Events

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.

Title: Speeding up Multi-Scalar Multiplication over Fixed Points towards Efficient zkSNARKs

Abstract:

The arithmetic of computing multiple scalar multiplications in an elliptic curve group then adding them together is called multi-scalar multiplication (MSM). MSM over fixed points dominates the time consumption in pairing-based trusted setup zero-knowledge succinct non-interactive arguments of knowledge (zkSNARKs), thus fast algorithms of MSM over fixed points are desirable for practical applications.

Title: On the eigenvalues of the perfect matching derangement graph

Abstract:

The perfect matching derangement graph $M_{2n}$ is defined to be the graph whose vertices are all the perfect matchings of the complete graph $K_{2n}$, and two vertices are adjacent if they contain no common edges. The graph $M_{2n}$ is part of a larger study on the analogs of the Erdős-Ko-Rado theorem, and recently there have been interesting works on $M_{2n}$ and its eigenvalues.

Title: Polynomials, rank and cap sets

Abstract:

In this talk we will look at a variant of the polynomial method which was first used to prove that sets avoiding 3-term arithmetic progressions in groups like Z_4^n and F_q^n are exponentially small (compared to the size of the group). We will discuss lower and upper bounds for the size of the extremal subsets.  We will also mention some further applications of the method, for instance, the solution of the Erdős–Szemerédi theorem sunflower conjecture.

Title: Connectivity functions and connectivity intertwining

Abstract:

Connectivity functions provide a nice way of unifying matroid connectivity with various notions of connectivity in graphs. I will present some new and old open problems.

Title:  A vertex model for LLT polynomials and k-tilings of the Aztec diamond

Abstract:

We describe a Yang-Baxter integrable colored vertex model, from which we construct a class of partition functions that equal the LLT polynomials of Lascoux, Leclerc, and Thibon. Using the vertex model formalism, we can prove many properties of these polynomials.

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

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Title: Radical Sylvester-Gallai theorem for cubics - and beyond

Abstract:

In 1893, Sylvester asked a basic question in combinatorial geometry: given a finite set of distinct points $v_1, \ldots, v_m \in \R^N$ such that the line defined by any pair of distinct points $v_i, v_j$ contains a third point $v_k$ in the set, must all points in the set be collinear?

Title: P-partition power sums

Abstract:

The Hopf algebra of symmetric functions is spanned by several important bases, including by power sum symmetric functions, which encode the class values of the characters of the symmetric group under the Frobenius characteristic map.