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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.

Thursday, March 24, 2022 1:00 pm - 1:00 pm EDT (GMT -04:00)

Algebraic Combinatorics Seminar - Greta Panova

Title: Sorting probabilities for Young diagrams and beyond

Speaker: Greta Panova
Affiliation: University of Southern California
Zoom: Contact Logan Crew or Olya Mandelshtam

Abstract:

Sorting probability for a partially ordered set P is defined as the min |Pr[x<y] - Pr[y<x]| going over all pairs of elements x,y in P, where Pr[x<y] is the probability that in a uniformly random linear extension (extension to total order) x appears before y.

The celebrated 1/3-2/3 conjecture states that for every poset the sorting probability is at most 1/3, i.e. there are two elements x and y, such that 1/3\leq Pr[x<y] \leq 2/3.

Monday, March 28, 2022 11:30 am - 11:30 am EDT (GMT -04:00)

Algebraic Graph Theory Seminar - Xiaohong Zhang

Title: Oriented Cayley Graphs with all eigenvalues being integer multiples of $\sqrt{\Delta}$

Speaker: Xiaohong Zhang
Affiliation: University of Waterloo
Zoom: Contact Sabrina Lato

Abstract:

Let $G$ be a finite abelian group. An oriented Cayley graph on $G$ is a Cayley digraph $X(G,C)$ such that $C \cap (-C)=\emptyset$. Consider the $(0,1,-1)$ skew-symmetric adjacency matrix of an oriented Cayley graph $X=X(G,C)$.

Tuesday, March 29, 2022 3:00 pm - 3:00 pm EDT (GMT -04:00)

Graphs and Matroids Seminar - Zishen Qu

Title: Minimal induced subgraphs of two classes of 2-connected non-Hamiltonian graphs

Speaker: Zishen Qu
Affiliation: University of Waterloo
Zoom: http://matroidunion.org/?page_id=2477 or contact Shayla Redlin

Abstract:

Finding sufficient conditions for a class of graphs to be Hamiltonian is an old problem, with a wide variety of conditions such as Dirac's degree condition and Whitney's theorem on 4-connected planar triangulations. We discuss some past results on sufficient conditions for Hamiltonicity involving the exclusion of fixed induced subgraphs, and some properties of the graphs involved in such results.

Thursday, March 31, 2022 1:00 pm - 1:00 pm EDT (GMT -04:00)

Algebraic Combinatorics Seminar - Laura Colmenarejo

Title: Multiplying quantum Schubert polynomials using combinatorics

Speaker: Laura Colmenarejo
Affiliation: NC State University
Zoom: Contact Logan Crew or Olya Mandelshtam

Abstract:

Schubert polynomials are a very interesting family of polynomials in algebraic geometry due to their relation with the cohomology of the flag variety. Moreover, they are also very interesting from a combinatorial point of view because they can be considered generalizations of Schur functions. 

Friday, April 1, 2022 3:30 pm - 3:30 pm EDT (GMT -04:00)

Tutte Colloquium - Curtis Bright

Title: SAT Solving with Computer Algebra for Combinatorics

Speaker: Curtis Bright
Affiliation: University of Windsor and Carleton University
Location: MC 5501 or please contact Emma Watson for Zoom link

Abstract:

This talk will describe a method of solving combinatorial problems by coupling Boolean satisfiability (SAT) solvers with computer algebra systems (CASs), thereby combining the search and learning power of SAT solvers with the expressiveness and mathematical sophistication of CASs.