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Friday, March 16, 2018 - 10:00 ,
Location: Skiles 006 ,
Kisun Lee ,
Georgia Tech ,
klee669@gatech.edu ,
Organizer: Kisun Lee

Expanding the topic we discussed on last week, we consider the way to certify roots for system of equations with D-finite functions. In order to do this, we will first introduce the notion of D-finite functions, and observe the property of them. We also suggest two different ways to certify this, that is, alpha-theory and the Krawczyk method. We use the concept of majorant series for D-finite functions to apply above two methods for certification. After considering concepts about alpha-theory and the Krawczyk method, we finish the talk with suggesting some open problems about these.

Series: Dissertation Defense

I will discuss two topics in Dynamical Systems. A uniformly hyperbolic dynamical system preserving Borel probability measure μ is called fair dice like or FDL if there exists a finite Markov partition ξ of its phase space M such that for any integers m and j(i), 1 ≤ j(i) ≤ q one has μ ( C(ξ, j(0)) ∩ T^(-1) C(ξ, j(1)) ∩ ... ∩ T^(-m+1)C(ξ, j(m-1)) ) = q^(-m) where q is the number of elements in the partition ξ and C(ξ, j) is element number j of ξ. I discuss several results about such systems concerning finite time prediction regarding the first hitting probabilities of the members of ξ. Then I will discuss a natural modification to all billiard models which is called the Physical Billiard. For some classes of billiard, this modification completely changes their dynamics. I will discuss a particular example derived from the Ehrenfests' Wind-Tree model. The Physical Wind-Tree model displays interesting new dynamical behavior that is at least as rich as some of the most well studied examples that have come before.

Wednesday, March 14, 2018 - 14:00 ,
Location: Skiles 006 ,
Surena Hozoori ,
GaTech ,
Organizer: Anubhav Mukherjee

Assuming
some "compatibility" conditions between a Riemannian metric and a
contact structure on a 3-manifold, it is natural to ask whether
we can use methods in global geometry to get results in contact topology. There is a notion
of compatibility in this context which relates convexity concepts in
those geometries and is well studied concerning geometry questions, but
is not exploited for topological questions. I will talk about "contact
sphere theorem" due to Etnyre-Massot-Komendarczyk,
which might be the most interesting result for contact topologists.

Series: Analysis Seminar

We consider totally irregular measures $\mu$ in $\mathbb{R}^{n+1}$, that is, $$\limsup_{r\to0}\frac{\mu(B(x,r))}{(2r)^n} >0 \;\; \& \;\; \liminf_{r\to0}\frac{\mu(B(x,r))}{(2r)^n}=0$$for $\mu$ almost every $x$. We will show that if $T_\mu f(x)=\int K(x,y)\,f(y)\,d\mu(y)$ is an operator whose kernel $K(\cdot,\cdot)$ is the gradient of the fundamental solution for a uniformly elliptic operator in divergence form associated with a matrix with H\"older continuous coefficients, then $T_\mu$ is not bounded in $L^2(\mu)$.This extends a celebrated result proved previously by Eiderman, Nazarov and Volberg for the $n$-dimensional Riesz transform and is part of the program to clarify the connection between rectifiability of sets/measures on $\mathbb{R}^{n+1}$ and boundedness of singular integrals there. Based on joint work with Mihalis Mourgoglou and Xavier Tolsa.

Series: Research Horizons Seminar

There
is so much that the GT library can do for you, from providing research
materials to assistance with data visualization to patent guidance.
However, rather than trying to guess what you want from us, this year we
asked!
Based on the response to a short ranking survey I sent out last month, this session will cover: 1. How to find grants, fellowships, and travel money with the sponsorship database, Pivot. There are opportunities for postdocs and non US citizens too!2. How to use MathSciNet. We will cover navigating its classification index to actually getting the article
you want. 3. How to find and download articles from our systems, Google Scholar, and from other libraries. And if we have time: 4. How to make a poster and cheaply print it.

Series: Algebra Seminar

The structure of non-archimedean curves X and their tame covers f:Y-->X is well understoodand can be adequately described in terms of a (simultaneous) semistable model. In particular, asindicated by the lifting theorem of Amini-Baker-Brugalle-Rabinoff, it encodes all combinatorialand residual algebra-geometric information about f. My talk will be mainly concerned with the morecomplicated case of wild covers, where new discrete invariants appear, with the different function being the most basic one. I will recall its basic properties following my joint work with Cohen and Trushin,and will then pass to the latest results proved jointly with U. Brezner: the different functioncan be refined to an invariant of a residual type, which is a (sort of) meromorphic differential form on the reduction, so that a lifting theorem in the style of ABBR holds for simplest wild covers.

Series: Geometry Topology Seminar

Series: CDSNS Colloquium

The derivative nonlinear Schrödinger equation (DNLS) is an integrable, mass-critical PDE. The integrals of motion may be written as an infinite sequence of functionals on Sobolev spaces of increasing regularity. I will show how to associate to them a family of invariant Gibbs measures, if the L^2 norm of the solution is sufficiently small (mass-criticality). A joint work with R. Lucà (Basel) and D. Valeri (Beijing).

Series: Dissertation Defense

Constrained low rank approximation is a general framework for data analysis, which usually has the advantage of being simple, fast, scalable and domain general. One of the most known constrained low rank approximation method is nonnegative matrix factorization (NMF). This research studies the design and implementation of several variants of NMF for text, graph and hybrid data analytics. It will address challenges including solving new data analytics problems and improving the scalability of existing NMF algorithms. There are two major types of matrix representation of data: feature-data matrix and similarity matrix. Previous work showed successful application of standard NMF for feature-data matrix to areas such as text mining and image analysis, and Symmetric NMF (SymNMF) for similarity matrix to areas such as graph clustering and community detection. In this work, a divide-and-conquer strategy is applied to both methods to improve their time complexity from cubic growth with respect to the reduced low rank to linear growth, resulting in DC-NMF and HierSymNMF2 method. Extensive experiments on large scale real world data shows improved performance of these two methods.Furthermore, in this work NMF and SymNMF are combined into one formulation called JointNMF, to analyze hybrid data that contains both text content and connection structure information. Typical hybrid data where JointNMF can be applied includes paper/patent data where there are citation connections among content and email data where the sender/receipts relation is represented by a hypergraph and the email content is associated with hypergraph edges. An additional capability of the JointNMF is prediction of unknown network information which is illustrated using several real world problems such as citation recommendations of papers and activity/leader detection in organizations.The dissertation also includes brief discussions of relationship among different variants of NMF.

Series: Other Talks

This is an Atlanta Science Festival performance in which mathematicians team up with dancers to give an artistic interpretation to the public of some mathematicians and some mathematical concepts. This year's show will have an emphasis on graph theory. There will be two performances at Drew Charter School in East Atlanta. For tickets go to https://www.freshtix.com/events/mathematics-in-motion---4pm-showing or https://www.freshtix.com/events/mathematics-in-motion---7pm-showing .