Seminars and Colloquia by Series

Linear Colorings of Subcubic Graphs

Series
ACO Student Seminar
Time
Friday, September 14, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Chun-Hung Liu – Georgia Tech, Math
A linear coloring of a graph is a proper coloring of the vertices of the graph so that each pair of color classes induce a union of disjoint paths. In this talk, I will prove that for every connected graph with maximum degree at most three and every assignment of lists of size four to the vertices of the graph, there exists a linear coloring such that the color of each vertex belongs to the list assigned to that vertex and the neighbors of every degree-two vertex receive different colors, unless the graph is $C_5$ or $K_{3,3}$. This confirms a conjecture raised by Esperet, Montassier, and Raspaud. Our proof is constructive and yields a linear-time algorithm to find such a coloring. This is joint work with Gexin Yu.

Surface bundles over surfaces

Series
Geometry Topology Working Seminar
Time
Friday, September 14, 2012 - 13:05 for 2 hours
Location
Skiles 006
Speaker
Dan Margalit – GaTech
We will introduce characteristic classes of surface bundles over surfaces. This will be a slower version of a talk I gave over the summer. The goal is to get to some of the recent papers on the subject.

Analysis of Boolean functions, influence and noise

Series
ACO Distinguished Lecture
Time
Thursday, September 13, 2012 - 16:30 for 1 hour (actually 50 minutes)
Location
Weber SST Room 2
Speaker
Gil Kalai – Hebrew University of Jerusalem

Please Note: Refreshments at 4PM in Lobby of Weber SST building

A few results and two general conjectures regarding analysis of Boolean functions, influence, and threshold phenomena will be presented. Boolean functions are functions of n Boolean variables with values in {0,1}. They are important in combinatorics, theoretical computer science, probability theory, and game theory. Influence. Causality is a topic of great interest everywhere, and if causality is not complicated enough, we can ask what is the influence one event has on another one. Ben-Or and Linial studied influence in the context of collective coin flipping---a problem in theoretical computer science. Fourier analysis. Over the last two decades, Fourier analysis of Boolean functions and related objects played a growing role in discrete mathematics, and theoretical computer science. Threshold phenomena. Threshold phenomena refer to sharp transition in the probability of certain events depending on a parameter p near a critical value. A classic example that goes back to Erdos and Renyi, is the behavior of certain monotone properties of random graphs. Influence of variables on Boolean functions is connected to their Fourier analysis and threshold behavior, as well as to discrete isoperimetry and noise sensitivity. The first Conjecture to be described (with Friedgut) is called the Entropy-Influence Conjecture. (It was featured on Tao's blog.) It gives a far-reaching extension to the KKL theorem, and theorems by Friedgut, Bourgain, and the speaker. The second Conjecture (with Kahn) proposes a far-reaching generalization of results by Friedgut, Bourgain and Hatami.

Toric Manifolds - Four Dimensions from Two

Series
Geometry Topology Student Seminar
Time
Wednesday, September 12, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jamie Conway – Georgia Tech
We will investigate a method of "seeing" properties of four dimensional symplectic spaces by looking at two dimensional pictures. We will see how to calculate the Euler characteristic, identify embedded surfaces, see intersection numbers, and how to see induced contact structures on the boundary of these manifolds.

Nonlinear transformations of moment sequences

Series
Analysis Seminar
Time
Wednesday, September 12, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Antonio Duran – University of Seville
In this talk we discuss some nonlinear transformations between moment sequences. One of these transformations is the following: if (a_n)_n is a non-vanishing Hausdorff moment sequence then the sequence defined by 1/(a_0 ... a_n) is a Stieltjes moment sequence. Our approach is constructive and use Euler's idea of developing q-infinite products in power series. Some others transformations will be considered as well as some relevant moment sequences and analytic functions related to them. We will also propose some conjectures about moment transformations defined by means of continuous fractions.

Orthogonal Polynomials and Random Matrices

Series
Research Horizons Seminar
Time
Wednesday, September 12, 2012 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Doron Lubinsky – School of Mathematics, Georgia Tech
Orthogonal polynomials turn out to be a useful tool in analyzing random matrices. We present some old and new aspects.

PhaseLift: Exact Phase Retrieval via Convex Programming

Series
Stelson Lecture Series
Time
Tuesday, September 11, 2012 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Emmanuel Candes – Departments of Mathematics and Statistics, Stanford University

Please Note: Mathematics lecture

This talks introduces a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Our approach combines multiple structured illuminations together with ideas from convex programming to recover the phase from intensity measurements, typically from the modulus of the diffracted wave. We demonstrate empirically that any complex-valued object can be recovered from the knowledge of the magnitude of just a few diffracted patterns by solving a simple convex optimization problem inspired by the recent literature on matrix completion. More importantly, we also demonstrate that our noise-aware algorithms are stable in the sense that the reconstruction degrades gracefully as the signal-to-noise ratio decreases. Finally, we present some novel theory showing that our entire approach may be provably surprisingly effective.

Discrete Mathematical Biology Working Seminar

Series
Other Talks
Time
Tuesday, September 11, 2012 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Will Perkins – Georgia Tech
We will discuss how best to model and predict the co-transcriptional effects of RNA folding. That is, using the fact that the RNA molecule begins folding as the sequence is still being transcribed, can we find better predictions for the secondary structure? And what is a good mathematical model for the process?

Robust principal component analysis? Some theory and some applications

Series
Stelson Lecture Series
Time
Monday, September 10, 2012 - 16:25 for 1 hour (actually 50 minutes)
Location
Clough Commons Room 144
Speaker
Emmanuel Candes – Stanford University

Please Note: General audience lecture

This talk is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions, it is possible to recover both the low-rank and the sparse components exactly by solving a very convenient convex program. This suggests the possibility of a principled approach to robust principal component analysis since our methodology and results assert that one can recover the principal components of a data matrix even though a positive fraction of its entries are arbitrarily corrupted. This extends to the situation where a fraction of the entries are missing as well. In the second part of the talk, we present applications in computer vision. In video surveillance, for example, our methodology allows for the detection of objects in a cluttered background. We show how the methodology can be adapted to simultaneously align a batch of images and correct serious defects/corruptions in each image, opening new perspectives.

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