Seminars and Colloquia by Series

Two-three linked graphs

Series
Graph Theory Seminar
Time
Thursday, November 2, 2017 - 13:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Shijie Xie – Math, GT
Let G be a graph containing 5 different vertices a0, a1, a2, b1 and b2. We say that (G, a0, a1, a2, b1, b2) is feasible if G contains disjoint connected subgraphs G1, G2, such that {a0, a1, a2}⊆V(G1) and {b1, b2}⊆V(G2). In this talk, we will introduce ideal frames, slim connectors and fat connectors. We will first deal with the ideal frames without fat connectors, by studying 3-edge and 5-edge configurations. Joint work with Changong Li, Robin Thomas, and Xingxing Yu.

Modern Erdos Magic

Series
School of Mathematics Colloquium
Time
Thursday, November 2, 2017 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Joel Spencer – Courant Institute, New York University
Traditional Erdos Magic (a.k.a. The Probabilistic Method) proves the existence of an object with certain properties by showing that a random (appropriately defined) object will have those properties with positive probability. Modern Erdos Magic analyzes a random process, a random (CS take note!) algorithm. These, when successful, can find a "needle in an exponential haystack" in polynomial time. We'll look at two particular examples, both involving a family of n-element sets under suitable side conditions. The Lovasz Local Lemma finds a coloring with no set monochromatic. A result of this speaker finds a coloring with low discrepency. In both cases the original proofs were not implementable but Modern Erdos Magic finds the colorings in polynomial times. The methods are varied. Basic probability and combinatorics. Brownian Motion. Semigroups. Martingales. Recursions ... and Tetris!

Modern Erdos Magic

Series
Joint School of Mathematics and ACO Colloquium
Time
Thursday, November 2, 2017 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Joel Spencer – Courant Institute, New York University
Traditional Erdos Magic (a.k.a. The Probabilistic Method) proves the existence of an object with certain properties by showing that a random (appropriately defined) object will have those properties with positive probability. Modern Erdos Magic analyzes a random process, a random (CS take note!) algorithm. These, when successful, can find a "needle in an exponential haystack" in polynomial time. We'll look at two particular examples, both involving a family of n-element sets under suitable side conditions. The Lovasz Local Lemma finds a coloring with no set monochromatic. A result of this speaker finds a coloring with low discrepency. In both cases the original proofs were not implementable but Modern Erdos Magic finds the colorings in polynomial times. The methods are varied. Basic probability and combinatorics. Brownian Motion. Semigroups. Martingales. Recursions ... and Tetris!

Bispectrality and superintegrability

Series
Analysis Seminar
Time
Wednesday, November 1, 2017 - 01:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Plamen Iliev – Georgia Tech
The bispectral problem concerns the construction and the classification of operators possessing a symmetry between the space and spectral variables. Different versions of this problem can be solved using techniques from integrable systems, algebraic geometry, representation theory, classical orthogonal polynomials, etc. I will review the problem and some of these connections and then discuss new results related to the generic quantum superintegrable system on the sphere.

Periods, motivic Gamma functions, and Hodge structures

Series
Athens-Atlanta Number Theory Seminar
Time
Monday, October 30, 2017 - 17:15 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Spencer Bloch – University of Chicago
Golyshev and Zagier found an interesting new source of periods associated to (eventually inhomogeneous) solutions generated by the Frobenius method for Picard Fuchs equations in the neighborhood of singular points with maximum unipotent monodromy. I will explain how this works, and how one can associate "motivic Gamma functions" and generalized Beilinson style variations of mixed Hodge structure to these solutions. This is joint work with M. Vlasenko.

Gonality and the strong uniform boundedness conjecture for periodic points

Series
Athens-Atlanta Number Theory Seminar
Time
Monday, October 30, 2017 - 16:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Bjorn Poonen – Massachusetts Institute of Technology
The function field case of the strong uniform boundedness conjecturefor torsion points on elliptic curves reduces to showing thatclassical modular curves have gonality tending to infinity.We prove an analogue for periodic points of polynomials under iterationby studying the geometry of analogous curves called dynatomic curves.This is joint work with John R. Doyle.

Transverse invariants, knot Floer homology and branched covers

Series
Geometry Topology Seminar
Time
Monday, October 30, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Shea Vela-Vick – LSU
Heegaard Floer theory provides a powerful suite of tools for studying 3-manifolds and their subspaces. In 2006, Ozsvath, Szabo and Thurston defined an invariant of transverse knots which takes values in a combinatorial version of this theory for knots in the 3—sphere. In this talk, we discuss a refinement of their combinatorial invariant via branched covers and discuss some of its properties. This is joint work with Mike Wong.

Dynamical Systems with Elastic Reflections

Series
Dynamical Systems Working Seminar
Time
Friday, October 27, 2017 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 154
Speaker
Hassan Attarchi – Georgia Tech
This presentation is about the results of a paper by Y. Sinai in 1970. Here, I will talk about dynamical systems which resulting from the motion of a material point in domains with strictly convex boundary, that is, such that the operator of the second quadratic form is negative-definite at each point of the boundary, where the boundary is taken to be equipped with the field of inward normals. It was proved that such systems are ergodic and are K-systems. The basic method of investigation is the construction of transversal foliations for such systems and the study of their properties.

Progress in showing cutoff for random walks on the symmetric group

Series
Combinatorics Seminar
Time
Friday, October 27, 2017 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Megan Bernstein – Georgia Tech
Cutoff is a remarkable property of many Markov chains in which they rapidly transition from an unmixed to a mixed distribution. Most random walks on the symmetric group, also known as card shuffles, are believed to mix with cutoff, but we are far from being able to proof this. We will survey existing cutoff results and techniques for random walks on the symmetric group, and present three recent results: cutoff for a biased transposition walk, cutoff for the random-to-random card shuffle (answering a 2001 conjecture of Diaconis), and pre-cutoff for the involution walk, generated by permutations with a binomially distributed number of two-cycles. The results use either probabilistic techniques such as strong stationary times or diagonalization through algebraic combinatorics and representation theory of the symmetric group. Includes joint work with Nayantara Bhatnagar, Evita Nestoridi, and Igor Pak.

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