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

Friday, October 30, 2020 — 3:30 PM EDT

**Title: **The Tutte Symmetric Function

Speaker: | Logan Crew |

Affiliation: | University of Waterloo |

Zoom: | Please email Emma Watson |

**Abstract:**

The Tutte polynomial is one of the most celebrated and most well-studied graph functions, in part because it specializes to every graph polynomial with a linear deletion-contraction relation, such as the chromatic polynomial. In the 1990s, Stanley generalized the Tutte polynomial to a symmetric function, but at the cost of the deletion-contraction relation.

Thursday, October 29, 2020 — 1:00 PM EDT

**Title:** qRSt: A probabilistic Robinson--Schensted correspondence for Macdonald polynomials

Speaker: | Florian Aigner |

Affiliation: | Université du Québec à Montréal |

Zoom: | Contact Karen Yeats |

**Abstract:**

The Robinson--Schensted (RS) correspondence is a bijection between permutations and pairs of standard Young tableaux which plays a central role in the theory of Schur polynomials. In this talk, I will present a (q,t)-dependent probabilistic deformation of Robinson--Schensted which is related to the Cauchy identity for Macdonald polynomials.

Monday, October 26, 2020 — 11:30 AM EDT

**Title:** Pseuodrandom Cliquefree Graphs, Finite Geometry, and Spectra

Speaker: | Ferdinand Ihringer |

Affiliation: | Ghent University, Belgium |

Zoom: | Contact Soffia Arnadottir |

**Abstract:**

A regular graph is called optimally pseudorandom if its second largest eigenvalue in absolute value is, up to a constant factor, as small as possible. Determining the largest degree of an optimally pseudorandom graph without a clique of size s is a well-known open problem in extremal graph theory.

Friday, October 23, 2020 — 3:30 PM EDT

**Title: **Semidefinite Programming Relaxations of the Traveling Salesman Problem

Speaker: | David P. Williamson |

Affiliation: | Cornell University |

Zoom: | Please email Emma Watson |

**Abstract:**

Finding a polynomial-time solvable relaxation of the traveling salesman problem whose integrality gap better matches what is seen in practice has been an outstanding open problem in combinatorial optimization for some time. We study several semidefinite programming relaxations of the traveling salesman problem proposed in the literature and show that all known relaxations have an unbounded integrality gap.

Thursday, October 22, 2020 — 1:00 PM EDT

**Title:** Coxeter combinatorics and spherical Schubert geometry

Speaker: | Reuven Hodges |

Affiliation: | University of Illinois |

Zoom: | Contact Karen Yeats |

**Abstract:**

This talk will introduce spherical elements in a finite Coxeter system. These spherical elements are a generalization of Coxeter elements, that conjecturally, for Weyl groups, index Schubert varieties in the flag variety G/B that are spherical for the action of a Levi subgroup.

Wednesday, October 21, 2020 — 4:30 PM EDT

**Title:** On the Theory of the Analytical Forms called Trees

Speaker: | Nick Olson-Harris |

Affiliation: | University of Waterloo |

Zoom: | Contact Maxwell Levit |

**Abstract:**

Trees are among the most fundamental of combinatorial structures. Nowadays they appear all over mathematics and computer science, but this has not always been the case. Trees were first introduced, at least under that name, in an 1857 paper of Cayley by the same title as this talk.

Monday, October 19, 2020 — 3:00 PM EDT

**Title:** The Hepp bound of a matroid: flags, volumes and integrals

Speaker: | Erik Panzer |

Affiliation: | University of Oxford |

Zoom: | Contact Rose McCarty |

**Abstract:**

Invariants of combinatorial structures can be very useful tools that capture some specific characteristics, and repackage them in a meaningful way. For example, the famous Tutte polynomial of a matroid or graph tracks the rank statistics of its submatroids, which has many applications, and relations like contraction-deletion establish a very close connection between the algebraic structure of the invariant (e.g. Tutte polynomials) and the actual matroid itself.

Monday, October 19, 2020 — 11:30 AM EDT

**Title:** Pretty Good State Transfer and Minimal Polynomials

Speaker: | Christopher van Bommel |

Affiliation: | University of Manitoba |

Zoom: | Contact Soffia Arnadottir |

**Abstract:**

We examine conditions for a pair of strongly cospectral vertices to have pretty good quantum state transfer in terms of minimal polynomials, and provide cases where pretty good state transfer can be ruled out.

Friday, October 9, 2020 — 3:30 PM EDT

**Title: **Generalization bounds for rational self-supervised learning algorithms

Speaker: | Boaz Barak |

Affiliation: | Harvard University |

Zoom: | Please email Emma Watson |

**Abstract:**

The generalization gap of a learning algorithm is the expected difference between its performance on the training data and its performance on fresh unseen test samples.Modern deep learning algorithms typically have large generalization gaps, as they use more parameters than the size of their training set. Moreover the best known rigorous bounds on their generalization gap are often vacuous.

Thursday, October 8, 2020 — 1:00 PM EDT

**Title:** Factorization problems in complex reflection groups

Speaker: | Alejandro Morales |

Affiliation: | University of Massachusetts Amherst |

Zoom: | Contact Karen Yeats |

**Abstract:**

The study of factorizations in the symmetric group is related to combinatorial objects like graphs embedded on surfaces and non-crossing partitions. We consider analogues for complex reflections groups of certain factorization problems of permutations first studied by Jackson, Schaeffer, Vassilieva and Bernardi.

Monday, October 5, 2020 — 11:30 AM EDT

**Title:** Efficient $(j,k)$-Domination

Speaker: | Brendan Rooney |

Affiliation: | Rochester Institute of Technology |

Zoom: | Contact Soffia Arnadottir |

**Abstract****:**

A function $f:V(G)\rightarrow\{0,\ldots,j\}$ is an efficient $(j,k)$-dominating function on $G$ if $\sum_{u\in N[v]}f(u)=k$ for all $v\in V(G)$ (here $N[v]=N(v)\cup\{v\}$ is the closed neighbourhood of $v$).

Friday, October 2, 2020 — 3:30 PM EDT

**Title: **Total Dual Integrality for Convex, Semidefinite and Extended Formulations

Speaker: | Levent Tuncel |

Affiliation: | University of Waterloo |

Zoom: | Please email Emma Watson |

**Abstract:**

Within the context of characterizations of exactness of convex relaxations of 0,1 integer programming problems, we present a notion of total dual integrality for Semidefinite Optimization Problems (SDPs), convex optimization problems and extended formulations of convex sets.

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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 centralized within our Indigenous Initiatives Office.