#### Contact Info

Combinatorics & Optimization

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext 33038

PDF files require Adobe Acrobat Reader.

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.

Combinatorics & Optimization

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext 33038

PDF files require Adobe Acrobat Reader.

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is co-ordinated within our Office of Indigenous Relations.