# Events - June 2022

Thursday, June 30, 2022 — 1:00 PM EDT

## Seminar - Thomas McConville

Title: Determinantal formulas with major indices

 Speaker: Thomas McConville Affiliation: Kennesaw State Room: MC 5483

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.

Monday, June 27, 2022 — 11:30 AM EDT

## Algebraic Graph Theory Seminar - Karen Meagher

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?"

Thursday, June 23, 2022 — 11:30 AM EDT

## Cryptography Reading Group - Raghvendra Rohit

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.

Tuesday, June 21, 2022 — 2:30 PM EDT

## Graphs and Matroids Seminar - Alvaro Carbonero Gonzales

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.

Monday, June 20, 2022 — 11:30 AM EDT

## Algebraic Graph Theory Seminar - Sam Mattheus

Title: Erdős-Ko-Rado results for flags in spherical buildings

Abstract: Over the last few years, Erdős-Ko-Rado theorems have been found in many different geometrical contexts including for example sets of subspaces in projective or polar spaces. A recurring theme throughout these theorems is that one can find sharp upper bounds by applying the Delsarte-Hoffman coclique bound to a matrix belonging to the relevant association scheme.

Friday, June 17, 2022 — 3:30 PM EDT

## Tutte Colloquium - Timo de Wolff

Title: An Introduction to Nonnegativity and Polynomial Optimization

Abstract:

In science and engineering, we regularly face polynomial optimization problems, that is: minimize a real, multivariate polynomial under polynomial constraints. Solving these problems is essentially equivalent to certifying of nonnegativity of real polynomials -- a key problem in real algebraic geometry since the 19th century.

Thursday, June 16, 2022 — 1:00 PM EDT

## Algebraic Combinatorics Seminar - Christian Gaetz

Title: 1-skeleton posets of Bruhat interval polytopes

Abstract:  Bruhat interval polytopes are a well-studied class of generalized permutohedra which arise as moment map images of various toric varieties and totally positive spaces in the flag variety. I will describe work in progress in which I study the 1-skeleta of these polytopes, viewed as posets interpolating between weak order and Bruhat order. In many cases these posets are lattices and the polytopes, despite not being simple, have interesting h-vectors.

Tuesday, June 14, 2022 — 3:00 PM EDT

## Graphs and Matroids Seminar - Kathie Cameron

Title: Theorems and Exchange Graph Algorithms concerning Paths, Cycles and Trees

 Speaker Kathie Cameron Affiliation: Wilfred Laurier University Room: MC 6029

Abstract: Carsten Thomassen and I proved that in any graph G, the number of cycles containing a specified edge as well as all the odd-degree vertices is odd if and only if G is eulerian. Where all vertices have even degree this is a theorem of Sunichi Toida and where all vertices have odd degree it is Andrew Thomason's generalization of Smith's Theorem.

Monday, June 13, 2022 — 8:00 PM EDT

## Algebraic Graph Theory Seminar - Gary Greaves

Title: Maximal cliques in strongly regular graphs

Abstract: In this talk, I will introduce a cubic polynomial that can be associated to a strongly regular graph Γ. The roots of this polynomial give rise to upper and lower bounds for the size of a maximal clique in Γ. I will explain how we can use this cubic polynomial to rule out the existence of strongly regular graphs that correspond to an infinite family of otherwise feasible parameters. This talk is based on joint work with Jack Koolen and Jongyook Park.

Friday, June 10, 2022 — 3:30 PM EDT

## Tutte Colloquium - Swee Hong Chan

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).

Thursday, June 9, 2022 — 2:30 PM EDT

## Algebraic Graph Theory Seminar - Sabrina Lato

Title: Algebraic Graph Theory

 Speaker: Sabrina Lato Affiliation: University of Waterloo Location: MC 6029

Abstract:

A graph is distance-regular if we can write the distance adjacency matrices as polynomials in the adjacency matrix. Distance-regular graphs are a class of graphs of significant interest to algebraic graph theorists for their structural and algebraic properties. The notion of distance-regularity can be weakened to a local property on vertices, but when every vertex in the graph is locally distance-regular, the graph will either be distance-regular or in the closely related class of distance-biregular graphs.

Thursday, June 9, 2022 — 1:00 PM EDT

## Seminar - Zachary Hamacker

Title: Virtual characters of permutation statistics

 Speaker: Zachary Hamacker Affiliation: University of Florida Room: MC 5483

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.

Thursday, June 9, 2022 — 11:30 AM EDT

## Cryptography Reading Group - Jean Belo Klamti

Title: Generalized Subspace Subcode with Application in Cryptology

 Speaker: Jean Belo Klamti Affiliation: University of Waterloo Attend: Contact Jesse Elliott

Abstract:

Most codes with an algebraic decoding algorithm are derived from Reed-Solomon codes. They are obtained by taking equivalent codes, for example Generalized Reed-Solomon codes, or by using the so-called subfield subcode method, which leads to Alternant codes over the underlying prime field, or over some intermediate subfield. The main advantage of these constructions is to preserve both the minimum distance and the decoding algorithm of the underlying Reed-Solomon code.

Tuesday, June 7, 2022 — 2:30 PM EDT

## Graphs and Matroids Seminar - Ronen Wdowinski

Title: Linear arboricity of sparse multigraphs via orientations

 Speaker: Ronen Wdowinski Affiliation: University of Waterloo Room: MC 5417

Abstract:

The linear arboricity $la(G)$ of a loopless multigraph $G$ is the minimum number of colors required to edge-color $G$ into linear forests, that is, forests whose components are all paths. The Linear Arboricity Conjecture of Akiyama, Exoo, and Harary asserts that the linear arboricity of a simple graph $G$ is at most $\lceil (\Delta(G)+1)/2 \rceil$.

Monday, June 6, 2022 — 11:30 AM EDT

## Algebraic Graph Theory Seminar - Alison Marr

Title: Distance magic labeling on directed graphs

 Speaker: Alison Marr Affiliation: Southwestern University Zoom: Contact Sabrina Lato for link

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.

Monday, June 6, 2022 — 10:00 AM to Tuesday, June 7, 2022 — 5:00 PM EDT

## Algebraic Combinatorics Virtual Expedition (AlCoVE)

AlCoVE aims to bring together researchers interested in algebraic combinatorics from around the world. Each talk will be 30 minutes and between talks, there will be casual social activities for spending time with your friends and making new friends.

To access the Zoom links, you must first register for the conference.

#### Registration

To register, click here.

Thursday, June 2, 2022 — 12:00 PM EDT

## Algebraic Combinatorics Seminar - Per Alexandersson

Title: Cyclic sieving with focus on open problems

 Speaker: Per Alexandersson Affiliation: Stockholm University Room/Zoom: MC5479 or for Zoom link contact Logan Crew or Olya Mandelshtam

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.

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