Using association schemes to prove Erdős-Ko-Rado type results

The Erdős-Ko-Rado (EKR) theorem is a fundamental result in extremal set theory which asserts that if $\mathcal{F}$ is a collection of pairwise intersecting $k$-subsets of $\{1,2,\ldots,n\}$, for $n\geq 2k$, then $|\mathcal{F}| \leq \binom{n-1}{k-1}$. Moreover, if $n\geq 2k+1$ then equality holds if and only if $\mathcal{F}$ is an orbit of a conjugate of a stabilizer of a point of the symmetric group $\sym(n)$ in its natural action.
    
 The EKR theorem has been extended to various combinatorial objects throughout the years. In this talk, I will present some powerful algebraic combinatorics tools,  such as association schemes and representation theory, to prove EKR type results on the symmetric group.

It will also be held virtually via Zoom.

Join the Zoom Meeting HERE!

Feel free to invite any friends or colleagues who may be interested.

We look forward to (virtually) sharing the passion for math with you!