Future students

Title: Determinantal formulas with major indices

Abstract: Krattenthaler and Thibon discovered a beautiful formula for the determinant of the matrix indexed by permutations whose entries are q^maj( u*v^{-1} ), where “maj” is the major index. Previous proofs of this identity have applied the theory of nonsymmetric functions or the representation theory of the Tits algebra to determine the eigenvalues of the matrix.

Title: A Brief Introduction to World of Erd\H{o}s-Ko-Rado Theorems

Abstract:   The Erd\H{o}s-Ko-Rado (EKR) theorem is a famous result that is one of the cornerstones of extremal set theory. This theorem answers the question "What is the largest family of intersecting sets, of a fixed size, from a base set?"

Title: On the Security of the NIST lightweight Finalist Ascon

Abstract: 

The ongoing NIST lightweight cryptographic standardization project for the selection of ciphers which are suitable for constrained environments is in the final stage. The authenticated encryption algorithm Ascon, designed by Dobrauing et al., is one out of the 10 finalists. Ascon is also one of the winners of the CAESAR competition in the lightweight applications category.

Title: An into introduction to the chromatic number of digraph

Abstract: A proper $k$-coloring of a digraph $D$ is a coloring of the vertices such that every color class is acyclic, and the dichromatic number of a digraph $D$ is the minimum number $k$ such that there is a proper $k$-coloring of $D$. Many questions about the chromatic number can be asked about the dichromatic number, but as one will quickly observe, unsuspected complications arise when dealing with digraphs.

Title: Virtual characters of permutation statistics

Abstract:

Functions of permutations are studied in a wide variety of fields including probability, statistics and theoretical computer science. I will introduce a method for studying such functions using representation theory and symmetric functions. As a consequence, one can extract detailed information about asymptotic behavior of many permutation statistics with respect to non-uniform measures that are invariant under conjugation. The key new tool is a combinatorial formula called the path Murnaghan-Nakayama rule that gives the Schur expansion of a novel basis of the ring of symmetric functions. This is joint work with Brendon Rhoades.

Title: Cyclic sieving with focus on open problems

Abstract:

The cyclic sieving phenomenon (CSP) connects a cyclic group action on a family of combinatorial objects with some q-analog of that set. We discuss some recent results and open problems for standard and semistandard tableaux, as well as some other families of combinatorial objects.
Several open problems with various levels of difficulty will be presented.

Title: Distance magic labeling on directed graphs

Abstract:

This talk will explore two new types of distance magic labelings on directed graphs. Results on some specific classes of directed graphs will be discussed. We will also look at various properties of these two types of labelings and some construction techniques.

Title: Faster Algorithms for Isogeny Problems using Torsion Point Images. 

Abstract:

In this talk, we will discuss cryptanalysis of some SIDH-type protocols due to Christophe Petit: https://eprint.iacr.org/2017/571.pdf. While finding isogenies between supersingular elliptic curves remains computationally hard to solve, knowledge of images of specific torsion points by the unknown isogeny helps build faster attacks.

Title: On Donuts and Quasigraphic matroids

Abstract:

Quasigraphic matroids are graph-like objects that give a common generalization of lift and frame matroids. Donuts are edible topological surfaces. I will talk about a surprising link between these two types of object, assuming no prior knowledge of quasigraphic matroids or donuts.

Title: Combinatorial atlas for log-concave inequalities

Abstract:

The study of log-concave inequalities for combinatorial objects have seen much progress in recent years. One such progress is the solution to the strongest form of Mason’s conjecture (independently by Anari et. al. and Brándën-Huh).