Thursday, June 30, 2022 — 1:00 PM EDT

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

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

Speaker: Karen Meagher
Affiliation: University of Regina
Zoom: Please contact Sabrina Lato for Zoom link

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

Title: On the Security of the NIST lightweight Finalist Ascon

Speaker: Raghvendra Rohit
Affiliation: Technology Institute in Abu Dhabi
Zoom: Please contact Jesse Elliott for zoom link

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

Title: An into introduction to the chromatic number of digraph

Speaker: Alvaro Carbonero Gonzales
Affiliation: University of Waterloo
Room: MC 5417, please contact Shalya Redlin for zoom link

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

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

Speaker: Sam Matteus
Affiliation: Vrije Universiteit Brussel
Zoom: Please contact Sabrina Lato for zoom link

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

Title: An Introduction to Nonnegativity and Polynomial Optimization

Speaker: Timo de Wolff
Affiliation: TU Braunschweig
Location: MC 5501 or please contact Melissa Cambridge for Zoom link

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

Title: 1-skeleton posets of Bruhat interval polytopes

Speaker Christian Gaetz
Affiliation Harvard University
Room: MC 5479 or please contact Olya Mandelshtam for Zoom Link

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

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

Title: Maximal cliques in strongly regular graphs

Speaker: Gary Greaves
Affiliation: Nanyang Technological University
Zoom: Please contact Sabrina Lato for zoom link

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

Title: Combinatorial atlas for log-concave inequalities

Speaker: Swee Hong Can
Affiliation: UCLA
Location: MC 5501 or please contact Melissa Cambridge for Zoom link

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

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

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

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

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

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

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

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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