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Thursday, January 21, 2021 1:30 pm - 1:30 pm EST (GMT -05:00)

Algebraic Combinatorics Seminar - Jason Bell

Title: The growth of groups and algebras

Speaker: Jason Bell
Affiliation: University of Waterloo
Zoom: Contact Karen Yeats

Abstract:

We give an overview of the theory of growth functions for associative algebras and explain their significance when trying to understand algebras from a combinatorial point of view.  We then give a classification for which functions can occur as the growth function of a finitely generated associative algebra up to asymptotic equivalence. This is joint work with Efim Zelmanov.

Friday, January 22, 2021 3:30 pm - 3:30 pm EST (GMT -05:00)

Tutte Colloquium - David Gosset

Title: Fast simulation of planar Clifford circuits

Speaker: David Gosset
Aflliation: University of Waterloo
YouTube Link: https://youtu.be/LjmjiEPTSNo

Abstract:

Clifford circuits are a special family of quantum circuits that can be simulated on a classical computer in polynomial time using linear algebra. Recent work has shown that Clifford circuits composed of nearest-neighbor gates in planar geometries can solve certain linear algebra problems provably faster --as measured by circuit depth-- than classical computers.

Monday, January 25, 2021 11:30 am - 11:30 am EST (GMT -05:00)

Algebraic Graph Theory Seminar - Chris Godsil

Title: The Matchings Polynomial

Speaker: Chris Godsil
Affiliation: University of Waterloo
Zoom: Contact Soffia Arnadottir

Abstract:

A $k$-matching in a graph is a matching of size $k$, and $p(X,k)$ denotes the number of $k$-matchings in $X$.

The matching polynomial of a graph is a form of generating function for the sequence $(p(X,k))_{k\ge0}$.

If is closely related to the characteristic polynomial of a graph. I will discuss some of the many interesting properties of this polynomial, and some of the related open problems.

Thursday, January 28, 2021 1:00 pm - 1:00 pm EST (GMT -05:00)

Algebraic Combinatorics Seminar - Olya Mandelshtam

Title: The multispecies TAZRP and modified Macdonald polynomials

Speaker: Olya Mandelshtam
Affiliation: University of Waterloo
Zoom: Contact Karen Yeats

Abstract:

Recently, a formula for the symmetric Macdonald polynomials $P_{\lambda}(X;q,t)$ was given in terms of objects called multiline queues, which also compute probabilities of a statistical mechanics model called the multispecies asymmetric simple exclusion process (ASEP) on a ring. It is natural to ask whether the modified Macdonald polynomials $\widetilde{H}_{\lambda}(X;q,t)$ can be obtained using a combinatorial gadget for some other statistical mechanics model.

Friday, January 29, 2021 3:30 pm - 3:30 pm EST (GMT -05:00)

Tutte Colloquium - Michael Naehrig

Title: Finding twin smooth integers for isogeny-based cryptography

Speaker: Michael Naehrig
Affliation: Microsoft Research
Zoom: Please email Emma Watson

Abstract:

Efficient and secure instantiations of cryptographic protocols require careful parameter selection. For the isogeny-based cryptographic protocol B-SIDH, a variant of the Supersingular-Isogeny Diffie Hellman (SIDH) key exchange, one needs to find two consecutive B-smooth integers of cryptographic size such that their sum is prime. The smaller the smoothness bound B is, the more efficient the protocol becomes. This talk discusses a sieving algorithm to find such twin smooth integers that uses solutions to the Prouhet-Tarry-Escott problem.

Thursday, February 4, 2021 1:00 pm - 1:00 pm EST (GMT -05:00)

Algebraic Combinatorics Seminar - Jessica Striker

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.

Friday, February 5, 2021 3:30 pm - 3:30 pm EST (GMT -05:00)

Tutte Colloquium - Elchanan Mossel

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. 

Monday, February 8, 2021 11:30 am - 11:30 am EST (GMT -05:00)

Algebraic Graph Theory Seminar - Mark Kempton

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.

Thursday, February 11, 2021 1:00 pm - 1:00 pm EST (GMT -05:00)

Algebraic Combinatorics Seminar - Julien Courtiel

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.

Friday, February 12, 2021 3:30 pm - 3:30 pm EST (GMT -05:00)

Tutte Colloquium - Robert Hildebrand

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.