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Monday, June 21, 2021 11:30 am - 11:30 am EDT (GMT -04:00)

Algebraic Graph Theory Seminar - Paula Kimmerling

Title: Average Mixing Matrices of Trees and Stars

Speaker: Paula Kimmerling
Affiliation: Washington State University
Zoom: Contact Soffia Arnadottir

Abstract:

We define the average mixing matrix (AMM) of a continuous-time quantum walk on a graph using the orthogonal projections onto the eigenspaces of the adjacency matrix A. From there, one of the properties that has been studied is the rank of the AMM. This is easiest to do if the eigenvalues of A are simple, and we’ll review some of the results on this from Coutinho et. al. (2018).

Thursday, June 24, 2021 1:00 pm - 1:00 pm EDT (GMT -04:00)

Algebraic Combinatorics Seminar - Terrence George

Title: Arctic curves for groves

Speaker: Terrence George
Affiliation: University of Michigan
Zoom: Contact Stephen Melczer

Abstract:

The limit shape phenomenon is a "law of large numbers" for random surfaces: the random surface looks macroscopically like the "average surface". The first result of this kind was the celebrated arctic circle theorem for domino tilings of the aztec diamond. The limit shape has macroscopic regions with different qualitative behavior, and the arctic curve is the boundary separating these regions.

Friday, June 25, 2021 3:30 pm - 3:30 pm EDT (GMT -04:00)

Tutte Colloquium - Dmitriy Drusvyatskiy

Title: From low probability to high confidence in stochastic convex optimization

Speaker: Dmitriy Drusvyatskiy
Affliliation: University of Washington
Zoom: Contact Emma Watson

Abstract:

Standard results in stochastic convex optimization bound the number of samples that an algorithm needs to generate a point with small function value in expectation. More nuanced high probability guarantees are rare, and typically either rely on “light-tail” noise assumptions or exhibit worse sample complexity. In this work, we show that a wide class of stochastic optimization algorithms can be augmented with high confidence bounds at an overhead cost that is only logarithmic in the confidence level and polylogarithmic in the condition number.

Monday, June 28, 2021 11:30 am - 11:30 am EDT (GMT -04:00)

Algebraic Graph Theory Seminar - Steve Kirkland

Title: State transfer for paths with weighted loops at the end vertices

Speaker: Steve Kirkland
Affiliation: University of Manitoba
Zoom: Contact Soffia Arnadottir

Abstract:

We consider a continuous time quantum walk on an unweighted path on n vertices, to which a loop of weight w has been added at each end vertex. Let f(t) denote the fidelity of state transfer from one end vertex to the other at time t. In this talk we give upper and lower bounds on f(t) in terms of w, n and t; further, given a > 0 we discuss the values of t for which f(t) > 1-a.

Monday, July 5, 2021 11:30 am - 11:30 am EDT (GMT -04:00)

Algebraic Graph Theory Seminar - Lord Kavi

Title: The $k$-Independence Number

Speaker: Lord Kavi
Affiliation: University of Ottawa
Zoom: Contact Soffia Arnadottir

Abstract:

An independent set, also known as a stable set or coclique, in a graph is a set of vertices, no two of which are adjacent. The size of a largest independent set is called the independence number. Two classical eigenvalue bounds on the independence number, proved using eigenvalue interlacing are the Hoffman's ratio bound and the Cvetkovi\'{c}'s inertia bound.

Monday, July 12, 2021 11:30 am - 11:30 am EDT (GMT -04:00)

Algebraic Graph Theory Seminar - Gabor Lippner

Title: Asymptotic quantum state transfer using two loops with large weights

Speaker: Gabor Lippner
Affiliation: Northeastern University
Zoom: Contact Soffia Arnadottir

Abstract:

We study the question of asymptotic transfer strength between two nodes of a graph when large weight loop edges are located at these nodes.  It turns out that the limiting strength can be exactly computed and depends only on the extended neighborhoods of the nodes.

Monday, July 19, 2021 11:30 am - 11:30 am EDT (GMT -04:00)

Algebraic Graph Theory Seminar - Michael Tait

Title: Two conjectures on the spread of graphs

Speaker: Michael Tait
Affiliation: Villanova University
Zoom: Contact Soffia Arnadottir

Abstract:

Given a graph $G$ let $\lambda_1$ and $\lambda_n$ be the maximum and minimum eigenvalues of its adjacency matrix and define the spread of $G$ to be $\lambda_1 - \lambda_n$. In this talk we discuss solutions to a pair of 20 year old conjectures of Gregory, Hershkowitz, and Kirkland regarding the spread of graphs.

Title: In Memoriam: Tom Coleman’s Contributions to Applied Mathematics and Optimization

Speakers:

Yuying Li, Stephen Wright, Alex Pothen, Bruce Hendrickson, Peter Forsyth, and Somayeh Moazeni

Affiliation:

SIAM Annual Meeting (AN21)

Registration: https://www.siam.org/conferences/cm/conference/an21

Description:

Thomas F. Coleman—a leader in optimization and scientific computing, professor at the University of Waterloo, and a SIAM Fellow—passed away on April 20, 2021. Tom served as the Director of the Theory Center at Cornell and then as Dean of the Faculty of Mathematics at the University of Waterloo. His research spanned continuous optimization, combinatorial scientific computing, automatic differentiation, financial optimization, mathematical software, etc. In this session, his wife and collaborator, Yuying Li, and five of his students and colleagues will describe the pioneering contributions that Tom made to these fields in his research.

Monday, July 19, 2021 4:15 pm - 4:15 pm EDT (GMT -04:00)

Special SIAM Annual Meeting Session

Title: In Memoriam: Tom Coleman’s Contributions to Applied Mathematics and Optimization

Speaker: Yuying Li, Stephen Wright, Alex Pothen, Bruce Hendrickson, Peter Forsyth, and Somayeh Moazeni
Affiliation: SIAM Annual Meeting (AN21)
Registration: https://www.siam.org/conferences/cm/conference/an21

Description

Thursday, July 22, 2021 1:00 pm - 1:00 pm EDT (GMT -04:00)

Algebraic Combinatorics Seminar - Nadia Lafrenière

Title: The spectrum of the random-to-below Markov chain

Speaker: Nadia Lafrenière
Affiliation: Dartmouth College
Zoom: Contact Stephen Melczer

Abstract:

The random-to-below shuffle of a deck of cards consists of removing any card randomly (with uniform probability), and inserting it anywhere below (with uniform probability). When looking at the eigenvalues of its transition matrix, they all seem to be rational and positive.