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Seminars in Combinatorics and Optimization

Friday, June 14, 2024 3:30 pm - 4:30 pm EDT (GMT -04:00)

Tutte Colloquium - Chaitanya Swamy

Title: Stochastic Minimum Norm Combinatorial Optimization

Speaker: Chaitanya Swamy
Affiliation: University of Waterloo
Location: MC 5501

Abstract: We develop a framework for designing approximation algorithms for a wide class of (1-stage) stochastic-optimization problems with norm-based objective functions. We introduce the model of stochastic minimum-norm combinatorial optimization, wherein the costs involved are random variables with given distributions, and we are given a monotone, symmetric norm f. Each feasible solution induces a random multidimensional cost vector whose entries are independent random variables, and the goal is to find a solution that minimizes the expected f-norm of the induced cost vector. This is a very rich class of objectives, containing all l_p norms, as also Top-l norms (sum of l largest coordinates in absolute value), which enjoys various closure properties.

Monday, June 17, 2024 11:30 am - 12:30 pm EDT (GMT -04:00)

Algebraic Graph Theory - Julianna Tymoczko

Title: Webs and quantum representations

Speaker: Julianna Tymoczko
Affiliation: Smith College
Location: Please email Sabrina Lato for Zoom link.

Abstract: A web is a directed, labeled plane graph satisfying certain conditions coming from representation theory. Each web corresponds to a specific invariant vector in a tensor product of fundamental representations of a quantum group. In this talk, we introduce a process called stranding, which encodes as the monomial terms in a web’s associated vector as a collection of paths in the web graph.  We also describe how the strandings connect seemingly-unrelated ideas in combinatorics (e.g. noncrossing matchings) and geometry (e.g. certain algebraic varieties called Springer fibers).

Tuesday, June 18, 2024 3:00 pm - 4:00 pm EDT (GMT -04:00)

Graphs and Matroids Seminar - Thomas Lesgourgues

Title: Ramsey with purple edges

Speaker: Thomas Lesgourgues
Affiliation: University of Waterloo
Location: MC 5479

Abstract: Motivated by a question of David Angell, we study a variant of Ramsey numbers where some edges are coloured with both red and blue colours, (i.e. are called ‘purple’ edges). Specifically, we are interested in the largest number g = g(s, t, n), for some s and t and n < R(s, t), such that there exists a red-blue-purple colouring of Kn with g purple edges, without a red-purple Ks and without a blue-purple Kt. We determine g asymptotically for a large family of parameters. The talk will be introductory in nature. Since the concept of double-coloured edges is new in this context, there is a plethora of open questions. Joint work with Anita Liebenau and Nye Taylor.