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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 - 1:00 pm EDT (GMT -04:00)

Algebraic Combinatorics Seminar - John Noel

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 - 3:30 pm EDT (GMT -04:00)

Tutte Colloquium - Stephen Jordan

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 am - 11:30 am EDT (GMT -04:00)

Algebraic Graph Theory Seminar - Miguel Angel Fiol Mora

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 - 1:00 pm EDT (GMT -04:00)

Algebraic Combinatorics Seminar - Shiliang Gao

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 - 3:30 pm EDT (GMT -04:00)

Tutte Colloquium - Sophie Spirkl

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 - 3:30 pm EDT (GMT -04:00)

Tutte Colloquium - Ahmad Abdi

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 am - 11:30 am EDT (GMT -04:00)

Algebraic Graph Theory Seminar - Hermie Monterde

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.

Friday, November 5, 2021 3:30 pm - 3:30 pm EDT (GMT -04:00)

Tutte Colloquium - László Végh

Title: On complete classes of valuated matroids

Speaker: László Végh
Affiliation: London School of Economics
Zoom: Please email Emma Watson

Abstract:

Valuated matroids were introduced by Dress and Wenzel in 1992. They are a central object in discrete convex analysis, and play important roles in other areas such as mathematical economics and tropical geometry. Finding a constructive characterization, i.e., showing that all valuated matroids can be derived from a simple class by some basic operations has been a natural question proposed in various contexts.