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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 1:00 pm - 1:00 pm EDT (GMT -04:00)

C&O Reading Group - Matheus Ota

Title: Hardness of pricing routes for two-stage stochastic vehicle routing problems with scenarios, Part II

Speaker: Matheus Ota
Affiliation: University of Waterloo
Location: MC 6029

Abstract: Following state-of-the-art exact algorithms for vehicle routing problems, several recent exact algorithms for the two-stage vehicle routing problem with stochastic demands (VRPSD) are based on set partitioning formulations. To solve the corresponding LP relaxation, these algorithms rely on efficient routines for solving the associated pricing problems. In this paper, we study the complexity of solving such VRPSD pricing problems.

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

Wednesday, August 23, 2023 11:30 am - 11:30 am EDT (GMT -04:00)

C&O Reading Group - Niv Buchbinder

Title: Chasing Positive Bodies

Speaker: Niv Buchbinder
Affiliation: Tel Aviv University
Location: MC 5417

Abstract: We study the problem of chasing positive bodies in \ell_1: given a sequence of bodies K_t\subset R^n revealed online, where each K_t is defined by a mixed packing-covering linear program, the goal is to (approximately) maintain a point x_t \in K_t such that \sum_t \|x_t - x_{t-1}\|_1 is minimized. This captures the fully-dynamic low-recourse variant of any problem that can be expressed as a mixed packing-covering linear program and thus also the fractional version of many central problems in dynamic algorithms such as set cover, load balancing, hyperedge orientation, minimum spanning tree, and matching.