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Seminars in Combinatorics and Optimization
Algebraic and enumerative combinatorics seminar-Torin Greenwood
Title:Coloring the integers while avoiding monochromatic arithmetic
progressions
| Speaker | Torin Greenwood |
| Affiliation | North Dakota State University |
| Location | MC 5479 |
Abstract: Consider coloring the positive integers either red or blue one at a time in order. Van der Waerden's classical theorem states that no matter how you color the integers, you will eventually have k equally spaced integers all colored the same for any k. But, how can we minimize the number of times k equally spaced integers are colored the same? Even for k = 3, this question is unsolved. We will discuss progress towards proving an existing conjecture by leveraging a connection to coloring the continuous interval [0,1]. Our strategy relies on identifying classes of colorings with permutations and then using mixed integer linear programming. Joint work with Jonathan Kariv and Noah Williams.
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1pm,
Tutte colloquium-Kate Larson
Title: Soft Condorcet Optimization
| Speaker: | Kate Larson |
| Affiliation: | University of Waterloo |
| Location: | MC 5501 |
Abstract:
A common way to drive the progress of AI models and agents is to compare their performance on standardized benchmarks. This often involves aggregating individual performances across a potentially wide variety of tasks and benchmarks and many of the leaderboards that draw greatest attention are Elo-based.
In this paper, we describe a novel ranking scheme inspired by social choice frameworks, called Soft Condorcet Optimization (SCO), to compute the optimal ranking of agents: the one that makes the fewest mistakes in predicting the agent comparisons in the evaluation data. This optimal ranking is the maximum likelihood estimate when evaluation data (which we view as votes) are interpreted as noisy samples from a ground truth ranking, a solution to Condorcet's original voting system criteria and inherits desirable social-choice inspired properties since SCO ratings are maximal for Condorcet winners when they exist, which we show is not necessarily true for the classical rating system Elo.
We propose three optimization algorithms to compute SCO ratings and evaluate their empirical performance across a variety of synthetic and real-world datasets, to illustrate different properties.
With Marc Lanctot, Ian Gemp, Quentin Berthet, Yoram Bachrach, Manfred Diaz, Roberto-Rafael Maura-Rivero, Anna Koop, and Doina Precup
Algebraic and enumerative combinatorics seminar-Mike Cummings
Title:Combinatorial rules for the geometry of Hessenberg varieties
progressions
| Speaker | Mike Cummings |
| Affiliation | University of Waterloo |
| Location | MC 5479 |
Abstract:
Hessenberg varieties were introduced by De Mari, Procesi, and Shayman in the early 1990s and lie at the intersection of geometry, representation theory, and combinatorics. In 2012, Insko and Yong studied a class of Hessenberg varieties using patch ideals, a technique dating back to at least the 1970s from the study of Schubert varieties. In this talk, we will derive patch ideals and use them to study two classes of Hessenberg varieties. We will see the combinatorics that govern the behaviour of these patch ideals and translate these results to the geometric setting. Based in part on work with Sergio Da Silva, Megumi Harada, and Jenna Rajchgot.
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1pm,