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Series: Other Talks

The speaker has combined his two loves to create a dynamic presentation called "Mathemagics," suitable for all audiences, where he demonstrates and explains his secrets for performing rapid mental calculations faster than a calculator. Reader's Digest calls him "America's Best Math Whiz". He has presented his high energy talk for thousands of groups throughout the world. This event is free but reservations are required. The signup form will be available before 5pm on February 25.

See details about the speaker.

See details about the speaker.

Series: Other Talks

The SIAM Student Chapter at Georgia Tech will be hosting this conference. It is an extension of the ACES Workshop which has been held yearly by the universities of Auburn, Clemson, Emory, and South Carolina since 2006. As with the ACES Workshop, this conference is an opportunity for graduate students to present their research in applied mathematics and related fields as well as to meet with other graduate students from different universities and departments. See the conference site for more details.

Series: Combinatorics Seminar

Let a_1,...,a_k satisfy a_1+...+a_k=1 and suppose a k-uniform hypergraph on n

vertices satisfies the following property; in any partition of its vertices into k

sets A_1,...,A_k of sizes a_1*n,...,a_k*n, the number of edges intersecting

A_1,...,A_k is the number one would expect to find in a random k-uniform hypergraph.

Can we then infer that H is quasi-random? We show that the answer is negative if and

only if a_1=...=a_k=1/k. This resolves an open problem raised in 1991 by Chung and

Graham [J. AMS '91].

vertices satisfies the following property; in any partition of its vertices into k

sets A_1,...,A_k of sizes a_1*n,...,a_k*n, the number of edges intersecting

A_1,...,A_k is the number one would expect to find in a random k-uniform hypergraph.

Can we then infer that H is quasi-random? We show that the answer is negative if and

only if a_1=...=a_k=1/k. This resolves an open problem raised in 1991 by Chung and

Graham [J. AMS '91].

While hypergraphs satisfying the property corresponding to a_1=...=a_k=1/k are not

necessarily quasi-random, we manage to find a characterization of the hypergraphs

satisfying this property. Somewhat surprisingly, it turns out that (essentially)

there is a unique non quasi-random hypergraph satisfying this property. The proofs

combine probabilistic and algebraic arguments with results from the theory of

association schemes.

Joint work with Raphy Yuster

Friday, March 5, 2010 - 14:00 ,
Location: Skiles 269 ,
Anh Tran ,
Georgia Tech ,
Organizer:

I will explain another approach to the conjecture and in particular,

study it for 2-bridge knots. I will give the proof of the conjecture

for a very large class of 2-bridge knots which includes twist knots and

many more (due to Le). Finally, I will mention a little bit about the

weak version of the conjecture as well as some relating problems.

study it for 2-bridge knots. I will give the proof of the conjecture

for a very large class of 2-bridge knots which includes twist knots and

many more (due to Le). Finally, I will mention a little bit about the

weak version of the conjecture as well as some relating problems.

Series: SIAM Student Seminar

Last semester, I reviewed the relation between dynamical system,

Fokker-Planck equation and thermodynamics (free energy and Gibbs

distribution). This time let's go further. I will review the geometric

properties of a kind of dissipative evolution equations. I will explain

why this kind of evolutionary equations (Fokker-Planck equation,

nonlinear Fokker-Planck equation, Porous medium equation) are the

gradient flow of some energy function on a Riemannian manifold --

2-Wasserstein metric space.

Fokker-Planck equation and thermodynamics (free energy and Gibbs

distribution). This time let's go further. I will review the geometric

properties of a kind of dissipative evolution equations. I will explain

why this kind of evolutionary equations (Fokker-Planck equation,

nonlinear Fokker-Planck equation, Porous medium equation) are the

gradient flow of some energy function on a Riemannian manifold --

2-Wasserstein metric space.

Series: Stochastics Seminar

Abstract: We consider the hidden Markov model, where the dynamic of theprocess is modelled by a latent Markov chain Y and the observations X aresuch that: 1) given the realization of Y, the observations areindependent; 2) the distribution of the i-th observations (X_i) depends onthe i-th element of the Y (Y_i), only.The segmentation problem consists of estimating the underlying realization(path) of Y given the n observation. Usually the realization with maximumlikelihood, the so called Viterbi alignment is used. On the other hand, itis easy to see that the Viterbi alignment does not minimize the expectednumber of misclassification errors.We consider the segmentation problem in the framework of statisticallearning. This unified risk-based approach helps to analyse many existingalignments as well as defining many new ones. We also study theasymptotics of the risks and infinite alignments.

Series: School of Mathematics Colloquium

Much research in modern, quantitative seismology is motivated -- on

the one hand -- by the need to understand subsurface structures and

processes on a wide range of length scales, and -- on the other hand

-- by the availability of ever growing volumes of high fidelity

digital data from modern seismograph networks or multicomponent

acquisition systems developed for hydro-carbon exploration, and access

to increasingly powerful computational facilities. We discuss

(elastic-wave) inverse scattering of reflection seismic data,

wave-equation tomography, and their interconnection using techniques

from microlocal analysis and applied harmonic analysis. We introduce a

multi-scale approach and present a framework of partial reconstruction

in connection with limited boundary acquisition geometry. The formation of caustics

leads to one of the complications which will be discussed. We illustrate various

aspects of this research program with examples from global seismology and mineral

physics coupled to thermo-chemical convection.

the one hand -- by the need to understand subsurface structures and

processes on a wide range of length scales, and -- on the other hand

-- by the availability of ever growing volumes of high fidelity

digital data from modern seismograph networks or multicomponent

acquisition systems developed for hydro-carbon exploration, and access

to increasingly powerful computational facilities. We discuss

(elastic-wave) inverse scattering of reflection seismic data,

wave-equation tomography, and their interconnection using techniques

from microlocal analysis and applied harmonic analysis. We introduce a

multi-scale approach and present a framework of partial reconstruction

in connection with limited boundary acquisition geometry. The formation of caustics

leads to one of the complications which will be discussed. We illustrate various

aspects of this research program with examples from global seismology and mineral

physics coupled to thermo-chemical convection.

Series: Other Talks

Hosted by Academic Affairs Honors Program in collaboration with the College of Sciences.

To watch a 15-minute presentation by Dr. Nadkarni see the

YouTube link.

YouTube link.

Series: Analysis Seminar

Let mu be a measure with compact support, with orthonormal polynomials {p_{n}} and associated reproducing kernels {K_{n}}. We show that bulk universality holds in measure in {x:mu'(x)>0}. The novelty is that there are no local or global conditions on the measure. Previous results have required regularity as a global condition, and a Szego condition as a local condition.As a consequence, for a subsequence of integers, universality holds for a.e. x. Under additional conditions on the measure, we show universality holds in an L_{p} sense for all finite p>0.

Series: Analysis Working Seminar

We start the sufficiency proof of arXiv:1001.4043,

which

characterizes the two weight inequality for the Hilbert

transform. This session will be devoted to the martingale methods employed. Joint work with Ignacio

Uriate-Tuero, and

Eric Sawyer.

which

characterizes the two weight inequality for the Hilbert

transform. This session will be devoted to the martingale methods employed. Joint work with Ignacio

Uriate-Tuero, and

Eric Sawyer.