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Friday, July 21, 2023 3:30 pm - 3:30 pm EDT (GMT -04:00)

Joint Tutte Colloquium & Algorithms and Complexity Seminar - Leonid Gurvits

Title: Combinatorial and complexity theoretic aspects of Stabilities and Controllabilities of linear switched systems(discrete and continuous time)

Speaker: Leonid Gurvits
Affiliation: The City College of New York
Location: MC 5501

Abstract: I will talk about my "pre-hyperbolic" research, some of it done jointly with Alex Samorodnitsky and Alex Olshevsky.

Monday, July 24, 2023 11:30 am - 11:30 am EDT (GMT -04:00)

Algebraic Graph Theory - Hendrik Van Maldeghem

Title: Geometric approach to some rank 3 graphs

Speaker: Hendrik Van Maldeghem
Affiliation: Ghent University
Location: Please contact Sabrina Lato for Zoom link

Abstract: Rank 3 graphs are graphs whose full automorphism group acts as a rank 3 group on the vertices. Finite rank 3 groups are classified and hence finite rank 3 graphs are classified. The main examples arise from geometric structures such as projective and polar spaces, and there is one class of examples related to the exceptional groups of type E6. We present a combinatorial/geometric/projective construction of these graphs.  We then consider a class of regular sets, that is, subsets S of the vertices such that the number of vertices of S adjacent to some vertex v only depends on whether v belongs to S or not. We will explain how this leads to characterizations of certain automorphisms of the E6 graphs and other graphs.

Monday, July 24, 2023 3:30 pm - 3:30 pm EDT (GMT -04:00)

Graphs and Matroids Seminar - Tom Kelly

Title: Robustness for hypergraph embeddings via spreadness

Speaker: Tom Kelly
Affiliation: Georgia Tech
Location: MC 5479

Abstract: In joint work with Kang, K\"uhn, Methuku, and Osthus, we proved the following: If $p\geq{C\log^2n/n}$ and $L_{i,j}\subseteq[n]$ is a random subset of $[n]$ where each $k\in[n]$ is included in $L_{i,j}$ independently with probability $p$ for each $i,j\in[n]$, then asymptotically almost surely there is an order-$n$ Latin square in which the entry in the $i$th row and $j$th column lies in $L_{i,j}$.  We prove analogous results for Steiner triple systems and $1$-factorizations of complete graphs.  These results can be understood as stating that these ``design-like'' structures exist ``robustly''.

Thursday, July 27, 2023 3:00 pm - 3:00 pm EDT (GMT -04:00)

Graphs and Matroids Seminar - Lise Turner

Title: Cluster chromatic number of $G(n,p)$

Speaker: Lise Turner
Affiliation: University of Waterloo
Location: MC 6029

Abstract: A colouring of a graph $G$ is said to be $\kappa$-clustered if no colour class has a connected component with more than $\kappa$ vertices. In this talk, we give the $\kappa$-clustered chromatic number of $G(n,p)$ for $\kappa$ increasing at various rates with respect to $n$.

The talk is joint work with Jane Gao.

Monday, July 31, 2023 11:30 am - 11:30 am EDT (GMT -04:00)

Algebraic Graph Theory - Safet Penjić

Title: Short note about commutative association schemes and specific (directed) family of graphs

Speaker: Safet Penjić
Affiliation: University of Primorska
Location: Please contact Sabrina Lato for Zoom link

Abstract: In this talk, we consider the following problem:

{\bf Problem.} When the Bose--Mesner algebra ${\cal M}$ of commutative $d$-class association scheme ${\mathfrak X}$ (which is not necessarily symmetric) can be generated by a $01$-matrix $A$? With other words, for a given ${\mathfrak X}$ can we find $01$-matrix $A$ such that ${\cal M}=(\langle A\rangle, +, \cdot)$?

Monday, July 31, 2023 2:30 pm - 2:30 pm EDT (GMT -04:00)

URA Seminar - URA Presentations

Title: URA Presentations

Speakers: Tom Iagovet, Joseph Vendryes, Jacob Mausberg, Yun Xing
Affiliation: University of Waterloo
Location: MC 5479

Abstract: A series of presentations by a group of Spring 2023 Undergraduate Research Assistants. The topics of each presentation are detailed below.

Thursday, August 3, 2023 1:00 pm - 1:00 pm EDT (GMT -04:00)

Algebraic Combinatorics - Jerónimo Valencia

Title: Specializations of Macdonald polynomials using multiline queues and multiline diagrams

Speaker: Jerónimo Valencia 
Affiliation: University of Waterloo
Location: MC 5501

Abstract: Multiline queues were introduced by Ferrari and Martin to model the stationary states of the TASEP, a 1D non-equilibrium particle model. Later, Corteel, Mandelshtam, and Williams gave a formula for the Macdonald polynomial using a (X,q,t)-weighted version of multiline queues. This talk aims to develop the combinatorics of such objects in the t=0 case.

Friday, August 4, 2023 3:30 pm - 3:30 pm EDT (GMT -04:00)

Tutte Colloquium - Bill Jackson

Title: Rigidity of Simplicial Complexes

Speaker: Bill Jackson
Affiliation: Queen Mary University of London
Location: MC 5501

Abstract: A simplicial k-cycle is an abstract simplicial k-complex in which every (k-1)-face belongs to an even number of k-faces. A simplicial k-circuit is a minimal simplicial k-cycle (in the sense that none of its proper subcomplexes are simplicial k-cycles).

Thursday, August 10, 2023 1:00 pm - 1:00 pm EDT (GMT -04:00)

Algebraic Combinatorics - Patricia Klein

Title: From the Upper Bound Conjecture to Gorenstein linkage

Speaker: Patricia Klein
Affiliation: Texas A&M
Location: MC 5501

Abstract: In 1957, Motzkin conjectured that the maximum number of faces possible for a polytope on n vertices in d-space is achieved by the convex hull of n points on the moment curve in d-space.  This conjecture, called the Upper Bound Conjecture, was proved by McMullen in 1970 and generalized by Stanley in 1975.  On the road to Stanley's proof, a correspondence between squarefree monomial ideals and simplicial complexes was born.  That correspondence is called the Stanley--Reisner correspondence.  It has come to occupy a central place in combinatorial algebraic geometry. 

Monday, August 14, 2023 2:30 pm - 2:30 pm EDT (GMT -04:00)

URA Seminar - URA Presentations

Title: URA Presentations

Speakers: Benjamin Wong, Rick Lyu, and Yen-Kang Fu
Affiliation: University of Waterloo
Location: MC 5479

Abstract: A series of presentations by a group of Spring 2023 Undergraduate Research Assistants. The topics of each presentation are detailed below.

Quantum Max-Cut on Bipartite Graphs - Benjamin Wong