Seminars and Colloquia by Series

Subdivision and Algebraic Geometry for Certified Correct Computations

Series
Algebra Seminar
Time
Monday, February 11, 2013 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Michael Burr – Clemson University
Many real-world problems require an approximation to an algebraic variety (e.g., determination of the roots of a polynomial). To solve such problems, the standard techniques are either symbolic or numeric. Symbolic techniques are globally correct, but they are often time consuming to compute. Numerical techniques are typically fast, but include more limited correctness statements. Recently, attention has shifted to hybrid techniques that combine symbolic and numerical techniques. In this talk, I will discuss hybrid subdivision algorithms for approximating a variety. These methods recursively subdivide an initial region into smaller and simpler domains which are easier to characterize. These algorithms are typically recursive, making them both easy to implement (in practice) and adaptive (performing more work near difficult features). There are two challenges: to develop algorithms with global correctness guarantees and to determine the efficiency of such algorithms. I will discuss solutions to these challenges by presenting two hybrid subdivision algorithms. The first algorithm computes a piecewise-linear approximation to a real planar curve. This is one of the first numerical algorithms whose output is guaranteed to be topologically correct, even in the presence of singularities. The primitives in this algorithm are numerical (i.e., they evaluate a polynomial and its derivatives), but its correctness is justified with algebraic geometry and symbolic algebra. The second algorithm isolates the real roots of a univariate polynomial. I will analyze the number of subdivisions performed by this algorithm using a new technique called continuous amortization. I will show that the number of subdivisions performed by this algorithm is nearly optimal and is comparable with standard symbolic techniques for solving this problem (e.g., Descartes' rule of signs or Sturm sequences).

Atlanta Lecture Series in Combinatorics and Graph Theory VIII

Series
Other Talks
Time
Saturday, February 9, 2013 - 09:00 for 1 hour (actually 50 minutes)
Location
Georgia State University
Speaker
Van Vu – Yale University
Emory University, the Georgia Institute of Technology and Georgia State University, with support from the National Security Agency and the National Science Foundation, are hosting a series of mini-conferences. The eighth in the series will be held at Georgia State University on February 9 -10, 2013. This mini-conference's featured speaker is Dr. Van Vu, who will give two one-hour lectures. There will be five one-hour talks and a number of half-hour talks given by other invited speakers. For more info, check titles, abstracts, and schedule.

Random Matrices: Law of the Determinant

Series
School of Mathematics Colloquium
Time
Friday, February 8, 2013 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Van Vu – Yale University
Random matrix theory is a fast developing topic with connections to so many areas of mathematics: probability, number theory, combinatorics, data analysis, mathematical physics, to mention a few. The determinant is one of the most studied matrix functionals. In our talk, we are going to give a brief survey on the studies of this functional, dated back to Turan in the 1940s. The main focus will be on recent developments that establish the limiting law in various models.

Courtesy Listing: Modeling the toughness of metallic glasses

Series
Other Talks
Time
Friday, February 8, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Klaus 2443
Speaker
Chris Rycroft – UC Berkeley and LBNL

Please Note: School of Computational Science and Engineering job candidate talk

Metallic glasses are a new type of alloy whose atoms have an amorphous arrangement in contrast to most metals. They have many favorable properties such as excellent wear resistance and high tensile strength, but are prone to breakage in some circumstances, depending on their method of preparation. The talk will describe the development of a quasi-static projection method within an Eulerian finite-difference framework, for simulating a new physical model of a metallic glass. The simulations are capable of resolving the multiple timescales that are involved, and provide an explanation of the experimentally observed differences in breakage strength, which may aid in the use of these materials in practical applications. The same Eulerian simulation framework can be adapted to address a variety of other problems, such as fluid-structure interaction, and the mechanical modeling of multicellular clusters.

Discrete models in systems biology

Series
ACO Student Seminar
Time
Friday, February 8, 2013 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
David Murrugarra – School of Math, Georgia Tech –
Understanding how the physiology of organisms arises through the dynamic interaction of the molecular constituents of life is an important goal of molecular systems biology, for which mathematical modeling can be very helpful. Different modeling strategies have been used for this purpose. Dynamic mathematical models can be broadly divided into two classes: continuous, such as systems of differential equations and their stochastic variants and discrete, such as Boolean networks and their generalizations. This talk will focus on the discrete modeling approach. Applications will include the study of stochasticity under this setting. No background in mathematical biology is required, and the talk will be accessible to a broad audience.

Conormals and contact homology IV

Series
Geometry Topology Working Seminar
Time
Friday, February 8, 2013 - 11:30 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
John Etnyre – Ga Tech
In this series of talks I will begin by discussing the idea of studying smooth manifolds and their submanifolds using the symplectic (and contact) geometry of their cotangent bundles. I will then discuss Legendrian contact homology, a powerful invariant of Legendrian submanifolds of contact manifolds. After discussing the theory of contact homology, examples and useful computational techniques, I will combine this with the conormal discussion to define Knot Contact Homology and discuss its many wonders properties and conjectures concerning its connection to other invariants of knots in S^3.

Universality of isoradial dimers and conformal invariance of height distributions - Rescheduled

Series
Job Candidate Talk
Time
Thursday, February 7, 2013 - 16:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Zhongyang Li – University of Cambridge –
An isoradial graph is one which can be embedded into the plane such that each face is inscribable in a circle of common radius. We consider the superposition of an isoradial graph, and its interior dual graph, approximating a simply-connected domain, and prove that the height function associated to the dimer configurations is conformally invariant in the scaling limit, and has the same distribution as a Gaussian Free Field.

1-Bit Matrix Completion

Series
Stochastics Seminar
Time
Thursday, February 7, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skyles 006
Speaker
Mark Davenport – Georgia Institute of Technology
In this talk I will describe a theory of matrix completion for the extreme case of noisy 1-bit observations. In this setting, instead of observing a subset of the real-valued entries of a matrix M, we obtain a small number of binary (1-bit) measurements generated according to a probability distribution determined by the real-valued entries of M. The central question I will address is whether or not it is possible to obtain an accurate estimate of M from this data. In general this would seem impossible, but I will show that the maximum likelihood estimate under a suitable constraint returns an accurate estimate of M when $\|M\|_{\infty} \le \alpha$ and $\rank(M) \le r$. If the log-likelihood is a concave function (e.g., the logistic or probit observation models), then we can obtain this maximum likelihood estimate by optimizing a convex program. I will also provide lower bounds showing that this estimate is near-optimal and illustrate the potential of this method with some preliminary numerical simulations.

(5,2)-configurations in K_{1,6}-free graphs

Series
Graph Theory Seminar
Time
Thursday, February 7, 2013 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Chun-Hung Liu – Math, GT
A (5,2)-configuration in a graph G is a function which maps the vertices of G into 2-element subsets of {1,2,3,4,5} in such a way that for every vertex u, the union of the 2-element subsets assigned to u and all its neighbors is {1,2,3,4,5}. This notion is motivated by a problem in robotics. Fujita, Yamashita and Kameda showed that every 3-regular graph has a (5,2)-configuration. In this talk, we will prove that except for four graphs, every graph of minimum degree at least two which does not contain K_{1,6} as an induced subgraph has a (5,2)-configuration. This is joint work with Waseem Abbas, Magnus Egerstedt, Robin Thomas, and Peter Whalen.

One sided bump conditions and two weight boundedness of Calderon-Zygmund operators

Series
Analysis Seminar
Time
Wednesday, February 6, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Alexander Reznikov – Michigan State University
We consider a so-called "One sided bump conjecture", which gives asufficient condition for two weight boundedness of a Calderon-Zygmundoperator. The proof will essentially use the Corona decomposition, which isa main tool for a first proof of $A_2$ (also, $A_p$ and $A_p-A_\infty$)conjecture. We will focus on main difficulty, that does not allow to get afull proof of our one sided bump conjecture.

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