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Monday, November 6, 2023 11:30 am - 11:30 am EST (GMT -05:00)

Algebraic Graph Theory - Jane Breen

Title: Kemeny’s constant and random walks on graphs

Speaker: Jane Breen
Affiliation: Ontario Tech University
Location: Please contact Sabrina Lato for Zoom link.

Abstract: Kemeny's constant is an interesting and useful quantifier of how well-connected the states of a Markov chain are. This comes to the forefront when the Markov chain in question is a random walk on a graph, in which case Kemeny's constant is interpreted as a measure of how `well-connected' the graph is. Though it was first introduced in the 1960s, interest in this concept has recently exploded. This talk will provide an introduction to Markov chains, an overview of the history of Kemeny’s constant, discussion of some applications, and a survey of recent results, with an emphasis on those that are extensions or generalizations of simple random walks on graphs, to complement Sooyeong’s talk from two weeks ago.

Thursday, November 9, 2023 2:00 pm - 2:00 pm EST (GMT -05:00)

Algebraic and Enumerative Combinatorics Seminar - Spencer Daugherty

Title: Extended Schur Functions and Bases Related by Involutions

Speaker: Spencer Daugherty
Affiliation: North Carolina State University
Location: MC 6029

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:00 pm.

Abstract: The extended Schur basis and the shin basis generalize the Schur functions to the dual algebras of the quasisymmetric functions and the noncommutative symmetric functions. We define a creation operator and a Jacobi-Trudi rule for certain shin functions and show that a similar matrix determinant expression does not exist for every shin function.

Thursday, November 9, 2023 3:00 pm - 3:00 pm EST (GMT -05:00)

Graphs and Matroids Seminar - Josephine Reynes

Title: The Tutte Polynomial, Bipartite Representations of Graphs, and Grid Walking 

Speaker: Josephine Reynes
Affiliation: University of Waterloo
Location: MC 5417

Abstract: The Tutte Polynomial has many equivalent definitions. It can be defined by a deletion-contraction relation with the terms determined by the sequence of contractions, deletions, loops, and isthmi. This definition is independent of edge order. Another definition relies on a fixed edge ordering and examines the edge activities over maximal spanning forests. There is a direct relationship between edge activity and deletion/contraction for a given edge ordering. Furthermore, the monomials of the Tutte polynomial can be interpreted as grid walks. This allows for an approach to the Tutte polynomial on hypergraphs by examining the grid walks of the bipartite representation of the graph.

Friday, November 10, 2023 3:30 pm - 3:30 pm EST (GMT -05:00)

Distinguished Tutte Lecture - David B. Shmoys

Title: Algorithmic Tools for Congressional Districting: Fairness via Analytics

Speaker: David B. Shmoys
Affiliation: Cornell University
Location: MC 5501

Abstract: The American winner-take-all congressional district system empowers politicians to engineer electoral outcomes by manipulating district boundaries. To date, computational solutions mostly focus on drawing unbiased maps by ignoring political and demographic input, and instead simply optimize for compactness and other related metrics.

Monday, November 13, 2023 11:30 am - 11:30 am EST (GMT -05:00)

Algebraic Graph Theory - Roghayeh Maleki

Title: Distance-regular graphs that support a uniform structure

Speaker: Roghayeh Maleki
Affiliation: University of Primorska
Location: Please contact Sabrina Lato for Zoom link.

Abstract: Given a connected bipartite graph $G$, the adjacency matrix $A$ of $G$ can be decomposed as  $A=L+R$, where $L=L(x)$ and $R=R(x)$ are respectively the  lowering and the raising matrices with respect to a certain vertex $x$. The graph $G$ has a \textit{uniform structure} with respect to $x$ if the matrices $RL^2$, $LRL$, $L^2R$, and $L$ satisfy a certain linear dependency.

Thursday, November 16, 2023 2:00 pm - 2:00 pm EST (GMT -05:00)

Algebraic and Enumerative Combinatorics Seminar - Alejandro Morales Borrero

Title: Linear relations and Lorentzian property of chromatic symmetric functions

Speaker: Alejandro Morales Borrero
Affiliation: Université du Québec à Montréal
Location: MC 6029

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:00 pm.

Abstract: The chromatic symmetric function (CSF) of Dyck paths of Stanley and its Shareshian Wachs q-analogue (q-CSF) have important connections to Hessenberg varieties, diagonal harmonics and LLT polynomials. In the, so called, abelian case they are related to placements of non-attacking rooks by results of Stanley-Stembridge (1993) and Guay-Paquet (2013).

Friday, November 17, 2023 1:00 pm - 1:00 pm EST (GMT -05:00)

C&O Reading Group - Sepehr Assadi

Title: Multiplicative Weight Update (MWU) Method for Solving Packing/Covering LPs

Speaker: Sepehr Assadi
Affiliation: University of Waterloo
Location: MC 6029

Abstract: I will present an overview of the MWU technique for solving Packing/Covering LPs easily and efficiently. The talk will be based on a combination of results from the following resources: (1) https://epubs.siam.org/doi/pdf/10.1137/1.9781611976014.11 (2) https://www.cs.princeton.edu/~arora/pubs/MWsurvey.pdf

Friday, November 17, 2023 3:30 pm - 3:30 pm EST (GMT -05:00)

Tutte Colloquium - Luke Postle

Title: Hypergraph Matchings Avoiding Forbidden Submatchings

Speaker: Luke Postle
Affiliation: University of Waterloo
Location: MC 5501

Abstract: We overview a general theory for finding perfect or almost perfect matchings in a hypergraph G avoiding a given set of forbidden submatchings (which we view as a hypergraph H where V(H)=E(G)).

Monday, November 20, 2023 11:30 am - 11:30 am EST (GMT -05:00)

Algebraic Graph Theory - Prem Nigam Kar

Title: Quantum Automorphism Groups of Trees

Speaker: Prem Nigam Kar
Affiliation: Technical University of Denmark
Location: Please contact Sabrina Lato for Zoom link.

Abstract: We give a characterisation of quantum automorphism groups of trees. In particular, for every tree, we show how to iteratively construct its quantum automorphism group using free products and free wreath products. This can be considered a quantum version of Jordan’s theorem for the automorphism groups of trees. This is one of the first characterisations of quantum automorphism groups of a natural class of graphs with quantum symmetry. This talk is based on the following preprint: https://arxiv.org/abs/2311.04891

Thursday, November 23, 2023 2:00 pm - 2:00 pm EST (GMT -05:00)

Algebraic and Enumerative Combinatorics Seminar - Jason Bell

Title: Filtered deformations of commutative algebras

Speaker: Jason Bell
Affiliation: University of Waterloo
Location: MC 6029

Note: There will be no pre-seminar.

Abstract: We’ll look at different ways of deforming the multiplicative structure of “classical” algebras to obtain new algebras and explain how this algebraic structure can often be understood combinatorially.  We’ll then look at a special class of algebras one can produce this way called filtered deformations and we’ll discuss a conjecture of Etingof which asserts that in positive characteristic that filtered deformations of commutative rings should be in some natural sense very close to being commutative themselves. Not much background will be assumed.