Seminars and Colloquia Schedule

Synchronization of Cows

Series
Mathematical Biology Seminar
Time
Tuesday, September 7, 2010 - 17:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Mason Porter – Oxford University
The study of collective behavior---of animals, mechanical systems, or even abstract oscillators---has fascinated a large number of researchers from observational geologists to pure mathematicians. We consider the collective behavior of herds of cattle. We first consider some results from an agent-based model and then formulate a mathematical model for the daily activities of a cow (eating, lying down, and standing) in terms of a piecewise affine dynamical system. We analyze the properties of this bovine dynamical system representing the single animal and develop an exact integrative form as a discrete-time mapping. We then couple multiple cow "oscillators" together to study synchrony and cooperation in cattle herds, finding that it is possible for cows to synchronize less when the coupling is increased. [This research is in collaboration with Jie Sun, Erik Bollt, and Marian Dawkins.]

Character varieties of knots and tropical curves

Series
Tropical Geometry Seminar
Time
Wednesday, September 8, 2010 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Stavros Garoufalidis – Georgia Tech
The moduli space of representations of a fundamental group of a knot in SL(2,C) is an affine algebraic variety, and generically a complex curve, with an explicit projection to C^2. The ideal that defines this curve has special type described by binomial and linear equations. I will motivate this curve using elementary hyperbolic geometry, and its Newton polygon in the plane using geometric topology. Finally, I will describe a heuristic method for computing the Newton polygon without computing the curve itself, using tropical implitization, work in progress with Josephine Yu. The talk will be concrete, with examples of concrete curves that come from knots. This talk involves classical mathematics. A sequel of it will discuss quantum character varieties of knots and tropical curves.

The size of crossings in antichains

Series
Research Horizons Seminar
Time
Wednesday, September 8, 2010 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 171 (NOTICE THE CHANGE OF ROOM)
Speaker
Tom Trotter – School of Mathematics - Georgia Institute of Technology

Hosted by: Yao Li and Ricardo Restrepo

Combinatorial mathematics exhibits a number of elegant, simply stated problems that turn out to be surprisingly challenging. In this talk, I report on a problem of this type on which I have been working with Noah Streib, Stephen Young and Ruidong Wang from Georgia Tech, as well as Piotr Micek, Bartek Walczak and Tomek Krawczyk, all computer scientists from Poland. Given positive integers $k$ and $w$, what is the largest integer $t = f(k,w)$ for which there exists a family $\mathcal{F}$ of $t$ vectors in $N^{w}$ so that: \begin{enumerate} \item Any two vectors in the family $\mathcal{F}$ are incomparable in the product ordering; and \item There do not exist two vectors $A$ and $B$ in the family for which there are distinct $i$ and $j$ so that $a_i\ge k +b_i$ and $b_j \ge k + a_j$. \end{enumerate} The Polish group posed the problem to us at the SIAM Discrete Mathematics held in Austin, Texas, this summer. They were able to establish the following bounds: \[ k^{w-1} \le t \le k^w \] We were able to show that the lower bound is essentially correct by showing that there is a constant $c_w$ so that $t \l c_w k^{w-1}$. But recent work suggests that the lower bound might actually be tight.

The Point Mass Problem on the Real Line

Series
Analysis Seminar
Time
Wednesday, September 8, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Manwah Wong – Georgia Tech
In this talk, I will talk about recent developments on the point mass problem on the real line. Starting from the point mass formula for orthogonal polynomials on the real line, I will present new methods employed to compute the asymptotic formulae for the orthogonal polynomials and how these formulae can be applied to solve the point mass problem when the recurrence coefficients are asymptotically identical. The technical difficulties involved in the computation will also be discussed.

Non-loose torus knots.

Series
Geometry Topology Working Seminar
Time
Thursday, September 9, 2010 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Amey Kaloti – Georgia Tech. –

This talk is part of the oral exam for the speaker. Please note the special time, place. Also the talk itself will be 45 min long.

Non-loose knots is a special class of knots studied in contact geometry. Last couple of years have shown some applications of these kinds of knots. Even though defined for a long time, not much is known about their classification except for the case of unknot. In this talk we will summarize what is known and tell about the recent work in which we are trying to give classification in the case of trefoil.

On randomizing two derandomized greedy algorithms

Series
Combinatorics Seminar
Time
Friday, September 10, 2010 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Kevin Costello – SoM, Georgia Tech
Many of the simplest and easiest implemented approximation algorithms can be thought of as derandomizations of the naive random algorithm.  Here we consider the question of whether performing the algorithm on a random reordering of the variables provides an improvement in the worst case expected performance. (1) For Johnson's algorithm for Maximum Satisfiability, we show this is indeed the case: While in the worst case Johnson's algorithm only provides a 2/3 approximation, the additional randomization step guarantees a 2/3+c approximation for some positive c. (2) For the greedy algorithm for MAX-CUT, we show to the contrary that the randomized version does NOT provide a 1/2+c approximation for any c on general graphs. This is in contrast to a result of Mathieu and Schudy showing it provides a 1-epsilon approximation on dense graphs. Joint with Asaf Shapira and Prasad Tetali.