Seminars and Colloquia by Series

Testing Odd-Cycle Freeness of Boolean Functions

Series
Combinatorics Seminar
Time
Friday, April 22, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Elena Grigorescu – College of Computing, Georgia Tech
In the Property Testing model an algorithm is required to distinguish between the case that an object has a property or is far from having the property. Recently, there has been a lot of interest in understanding which properties of Boolean functions admit testers making only a constant number of queries, and a common theme investigated in this context is linear invariance. A series of gradual results has led to a conjectured characterization of all testable linear invariant properties. Some of these results consider properties where the query upper bounds are towers of exponentials of large height dependent on the distance parameter. A natural question suggested by these bounds is whether there are non-trivial families with testers making only a polynomial number of queries in the distance parameter.In this talk I will focus on a particular linear-invariant property where this is indeed the case: odd-cycle freeness.Informally, a Boolean function fon n variables is odd-cycle free if there is no x_1, x_2, .., x_2k+1 satisfying f(x_i)=1 and sum_i x_i = 0.This property is the Boolean function analogue of bipartiteness in the dense graph model. I will discuss two testing algorithms for this property: the first relies on graph eigenvalues considerations and the second on Fourier analytic techniques. I will also mention several related open problems. Based on joint work with Arnab Bhattacharyya, Prasad Raghavendra, Asaf Shapira

On the Huynh-Le Quantum Determinant and the Head and Tail of the Colored Jones Polynomial

Series
Geometry Topology Seminar
Time
Friday, April 22, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
C. Armond – Louisiana State University
In this talk I will describe how the quantum determinant modelof the Colored Jones polynomial, developed by Vu Huynh and Thang Le can beinterpreted in a combinatorial way as walks along a braid. Thisinterpretation can then be used to prove that the leading coefficients ofthe colored Jones polynomial stabalize, defining two power series calledthe head and the tail. I will also show examples where the head and tailcan be calculated explicitly and have applications in number theory.

Khovanov Homology and Slice Genus

Series
SIAM Student Seminar
Time
Friday, April 22, 2011 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 246
Speaker
Amey Kaloti – School of Mathematics, Georgia Tech

Please Note: Hosted also by Ben Webb

We will try to define what Khovanov homology for a link in a S^3 is. We will then try to give a proof figuring out unknotting number of certain kinds of knots in S^3.

Meixner matrix ensembles

Series
Stochastics Seminar
Time
Thursday, April 21, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Wlodek Bryc – University of Cincinnati

Please Note: Hosted by Christian Houdre and Liang Peng.

In this talk I will discuss random matrices that are matricial analogs of the well known binomial, Poisson, and negative binomial random variables. The common thread is the conditional variance of X given S = X+X', which is a quadratic polynomial in S and in the univariate case describes the family of six Meixner laws that will be described in the talk. The Laplace transform of a general n by n Meixner matrix ensemble satisfies a system of PDEs which is explicitly solvable for n = 2. The solutions lead to a family of six non-trivial 2 by 2 Meixner matrix ensembles. Constructions for the "elliptic cases" generalize to n by n matrices. The talk is based on joint work with Gerard Letac.

Control of Multi-Robot Networks

Series
Graph Theory Seminar
Time
Thursday, April 21, 2011 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Magnus Egerstedt – ECE, GT
Arguably, the overarching scientific challenge facing the area of networked robot systems is that of going from local rules to global behaviors in a predefined and stable manner. In particular, issues stemming from the network topology imply that not only must the individual agents satisfy some performance constraints in terms of their geometry, but also in terms of the combinatorial description of the network. Moreover, a multi-agent robotic network is only useful inasmuch as the agents can be redeployed and reprogrammed with relative ease, and we address these two issues (local interactions and programmability) from a controllability point-of-view. In particular, the problem of driving a collection of mobile robots to a given target destination is studied, and necessary conditions are given for this to be possible, based on tools from algebraic graph theory. The main result will be a necessary condition for an interaction topology to be controllable given in terms of the network's external, equitable partitions.

Topology of representation varieties of surface groups

Series
School of Mathematics Colloquium
Time
Thursday, April 21, 2011 - 11:01 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Richard Wentworth – University of Maryland –
This will be a survey talk on some aspects of the geometry and topology of moduli spaces of representations of surface groups into Lie groups. I will discuss recent generalizations of the techniques of Atiyah and Bott on equivariant Morse theory. These extend results on stable bundles to Higgs bundles and associated moduli spaces, which correspond to representation varieties into noncompact Lie groups

Hydrodynamic Analogues of Quantum Systems

Series
Math Physics Seminar
Time
Wednesday, April 20, 2011 - 15:00 for 1 hour (actually 50 minutes)
Location
Physics Howey L5
Speaker
John Bush – Department of Mathematics, MIT

Please Note: Hosted by Predrag Cvitanović, School of Physics, Georgia Tech.

Yves Couder and coworkers have recently reported the results of a startling series of experiments in which droplets bouncing on a fluid surface exhibit wave-particle duality and, as a consequence, several dynamical features previously thought to be peculiar to the microscopic realm, including single-particle diffraction, interference, tunneling and quantized orbits. We explore this fluid system in light of the Madelung transformation, whereby Schrodinger's equation is recast in a hydrodynamic form. Doing so reveals a remarkable correspondence between bouncing droplets and subatomic particles, and provides rationale for the observed macroscopic quantum behaviour. New experiments are presented, and indicate the potential value of this hydrodynamic approach to both visualizing and understanding quantum mechanics.

Music, Time-Frequency Shifts, and Linear Independence

Series
Research Horizons Seminar
Time
Wednesday, April 20, 2011 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Chris Heil – School of Mathematics - Georgia Institute of Technology

Please Note: Hosts: Amey Kaloti and Ricardo Restrepo

Fourier series provide a way of writing almost any signal as a superposition of pure tones, or musical notes.  But this representation is not local, and does not reflect the way that music is actually generated by instruments playing individual notes at different times.  We will discuss time-frequency representations, which are a type of local Fourier representation of signals.  This gives us a mathematical model for representing music.  While the model is crude for music, it is in fact apowerful mathematical representation that has appeared widely throughout mathematics (e.g., partial differential equations), physics (e.g., quantum mechanics), and engineering (e.g., time-varying filtering).  We ask one very basic question: are the notes in this representation linearly independent?  This seemingly trivial question leads to surprising mathematical difficulties.

A statistical model applied to 544 in vivo HIV-1 recombinants reveals that viral genomic features, especially RNA structure, promote recombination

Series
Mathematical Biology Seminar
Time
Wednesday, April 20, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Karin Dorman – Departments of Statistics and of Genetics, Development and Cell Biology, Iowa State University
It has long been postulated and somewhat confirmed with limited biological experiment, that RNA structure affects the propensity of HIV-1 reverse transcriptase to undergo strand transfer, a prerequisite for recombination. Our goal was to use the large resource of in vivo recombinants isolated from patients and stored in the HIV database to determine whether there were signals in the HIV-1 genetic sequence, such as propensity to form RNA secondary structure, that promote recombination. Starting from 65,000 HIV-1 sequences at least 400 nucleotides long, we identified 2,360 recombinants involving exactly two distinct subtypes. Since we were interested in mechanistic causes, rather than selective causes, we reduced the number of recombinants to 544 verifiably unique events. We then fit a Gaussian Markov Random Field model with covariates in the mean to assess the impact of genetic features on recombination. We found SHAPE reactivities to be most strongly and negatively correlated with recombination rates, which agrees with the observation that pairing probabilities had an opposite, strong relationship with recombination. Less strongly associated, but still significant, we found G-rich stretches positively correlated, thermal stability negatively correlated, and GC content positively correlated with recombination. Interestingly, known in vitro hotspots did not explain much of the in vivo recombination.

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