Monday, September 27, 2021 — 11:30 AM EDT

Title: Graph Continued Fractions

Speaker: Thomás Spier
Affiliation: Matemática Pura e Aplicada (IMPA)
Zoom: Contact Soffia Arnadottir

Abstract:

This talk is about a connection between matching polynomials and continued fractions. For the matching polynomials: we prove a refinement of a theorem by Ku and Wong, which extends the classical Gallai-Edmonds decomposition;

Thursday, September 30, 2021 — 10:00 AM EDT

Title: Semidefinite Optimization Approaches for Reactive Optimal Power Flow Problems

Speaker: Miguel Anjos
Affiliation: University of Edinburgh
Zoom: Register through The Fields Institute

Abstract:

The Reactive Optimal Power Flow (ROPF) problem consists in computing an optimal power generation dispatch for an alternating current transmission network that respects power flow equations and operational constraints. Some means of voltage control are modelled in ROPF such as the possible activation of shunts, and these controls are modelled using discrete variables. The ROPF problem belongs to the class of nonconvex MINLPs, which are NP-hard problems. We consider semidefinite optimization approaches for solving ROPF problems and their integration into a branch-and-bound algorithm.

Thursday, September 30, 2021 — 11:00 AM EDT

Title: Structured (In)Feasibility: Nonmonotone Operator Splitting in Nonlinear Spaces

Speaker: Bissan Ghaddar
Affiliation: Western University
Zoom: Register through The Fields Institute

Abstract:

Several challenging optimization problems in power networks involve operational decisions, non-linear models of the underlying physics described by the network as well as uncertainty in the system parameters. However, these networks exhibit a nice structure. This talk provides an overview of approaches that combine recent advances in robust optimization and conic relaxations of polynomial optimization problems along with exploiting the structure of the underlying problem. These approaches are demonstrated on applications arising in power networks.

Thursday, September 30, 2021 — 1:00 PM EDT

Title: Forcing Quasirandomness in Permutations

Speaker: John Noel
Affiliation: University of Victoria
Zoom: Contact Steve Melczer

Abstract:

A striking result in graph theory is that the property of a graph being quasirandom (i.e. resembling a random graph) is characterized by the number of edges and the number of 4-cycles being close to the expected number in a random graph. Král’ and Pikhurko (2013) proved an analogous result for permutations; i.e. that quasirandom permutations are characterized by the densities of all permutations of length 4.

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.

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.

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