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Thursday, May 20, 2021 1:00 pm - 1:00 pm EDT (GMT -04:00)

Algebraic Combinatorics Seminar - Steven Karp

Title: q-Whittaker functions, finite fields, and Jordan forms

Speaker: Steven Karp
Affiliation: UQAM
Zoom: Contact Steve Melczer

Abstract:

The q-Whittaker symmetric function associated to an integer partition is a q-analogue of the Schur symmetric function. We give a new formula for the q-Whittaker function in terms of partial flags compatible with a nilpotent endomorphism over the finite field of size 1/q.

Friday, May 21, 2021 3:30 pm - 3:30 pm EDT (GMT -04:00)

Tutte Colloquium - Steve Melczer

Title: Positivity Problems for Linear Recurrences

Speaker: Steve Melczer
Affliliation: University of Waterloo
Zoom: Contact Emma Watson

Abstract:

Although sequences satisfying linear recurrence relations have been studied for centuries, and appear as some of the first examples of combinatorial sequences encountered in an introductory combinatorics class, there are natural examples of simply stated problems related to their basic behaviour whose decidability is unknown. In this talk we survey some open computability and complexity questions related to the positivity of linearly recurrent sequences, before examining a new approach to proving positivity using rigorous numerical methods for functions satisfying linear differential equations.

Friday, May 28, 2021 3:30 pm - 3:30 pm EDT (GMT -04:00)

Tutte Colloquium - Jon Yard

Title: Algebraic formulations of Zauner's conjecture

Speaker: Jon Yard
Affliliation: University of Waterloo
Zoom: Contact Emma Watson

Abstract:

Tight complex projective 2-designs are simultaneously maximal sets of equiangular lines and minimal complex projective 2-designs. In quantum information theory, they define optimal measurements known as SIC-POVMs (Symmetric Informationally Complete Positive Operator-Valued Measures).  They are conjectured by Zauner to exist in every dimension, even as specific group orbits. 

Monday, May 31, 2021 11:30 am - 11:30 am EDT (GMT -04:00)

Algebraic Graph Theory Seminar - Jo Ellis-Monaghan

Title: An algebraic framework for twualities of embedded graphs

Speaker: Jo Ellis-Monaghan
Affiliation: Korteweg-de Vries Instituut voor Wiskunde, Universiteit van Amsterdam
Zoom: Contact Soffia Arnadottir

Abstract:

We develop algebraic tools to identify and generate new surface embeddings of graphs with various forms of self-twuality including geometric duality, Petrie duality, Wilson duality, and both forms of triality (which is like duality, but of order three instead of two).  These operations are of particular interest because of their interplay with graph symmetries and graph polynomials.

Thursday, June 3, 2021 1:00 pm - 1:00 pm EDT (GMT -04:00)

Algebraic Combinatorics Seminar - Oliver Pechenik

Title: What is the degree of a Grothendieck polynomial?

Speaker: Oliver Pechenik
Affiliation: University of Waterloo
Zoom: Contact Stephen Melczer

Abstract:

Jenna Rajchgot observed that the Castelnuovo-Mumford regularity of matrix Schubert varieties is computed by the degrees of the corresponding Grothendieck polynomials. We give a formula for these degrees.

Friday, June 4, 2021 3:30 pm - 3:30 pm EDT (GMT -04:00)

Tutte Colloquium - Kanstantsin Pashkovich

Title: On the approximability of the maximum cardinality stable matching problem with ties  

Speaker: Kanstantsin Pashkovich
Affliliation: University of Waterloo
Zoom: Contact Emma Watson

Abstract:

The maximum cardinality stable matching problem is central in game theory. When participants are allowed to have ties in their preferences, the problem of finding a stable matching of maximum cardinality is NP-hard, even when the ties are of size two. Moreover, in this setting it is UGC-hard to provide an approximation for the maximum cardinality stable matching problem with a constant factor smaller than 4/3.

Thursday, June 10, 2021 1:00 pm - 1:00 pm EDT (GMT -04:00)

Algebraic Combinatorics Seminar - Lukas Nabergall

Title: Enumerating hereditary classes of chord diagrams

Speaker: Lukas Nabergall
Affiliation: University of Waterloo
Zoom: Contact Stephen Melczer

Abstract:

A class of combinatorial structures is hereditary if membership in the class is closed under taking substructures. Hereditary classes have been extensively studied for a variety of objects, notably graphs and permutations. A central problem is to determine the number of objects of size n in a given hereditary class. We discuss this problem for chord diagrams, perfect matchings of [2n].

Thursday, June 10, 2021 4:00 pm - 4:00 pm EDT (GMT -04:00)

Joint Colloquium - Shayla Redlin

Title: Counting Antichains in the Boolean Lattice

Speaker: Shayla Redlin
Affiliation: University of Waterloo
Zoom: Contact Maxwell Levit

Abstract:

How many antichains are there in the Boolean lattice P(n)? Sperner's theorem (1928) tells us that the largest antichain in P(n) has size A = (n choose n/2). A subset of an antichain is an antichain, so there are at least 2^A antichains in P(n). Interestingly, it turns out that this is close to the total, as Kleitman (1969) showed that the number of antichains is 2^(A(1+x)) where x goes to zero as n goes to infinity.

Friday, June 11, 2021 3:30 pm - 3:30 pm EDT (GMT -04:00)

Tutte Colloquium - Cécile Pierrot

Title: The discrete logarithm problem in finite fields

Speaker: Cécile Pierrot
Affliliation: French National Institute for Computer Science Research (INRIA)
Zoom: Contact Emma Watson

Abstract:

The security of currently deployed public key protocols relies on the presumed hardness of problems often coming from number theory, such as factoring a large integer or solving the discrete logarithm problem in some group.

In this talk we focus on discrete logarithms in finite fields. We explain what is a discrete logarithm, why cryptographers need them, and we focus then on algorithms to solve the related problem, together with open questions in this area.

Thursday, June 17, 2021 1:00 pm - 1:00 pm EDT (GMT -04:00)

Algebraic Combinatorics Seminar - Angèle Hamel

Title: Identities for ninth variation Schur Q-functions

Speaker: Angèle Hamel
Affiliation: Wilfrid Laurier University
Zoom: Contact Stephen Melczer

Abstract:

Recently Okada defined algebraically ninth variation skew Q-functions, in parallel to Macdonald's ninth variation skew Schur functions. Here we introduce a skew shifted tableaux definition of these ninth variation skew Q-functions, and prove by means of a non-intersecting lattice path model a Pfaffian outside decomposition result in the form of a ninth variation version of Hamel's Pfaffian outside decomposition identity.