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Monday, March 7, 2022 11:30 pm - 11:30 pm EST (GMT -05:00)

Algebraic Graph Theory Seminar - Bill Martin

Title: Polynomial ideals, association schemes, and the Q-polynomial property

Speaker: Bill Martin
Afiliation: Worcester Polytechnic Institute
Zoom: Contact Sabrina Lato

Abstract:

Let X ⊆ S^{m−1} be a spherical code in C^m. We study the ideal I ⊆ C[z_1, . . . , z_m] of polynomials that vanish on the points of X: I = { F(z) | (∀a ∈ X) (F(a) = 0) }. The primary example of interest is where the Gram matrix of X is proportional to the first idempotent in some Q-polynomial ordering of an association scheme (X, R) defined on X.

Tuesday, March 8, 2022 4:00 pm - 4:00 pm EST (GMT -05:00)

Graphs and Matroids Seminar - Sang-il Oum

Title: Obstructions for matroids of path-width at most k and graphs of linear rank-width at most k

Speaker: Sang-il Oum
Affiliation: Institute for Basic Science / KAIST
Zoom: Join via http://matroidunion.org/?page_id=2477 or please email Shayla Redlin

Abstract:

Every minor-closed class of matroids of bounded branch-width can be characterized by a minimal list of excluded minors, but unlike graphs, this list could be infinite in general. However, for each fixed finite field $\mathbb F$, the list contains only finitely many $\mathbb F$-representable matroids, due to the well-quasi-ordering of $\mathbb F$-representable matroids of bounded branch-width under taking matroid minors [J. F. Geelen, A. M. H. Gerards, and G. Whittle (2002)].

Thursday, March 10, 2022 11:30 am - 11:30 am EST (GMT -05:00)

Cryptography Reading Group

Title: “Lattice-Based Zero-Knowledge Arguments for Integer Relations” by Benoit Libert, San Ling, Khoa Nguyen, and Huaxiong Wang

Speaker: Camryn Steckel
Affiliation: University of Waterloo
Zoom: Contact Jesse Elliott

Abstract:

We provide lattice-based protocols allowing to prove relations among committed integers. While the most general zero-knowledge proof techniques can handle arithmetic circuits in the lattice setting, adapting them to prove statements over the integers is non-trivial, at least if we want to handle exponentially large integers while working with a polynomial size modulus q.

Thursday, March 10, 2022 1:00 pm - 1:00 pm EST (GMT -05:00)

Algebraic Combinatorics Seminar - Joshua Swanson

Title: Type B q-Stirling numbers

Speaker: Joshua Swanson
Affiliation: USC
Location: MC 6029 or contact Logan Crew for Zoom link

Abstract:

The Stirling numbers of the first and second kind are classical objects in enumerative combinatorics which count the number of permutations or set partitions with a given number of blocks or cycles, respectively. Carlitz and Gould introduced q-analogues of the Stirling numbers of the first and second kinds, which have been further studied by many authors including Gessel, Garsia, Remmel, Wilson, and others, particularly in relation to certain statistics on ordered set partitions.

Friday, March 11, 2022 3:30 pm - 3:30 pm EST (GMT -05:00)

Tutte Colloquium - Walaa Moursi

Title: Strongly nonexpansive mappings revisited: uniform monotonicity and operator splitting

Speaker: Walaa Moursi
Affiliation: University of Waterloo
Location: MC 5501 or please contact Emma Watson for Zoom link

Abstract:

The correspondence between the class of nonexpansive mappings and the class of maximally monotone operators via the reflected resolvents of the latter has played an instrumental role in the convergence analysis of the splitting methods. Indeed, the performance of some of these methods, e.g., Douglas–Rachford and Peaceman–Rachford methods hinges on iterating the so-called splitting operator associated with the individual operators.

Tuesday, March 15, 2022 3:00 pm - 3:00 pm EDT (GMT -04:00)

Graphs and Matroids Seminar

Title: On packing dijoins in digraphs and weighted digraphs

Speaker: Ahmad Abdi
Affiliation: LSE
Zoom: http://matroidunion.org/?page_id=2477 or email shayla.redlin@uwaterloo.ca

Abstract:

Let D=(V,A) be a digraph. A dicut is the set of arcs in a cut where all the arcs cross in the same direction, and a dijoin is a set of arcs whose contraction makes D strongly connected. It is known that every dicut and dijoin intersect. Suppose every dicut has size at least k.

Thursday, March 17, 2022 1:00 pm - 1:00 pm EDT (GMT -04:00)

Algebraic and Enumerative Combinatorics Seminar

Title: A Multijection of Cokernels

Speaker: Alex McDonough
Affiliation: UC Davis
Zoom: Contact olya.mandelshtam@uwaterloo.ca

Absract:

I discovered an intriguing linear algebra relationship which I call a multijection. I used this construction to solve an open problem about higher-dimensional sandpile groups, but I think that it has more to say.

Friday, March 18, 2022 3:30 pm - 3:30 pm EDT (GMT -04:00)

Tutte Colloquium - Laura Mancinska

Title: Fixed-size schemes for certification of large quantum systems

Speaker: Laura Mancinska
Affiliation: QMATH, University of Copenhagen
Location: MC 5501 or please contact Emma Watson for Zoom link

Abstract:

In this talk I will introduce the concept of self-testing which aims to answer the fundamental question of how do we certify proper functioning of black-box quantum devices. We will see that there is a close link between self-testing and representations of algebraic relations. We will leverage this link to propose a family of protocols capable of certifying quantum states and measurements of arbitrarily large dimension with just four binary-outcome measurements.

This is a joint work with Chris Schafhauser and Jitendra Prakash.

Monday, March 21, 2022 11:30 am - 11:30 am EDT (GMT -04:00)

Algebraic Graph Theory Seminar

Title: Decomposing graphs and hypergraphs into complete bipartite subgraphs

Speaker: Sebastian Cioaba
Affiliation: University of Delaware
Zoom: Contact Sabrina Lato

Abstract:

The problem of decomposing (partitioning or covering) graphs into complete bipartite subgraphs (bicliques) has a long history. In this talk, I will describe the basic results including the use of spectral methods, the extension of the problem to hypergraphs and present some of the open problems in this area.

Tuesday, March 22, 2022 5:00 pm - 5:00 pm EDT (GMT -04:00)

Graphs and Matroids Seminar - O-joung Kwon

Title: Reduced bandwidth: a qualitative strengthening of twin-width in minor-closed classes (and beyond)

Speaker: O-joung Kwon
Affiliation: Hanyang University
Zoom: http://matroidunion.org/?page_id=2477 or contact Shayla Redlin

Abstract:

In a reduction sequence of a graph, vertices are successively identified until the graph has one vertex. At each step, when identifying $u$ and $v$, each edge incident to exactly one of $u$ and $v$ is coloured red.