Wednesday, October 24, 2018 - 12:20 , Location: Skiles 005 , Thang Le , Georgia Tech , Organizer: Trevor Gunn
A knot is a simple closed curve in the 3-space. Knots appeared as one of the first objects of study in topology. At first knot theory was rather isolated in mathematics. Lately due to newly discovered invariants and newly established connections to other branches of mathematics, knot theory has become an attractive and fertile area where many interesting, intriguing ideas collide. In this talk we discuss a new class of knot invariants coming out of the Jones polynomial and an algebra of surfaces based on knots (skein algebra) which has connections to many important objects including hyperbolic structures of surfaces and quantum groups. The talk is elementary.
Wednesday, October 17, 2018 - 12:20 , Location: Skiles 005 , Yoav Len , Georgia Tech , Organizer: Trevor Gunn
Tropical geometry provides a combinatorial approach for studying geometric objects by reducing them to graphs and polytopes. In recent years, tropical techniques have been applied in numerous areas such as optimization, number theory, phylogenetic trees in biology, and auction systems in economics. My talk will focus on geometric counting problems and their tropical counterpart. By considering these combinatorial gadgets, we gain newinsights into old problems, and tools for approaching new problems.
Wednesday, October 10, 2018 - 12:20 , Location: Skiles 005 , Guillermo Goldsztein , Georgia Tech , Organizer: Trevor Gunn
In 1665, Huygens discovered that, when two pendulum clocks hanged from a same wooden beam supported by two chairs, they synchronize in anti-phase mode. Metronomes provides a second example of oscillators that synchronize. As it can be seen in many YouTube videos, metronomes synchronize in-phase when oscillating on top of the same movable surface. In this talk, we will review these phenomena, introduce a mathematical model, and analyze the the different physical effects. We show that, in a certain parameter regime, the increase of the amplitude of the oscillations leads to a bifurcation from the anti-phase synchronization being stable to the in-phase synchronization being stable. This may explain the experimental observations.
Wednesday, October 3, 2018 - 12:20 , Location: Skiles 005 , Justin Lanier , Georgia Tech , Organizer: Trevor Gunn
After briefly describing my research interests, I’ll speak on two results that involve points moving around on surfaces. The first result shows how to “hear the shape of a billiard table.” A point bouncing around a polygon encodes a sequence of edges. We show how to recover geometric information about the table from the collection of all such bounce sequences. This is joint work with Calderon, Coles, Davis, and Oliveira. The second result answers the question, “Given n distinct points in a closed ball, when can a new point be added in a continuous fashion?” We answer this question for all values of n and for all dimensions. Our results generalize the Brouwer fixed point theorem, which gives a negative answer when n=1. This is joint work with Chen and Gadish.
Wednesday, September 26, 2018 - 12:20 , Location: Skiles 005 , Igor Pak , University of California, Los Angeles , email@example.com , Organizer: Trevor Gunn
Integer sequences arise in a large variety of combinatorial problems as a way to count combinatorial objects. Some of them have nice formulas, some have elegant recurrences, and some have nothing interesting about them at all. Can we characterize when? Can we even formalize what is a "formula"? I will try to answer these questions by presenting many examples, results and open problems. Note: This is an introductory general audience talk unrelated to the colloquium.
Wednesday, September 19, 2018 - 12:20 , Location: Skiles 005 , Blair Sullivan , North Carolina State University , firstname.lastname@example.org , Organizer: Trevor Gunn
In this talk, we describe transforming a theoretical algorithm from structural graph theory into open-source software being actively used for real-world data analysis in computational biology. Specifically, we apply the r-dominating set algorithm for graph classes of bounded expansion in the setting of metagenome analysis. We discuss algorithmic improvements required for a practical implementation, alongside exciting preliminary biological results (on real data!). Finally, we include a brief retrospective on the collaboration process. No prior knowledge in metagenomics or structural graph theory is assumed. Based on joint work with T. Brown, D. Moritz, M. O’Brien, F. Reidl and T. Reiter.