Events

Title: Multiplying quantum Schubert polynomials using combinatorics

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. 

Title: SAT Solving with Computer Algebra for Combinatorics

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. 

Title: Yet Another Proof of the Erdős-Ko-Rado Theorem

Abstract:

We give a short new algebraic proof of the Erdős-Ko-Rado theorem, that for k < n/2, the largest families of k-sets of an n-element set such that any two of its members intersect are precisely those families composed of all k-sets that contain some fixed element.

Title: A local version of Hadwiger’s Conjecture

Abstract:

In 1943, Hadwiger famously conjectured that graphs with no $K_t$ minors are $t-1$ colourable. There has also been significant interest in several variants of the problem, such as list colouring or only forbidding certain classes of minors.

Title: Modular relations between chromatic symmetric functions

Abstract:

In 1995, Stanley introduced the chromatic symmetric functions. The study of chromatic symmetric functions of graphs inspired two main research directions.

Title: Deletion-contraction for a unified Laplacian and applications

Abstract:

We define a graph Laplacian with vertex weights in addition to the more classical edge weights, which unifies the combinatorial Laplacian and the normalised Laplacian.

Title: Lattice path matroids, lattice path polymatroids, and excluded minors

Abstract:

We define lattice path matroids, polymatroids, Boolean polymatroids, and lattice path polymatroids, which are a subclass of Boolean polymatroids. 

Title: Generating Short Monotone Paths in 0/1 LPs: From Circuits to Simplex

Abstract: 

Even after decades of study, it is unknown whether there exists a pivot rule for the Simplex method that always solves an LP with only a polynomial number of pivots.  This remains unknown even in the special case of 0/1 LPs - i.e., LPs defined over 0/1 polytopes - a case that includes many extensively studied problems in combinatorial optimization.

Title: The one-sided cycle shuffles in the symmetric group algebra

Abstract:

Elements in the group algebra of a symmetric group S_n are known to have an interpretation in terms of card shuffling. I will discuss a new family of such elements, recently constructed by Nadia Lafrenière: Given a positive integer n, we define n elements t_1, t_2, ..., t_n in

Join us for a panel discussion focused on understanding and promoting equity, diversity, and inclusion (EDI) in academic settings. All members of our academic communities should strive to create equitable, diverse, and inclusive environments.