October 2021

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Friday, October 1, 2021 — 3:30 PM EDT

Title: Quantum information science for combinatorial optimization

Speaker: Stephen Jordan Affiliation: Microsoft Quantum & University of Maryland Zoom: Please email Emma Watson

Abstract:

Due to input-output bottlenecks, quantum computers are expected to be most applicable to problems for which the quantity of data specifying the instance is small but the computational cost of finding a solution is large. Aside from cryptanalysis and quantum simulation, combinatorial optimization provides some of the best candidates for problems of real-world impact fitting these criteria. Many of these problems are NP-hard and thus unlikely to be solvable on quantum computers with polynomial worst-case time complexity.

Monday, October 4, 2021 — 11:30 to 11:30 AM EDT

Title: Four families of polynomials in spectral graph theory

Speaker: Miguel Angel Fiol Mora Affiliation: Universitat Politècnica de Catalunya Zoom: Contact Soffia Arnadottir

Abstract:

 In this talk we describe four families of polynomials related to the spectrum of a graph. First, some known main results involving such polynomials, such as the spectral excess theorem characterizing distance-regularity, are discussed. Second, some new results giving bounds for the $k$-independence number $\alpha_k$ of a graph are presented. In this context, we comment on some relationships between the inertia (Cvetkovi\`c) and ratio (Hoffman) bounds of $\alpha_k$.

Thursday, October 7, 2021 — 1:00 PM EDT

Title: Newell-Littlewood numbers

Speaker: Shiliang Gao Affiliation: University of Illinois at Urbana-Champaign Zoom: Contact Steve Melczer

Abstract:

The Newell-Littlewood numbers are defined in terms of the Littlewood-Richardson coefficients. Both arise as tensor product multiplicities for a classical Lie group. A. Klyachko connected eigenvalues of sums of Hermitian matrices to the saturated LR-cone and established defining linear inequalities.

Friday, October 8, 2021 — 3:30 PM EDT

Title: Induced subgraphs and treewidth

Speaker: Sophie Spirkl Affiliation: University of Waterloo Zoom: Please email Emma Watson

Abstract:

Treewidth, introduced by Robertson and Seymour in the graph minors series, is a fundamental measure of the complexity of a graph. While their results give an answer to the question, “what minors occur in graphs of large treewidth?,” the same question for induced subgraphs is still open. I will talk about some conjectures and recent results in this area.

Joint work with Tara Abrishami, Maria Chudnovsky, Cemil Dibek, Sepehr Hajebi, Pawel Rzazewski, Kristina Vuskovic.

Friday, October 22, 2021 — 3:30 PM EDT

Title: Dyadic Linear Programming

Speaker: Ahmad Abdi Affiliation: London School of Economics Zoom: Please email Emma Watson

Abstract:

Most linear programming solvers use fixed-precision floating points to approximate the rational numbers. Though successful on most real-world instances, solvers sometimes run into serious issues when carrying out sequential floating-point arithmetic, due to compounded error terms. This practical limitation leads to the following theoretical problem:

Monday, October 25, 2021 — 11:30 to 11:30 AM EDT

Title: State transfer on graphs with twin vertices

Speaker: Hermie Monterde Affiliation: University of Manitoba Zoom: Contact Soffia Arnadottir

Abstract:

In this talk, we discuss algebraic and spectral properties of graphs with twin vertices that are important in quantum state transfer. We give a characterization of strong cospectrality between twin vertices, and characterize some types of state transfer that occur between them.

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