

biological information processing systems, allowing to identify features of the systems that are

relevant to their functions. While a general solution is still far away, I will focus on a

specific example illustrating the approach. Namely, for a a general stochastic network

exhibiting the kinetic proofreading behavior, I will show that the microscopic parameters of the

system are largely important only to the extent that they contribute to a single aggregate

parameter, the mean first passage time through the network, and the higher cumulants of the

escape time distribution are related to this parameter uniquely. Thus a phenomenological model

with a single parameter does a good job explaining all of the observable data generated by this

complex system.

should!) analyze. Can we ever hope to do the physicists' favorite trick of coarse-graining,

simplifying the networks to a much smaller set of effective dynamical variables that still

capture the relevant aspects of the kinetics? I will argue then that methods of statistical

physics provide hints at the existence of rigorous coarse-grained methodologies in modeling

biological information processing systems, allowing to identify features of the systems that are

relevant to their functions. While a general solution is still far away, I will focus on a

specific example illustrating the approach. Namely, for a a general stochastic network

exhibiting the kinetic proofreading behavior, I will show that the microscopic parameters of the

system are largely important only to the extent that they contribute to a single aggregate

parameter, the mean first passage time through the network, and the higher cumulants of the

escape time distribution are related to this parameter uniquely. Thus a phenomenological model

with a single parameter does a good job explaining all of the observable data generated by this

complex system.

Series: PDE Seminar

Couette flows are shear flows with a linear velocity profile.

Known by Orr in 1907, the vertical velocity of the linearized

Euler equations at Couette flows is known to decay in time, for

L^2 vorticity. It is interesting to know if the perturbed Euler

flow near Couette tends to a nearby shear flow. Such problems

of nonlinear inviscid damping also appear for other stable flows

and are important to understand the appearance of coherent

structures in 2D turbulence. With Chongchun Zeng, we constructed

non-parallel steady flows arbitrarily near Couette flows in

H^s (s<3/2) norm of vorticity. Therefore, the nonlinear inviscid

damping is not true in (vorticity) H^s (s<3/2) norm. We also

showed that in (vorticity) H^s (s>3/2) neighborhood of Couette

flows, the only steady structures (including travelling waves) are

stable shear flows. This suggests that the long time dynamics near

Couette flows in (vorticity) H^s (s>3/2) space might be simpler.

Similar results will also be discussed for the problem of

nonlinear Landau damping in 1D electrostatic plasmas.