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Friday, July 17, 2026 3:30 pm - 4:30 pm EDT (GMT -04:00)

Tutte Colloquium -Audrey Béliveau-Combinatorial Structure and Algorithms for Treatment Rankings

Speaker: Audrey Béliveau
Affiliation: University of Waterloo
Location: MC 5501

Abstract: 

Network meta-analysis (NMA) enables the comparison of multiple medical interventions by combining evidence on their efficacy or safety across clinical trials. Although these models produce rich probabilistic information about how treatments rank, what practitioners often want are simple, interpretable summaries; for example, whether a treatment is likely among the best, or whether one option is likely to outperform another.
The challenge is that, with n treatments, the number of possible questions one can ask about permutations, combinations, or partial orderings of various subsets of treatments grows exponentially. This leads to a large but highly structured combinatorial space, making exhaustive evaluation infeasible.
We develop algorithmic methods to explore this space efficiently and to identify all binary treatment hierarchy statements whose posterior probability exceeds a specified threshold (e.g., 95%). Our approach exploits structure in the ranking space to avoid redundant computations and then prunes conclusions that are logically implied by others, yielding a concise and non-redundant set of results. We illustrate the approach on an NMA of diabetes treatments.
Thursday, July 23, 2026 2:30 pm - 3:30 pm EDT (GMT -04:00)

Algebraic and Enumerative combinatorics seminar -Alexandre Zotine-A pipe dream framework for orbital varieties of type M² = 0

Speaker: Alexandre Zotine
Affiliation: University of Saarland
Location: MC 5479

Abstract: An orbital scheme D of type M² = 0 is the closure of a conjugacy class of some set of n × n upper triangular matrices which are nilpotent of order 2. The geometric components of the orbit scheme are called orbital varieties of type M² = 0, and recently their invariants have been connected to statistical mechanics. In the setting of M² = 0, there are combinatorial methods for studying these invariants via the action of the Borel group of upper triangular invertible matrices. In this talk, we introduce a new pipe dream framework for computing and understanding these invariants. This is joint work with Megumi Harada, Illya Kierkosz, Allen Knutson, Emma Naguit, Brett Nasserden, Naveena Rangunathan, and Adam van Tuyl.

There will be a pre-seminar presenting relevant background at beginning graduate level starting at 1:30pm in MC 5417.

Friday, July 24, 2026 11:30 am - 12:30 pm EDT (GMT -04:00)

CombOpt ReadingGroup -Mahtab Alghasi-The Local Dyadic Conjecture

Speaker:

 Mahtab Alghasi
Affiliation: University of Waterloo
Location: MC 6029

Abstract: A family of sets $\mathcal{C}$ over a finite ground set $E(\mathcal{C})$ is a clutter if no member of $\mathcal{C}$ properly contains another. A clutter is ideal if its covering polyhedron is integral. A rational number whose denominator is a power of two is called \emph{dyadic}.

A longstanding conjecture of Paul Seymour, known as the Dyadic Conjecture, predicts that, for every ideal clutter, the dual of the set covering linear program admits an optimal solution in which all variables take dyadic values. We present a local version of this conjecture and provide evidence for it by proving the proposed local statement for binary clutters under certain assumptions.
This is joint work with Bertrand Guenin and Levent Tuncel.
Friday, July 24, 2026 3:30 pm - 4:30 pm EDT (GMT -04:00)

Tutte Colloquium -Francisco J. Aragón Artacho-Graph-based splitting algorithms for optimization and feasibility problems

Speaker: Francisco J. Aragón Artacho
Affiliation: University of Alicante
Location: MC 5501

Abstract: When an optimization problem is structured, it is normally advantageous to use this feature when designing algorithms to solve it. Following the divide-and-conquer paradigm, splitting algorithms iteratively solve simpler problems that are defined by separately using some parts of the original problem. In this talk, we will recall some classical methods and present some recent advances in this subject, paying special attention to splitting methods devised by graphs.