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Events - June 2021

Monday, June 28, 2021 — 11:30 AM EDT

Title: State transfer for paths with weighted loops at the end vertices

Speaker: Steve Kirkland
Affiliation: University of Manitoba
Zoom: Contact Soffia Arnadottir

Abstract:

We consider a continuous time quantum walk on an unweighted path on n vertices, to which a loop of weight w has been added at each end vertex. Let f(t) denote the fidelity of state transfer from one end vertex to the other at time t. In this talk we give upper and lower bounds on f(t) in terms of w, n and t; further, given a > 0 we discuss the values of t for which f(t) > 1-a.

Friday, June 25, 2021 — 3:30 PM EDT

Title: From low probability to high confidence in stochastic convex optimization

Speaker: Dmitriy Drusvyatskiy
Affliliation: University of Washington
Zoom: Contact Emma Watson

Abstract:

Standard results in stochastic convex optimization bound the number of samples that an algorithm needs to generate a point with small function value in expectation. More nuanced high probability guarantees are rare, and typically either rely on “light-tail” noise assumptions or exhibit worse sample complexity. In this work, we show that a wide class of stochastic optimization algorithms can be augmented with high confidence bounds at an overhead cost that is only logarithmic in the confidence level and polylogarithmic in the condition number.

Thursday, June 24, 2021 — 1:00 PM EDT

Title: Arctic curves for groves

Speaker: Terrence George
Affiliation: University of Michigan
Zoom: Contact Stephen Melczer

Abstract:

The limit shape phenomenon is a "law of large numbers" for random surfaces: the random surface looks macroscopically like the "average surface". The first result of this kind was the celebrated arctic circle theorem for domino tilings of the aztec diamond. The limit shape has macroscopic regions with different qualitative behavior, and the arctic curve is the boundary separating these regions.

Monday, June 21, 2021 — 11:30 AM EDT

Title: Average Mixing Matrices of Trees and Stars

Speaker: Paula Kimmerling
Affiliation: Washington State University
Zoom: Contact Soffia Arnadottir

Abstract:

We define the average mixing matrix (AMM) of a continuous-time quantum walk on a graph using the orthogonal projections onto the eigenspaces of the adjacency matrix A. From there, one of the properties that has been studied is the rank of the AMM. This is easiest to do if the eigenvalues of A are simple, and we’ll review some of the results on this from Coutinho et. al. (2018).

Friday, June 18, 2021 — 3:30 PM EDT

Title: Lattice Walk Enumeration: Analytic, algebraic and geometric aspects

Speaker: Marni Mishna 
Affliliation: Simon Fraser University
Zoom: Contact Emma Watson

Abstract:

This talk will examine the rich topic of lattice path enumeration. A very classic object of combinatorics, lattice walks withstand study from a variety of perspectives. Even the simple task of classifying the two dimensional walks restricted to the first quadrant has brought into play a surprising diversity of techniques from algebra to analysis to geometry. We will consider walks under a few different lenses.

Friday, June 18, 2021 — 11:30 AM EDT

Title: The spectral radius of graphs with no odd wheels

Speaker: Dheer Noal Desai
Affiliation: University of Delaware
Zoom: Contact Soffia Arnadottir

Abstract:

The odd wheel W_{2k+1} is the graph formed by joining a vertex to a cycle of length 2k. In this talk, we will investigate the largest value of the spectral radius of the adjacency matrix of an n-vertex graph that does not contain W_{2k+1}.

Thursday, June 17, 2021 — 1:00 PM EDT

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.

Friday, June 11, 2021 — 3:30 PM EDT

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 10, 2021 — 4:00 PM EDT

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.

Thursday, June 10, 2021 — 1:00 PM EDT

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].

Friday, June 4, 2021 — 3:30 PM EDT

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 3, 2021 — 1:00 PM EDT

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.

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