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Please note: The University of Waterloo is closed for all events until further notice.

Events - February 2021

Friday, February 26, 2021 — 3:30 PM EST

Title: Flat Littlewood Polynomials Exist

Speaker: Robert Morris
Affliation: IMPA (Instituto de Matemática Pura e Aplicada)
Zoom: Please email Emma Watson

Abstract:

In a Littlewood polynomial, all coefficients are either 1 or -1. Littlewood proved many beautiful theorems about these polynomials over his long life, and in his 1968 monograph he stated several influential conjectures about them. One of the most famous of these was inspired by a question of Erdos, who asked in 1957 whether there exist "flat" Littlewood polynomials of degree n, that is, with |P(z)| of order n^{1/2} for all (complex) z with |z| = 1. 

Thursday, February 25, 2021 — 1:00 PM EST

Title: Chain decompositions for q,t-Catalan numbers

Speaker: Nick Loehr
Affiliation: Virginia Tech
Zoom: Contact Karen Yeats

Abstract:

The q,t-Catalan numbers Cat_n(q,t) are polynomials in q and t that reduce to the ordinary Catalan numbers when q=t=1. These polynomials have important connections to representation theory, algebraic geometry, and symmetric functions. Work of Garsia, Haglund, and Haiman has given us combinatorial formulas for Cat_n(q,t) as sums of Dyck vectors weighted by area and dinv. This talk narrates our ongoing quest for a bijective proof of the notorious symmetry property Cat_n(q,t)=Cat_n(t,q).

Monday, February 22, 2021 — 6:00 PM EST

*Note different start time

Title: Real Chromatic Roots of Graphs

Speaker: Gordon Royle
Affiliation: The University of Western Australia
Zoom: Contact Soffia Arnadottir

Abstract:

In February 1988, I arrived at C&O Waterloo for a postdoc with the late Ron Read. He handed me a paper by Beraha, Kahane and Weiss, and told me to apply it to determining the location of the complex roots of chromatic polynomials.  I’ve returned to the topic every few years since then, with varying degrees of success---some positive results, but still many open problems and conjectures remain.

Friday, February 12, 2021 — 3:30 PM EST

Title: Mixed Integer Programming - Strength of adding integer variables

Speaker: Robert Hildebrand
Affliation: Virginia Tech
Zoom: Please email Emma Watson

Abstract:

Mixed Integer Programming is the problem of optimizing a multi-variate function over some domain constraints where some variables are required to take integer values. From a complexity-theoretic perspective,  problems with fewer integer variables are easier to solve. However, this is not always the case in practice.  We will discuss how performance can be improved when adding integer variables in the context of cutting planes and branch and bound. We will compare several frameworks for doing so in both the context of converting lifting integer and continuous variables to more variables.  We will conclude with recent work on mixed-integer quadratic programming and mention some computational results.

Thursday, February 11, 2021 — 1:00 PM EST

Title: Solving Prellberg and Mortimer's conjecture - bijection(s)
between Motzkin paths and triangular walks

Speaker: Julien Courtiel
Affiliation: Université de Caen
Zoom: Contact Karen Yeats

Abstract:

In these difficult times, what we need to feel better is some colorful and elegant bijections.

This talk introduces the work we did with Andrew Elvey-Price (Tours, France) and Irène Marcovici (Nancy, France). Together we answered an open question from Mortimer and Prellberg, asking for a bijection between a family of walks inside a bounded triangular domain (think about a large equilateral triangle subdivided in several smaller equilateral triangles) and the famous Motzkin paths, but which have bounded height.

Monday, February 8, 2021 — 11:30 AM EST

Title: Cospectral Vertices and Isospectral Reductions

Speaker: Mark Kempton
Affiliation: Brigham Young University
Zoom: Contact Soffia Arnadottir

Abstract:

Understanding cospectral vertices in graphs is fundamental to understanding what the spectrum of the adjacency matrix can tell us about a graph.  Furthermore, cospectral vertices are necessary in constructions of graphs exhibiting perfect quantum state transfer.  I will talk about how to recognize cospectral vertices via a tool from network dynamics: the isospectral reduction of a graph.  I will explore possible ways of getting new constructions of cospectral vertices by looking at isospectral reductions.

Friday, February 5, 2021 — 3:30 PM EST

Title: Probabilistic Aspects of Voting, Intransitivity, and Manipulation

Speaker: Elchanan Mossel
Affliation: MIT Mathematics
Zoom: Please email Emma Watson

Abstract:

Marquis de Condorcet, a French philosopher, mathematician, and political scientist, studied mathematical aspects of voting in the eighteenth century. Condorcet was interested in studying voting rules as procedures for aggregating noisy signals and in the paradoxical nature of ranking  3 or more alternatives. We will begin with a quick survey of some of the main mathematical models, tools, and results in this theory and discuss some recent progress in the area. 

Thursday, February 4, 2021 — 1:00 PM EST

Title: Promotion and rowmotion – an ocean of notions

Speaker: Jessica Striker
Affiliation: North Dakota State University
Zoom: Contact Karen Yeats

Abstract: 

Dynamical Algebraic Combinatorics studies objects important in algebraic combinatorics through the lens of dynamical actions. In this talk, we give a flavor of this field by investigating ever more general domains in which the actions of promotion on tableaux (or tableaux-like objects) and rowmotion on order ideals (or generalizations of order ideals) correspond. This is based on joint works with J. Bernstein, K. Dilks, O. Pechenik, C. Vorland, and N. Williams.

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