Seminars and Colloquia Schedule

AWM lunch talk- Partition Identities Related to Stanley's Theorem

Series
Other Talks
Time
Wednesday, October 11, 2017 - 11:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Maxie Schmidt – Georgia Tech –

Lunch will be provided. The talk will be the first 25 minutes of the hour and then will be followed by discussion.

In a recent article to appear in the American Mathematical Mothly next year, we use the Lambert series generating function for Euler’s totient function to introduce a new identity for the number of 1’s in the partitions of n. New expansions for Euler’s partition function p(n) are derived in this context. These surprising new results connect the famous classical totient function from multiplicative number theory to the additive theory of partitions. We will define partitions and several variants of Euler's partition function in the talk to state our new results.

Computing Heegaard Floer homology by factoring mapping classes

Series
Geometry Topology Student Seminar
Time
Wednesday, October 11, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Justin Lanier – Georgia Tech
We will discuss the mapping class groupoid, how it is generated by handle slides, and how factoring in the mapping class groupoid can be used to compute Heegaard Floer homology. This talk is based on work by Lipshitz, Ozsvath, and Thurston.

Dynamical sampling and connections to operator theory and functional analysis

Series
Analysis Seminar
Time
Wednesday, October 11, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Akram Aldroubi – Vanderbilt University
Dynamical sampling is the problem of recovering an unknown function from a set of space-time samples. This problem has many connections to problems in frame theory, operator theory and functional analysis. In this talk, we will state the problem and discuss its relations to various areas of functional analysis and operator theory, and we will give a brief review of previous results and present several new ones.

Divisor Theory on Curves

Series
Student Algebraic Geometry Seminar
Time
Friday, October 13, 2017 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Libby Taylor – GA Tech
We will give an overview of divisor theory on curves and give definitions of the Picard group and the Jacobian of a compact Riemann surface. We will use these notions to prove Plucker’s formula for the genus of a smooth projective curve. In addition, we will discuss the various ways of defining the Jacobian of a curve and why these definitions are equivalent. We will also give an extension of these notions to schemes, in which we define the Picard group of a scheme in terms of the group of invertible sheaves and in terms of sheaf cohomology.

Determinant-Preserving Sparsification of SDDM Matrices with Applications to Counting and Sampling Spanning Trees

Series
ACO Student Seminar
Time
Friday, October 13, 2017 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
David Durfee – CS, Georgia Tech –
We show variants of spectral sparsification routines can preserve thetotal spanning tree counts of graphs, which by Kirchhoff's matrix-treetheorem, is equivalent to determinant of a graph Laplacian minor, orequivalently, of any SDDM matrix. Our analyses utilizes thiscombinatorial connection to bridge between statistical leverage scores/ effective resistances and the analysis of random graphs by [Janson,Combinatorics, Probability and Computing `94]. This leads to a routinethat in quadratic time, sparsifies a graph down to about $n^{1.5}$edges in ways that preserve both the determinant and the distributionof spanning trees (provided the sparsified graph is viewed as a randomobject). Extending this algorithm to work with Schur complements andapproximate Choleksy factorizations leads to algorithms for countingand sampling spanning trees which are nearly optimal for dense graphs.We give an algorithm that computes a $(1\pm \delta)$ approximation tothe determinant of any SDDM matrix with constant probability in about$n^2\delta^{−2}$ time. This is the first routine for graphs thatoutperforms general-purpose routines for computing determinants ofarbitrary matrices. We also give an algorithm that generates in about$n^2\delta^{−2}$ time a spanning tree of a weighted undirected graphfrom a distribution with total variation distance of $\delta$ fromthe w-uniform distribution.This is joint work with John Peebles, Richard Peng and Anup B. Rao.

Branched covers I

Series
Geometry Topology Working Seminar
Time
Friday, October 13, 2017 - 13:55 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
John Etnyre – Georgia Tech
In this series of talks I will introduce branched coverings of manifolds and sketch proofs of most the known results in low dimensions (such as every 3 manifold is a 3-fold branched cover over a knot in the 3-sphere and the existence of universal knots). Along the way several open problems will be discussed.

Local dimension and size of a poset

Series
Combinatorics Seminar
Time
Friday, October 13, 2017 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Heather Smith – Georgia Tech
The original notion of poset dimension is due to Dushnik and Miller (1941). Last year, Uerckerdt (2016) proposed a variant, called local dimension, which has garnered considerable interest. A local realizer of a poset P is a collection of partial linear extensions of P that cover the comparabilities and incomparabilities of P. The local dimension of P is the minimum frequency of a local realizer where frequency is the maximum multiplicity of an element of P. Hiraguchi (1955) proved that any poset with n points has dimension at most n/2, which is sharp. We prove that the local dimension of a poset with n points is O(n/log n). To show that this bound is best possible, we use probabilistic methods to prove the following stronger result which extends a theorem of Chung, Erdős, and Spencer (1983): There is an n-vertex bipartite graph in which each difference graph cover of the edges will cover one of the vertices Θ(n/log n) times. (This is joint work with Jinha Kim, Ryan R. Martin, Tomáš Masařı́k, Warren Shull, Andrew Uzzell, and Zhiyu Wang)

A Topological Proof of Birkhoff's Theorem

Series
Dynamical Systems Working Seminar
Time
Friday, October 13, 2017 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 154
Speaker
Bhanu Kumar – GT Math
Birkhoff's Theorem is a result useful in characterizing the boundary of certain open sets U ⊂ T^1 x [0, inf) which are invariant under "vertical-tilting" homeomorphisms H. We present the method used by A. Fathi to prove Birkhoff's theorem, which develops a series of lemmas using topological arguments to prove that this boundary is a graph.