Current students

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

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.

The Ontario Combinatorics Workshop is a meeting for researchers working in combinatorics from Ontario and surrounding areas to gather and share their latest research developments. The objective of this meeting is to have an atmosphere conducive to research discussion and collaboration. The setting of the meeting is informal to provide a friendly environment for students and post-doctoral fellows to present their results, to exchange ideas, and to gain exposure to various topics in combinatorics. It is also a place where students and faculties meet, which may foster future collaborations. 

Registration

To register, click here.

Title: Sorting probabilities for Young diagrams and beyond

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.

A celebration of Goulden and Jackson's combined 90 years of insight and inspiration that have shaped the fields of algebraic and combinatorial enumeration.

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

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.

Title: Decomposing graphs and hypergraphs into complete bipartite subgraphs

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.

DataFest 2022 registration is now OPEN!

Register online now!

All members of your team must register.

The American Statistical Association (ASA) DataFest is a celebration of data in which teams of undergraduates work around the clock to find and share meaning in a large, rich, and complex data set.

Title: A Multijection of Cokernels

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.