Contact Info
Combinatorics & Optimization
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 5198884567, ext 33038
PDF files require Adobe Acrobat Reader.
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Title: Packing and covering balls in planar graphs
Speaker: Louis Esperet Affiliation: GSCOP Laboratory Zoom: Join via http://matroidunion.org/?page_id=2477 or please email Shayla RedlinAbstract:
The set of all vertices at distance at most r from a vertex v in a graph G is called an rball. We prove that the minimum number of vertices hitting all rballs in a planar graph G is at most a constant (independent of r) times the maximum number of vertexdisjoint rballs in G.
Title: Lineup polytopes and exclusion principles
Speaker: Federico Castillo Affiliation: Universidad Catolica de Chile Zoom link: Contact Logan CrewAbstract:
The set of all possible spectra of 1reduced density operators for systems of N particles on a ddimensional Hilbert space is a polytope called hypersimplex and this is related to Pauli's exclusion principle. If the spectrum of the original density operators is fixed, the set of spectra (ordered decreasingly) of 1reduced density operators is also a polytope.
Title: Counting planar maps, 50 years after William Tutte
Speaker: Mireille BousquetMélou Affiliation: CNRS, Université de Bordeaux Location: MC 5501 or please contact Emma Watson for Zoom linkAbstract:
Every planar map can be properly coloured with four colours. But how many proper colourings has, on average, a planar map with $n$ edges? What if we allow a prescribed number of "monochromatic" edges, the endpoints of which share the same colour? What if we have $q$ colours rather than four?
Title: Polynomial ideals, association schemes, and the Qpolynomial property
Speaker: Bill Martin Afiliation: Worcester Polytechnic Institute Zoom: Contact Sabrina LatoAbstract:
Let X ⊆ S^{m−1} be a spherical code in C^m. We study the ideal I ⊆ C[z_1, . . . , z_m] of polynomials that vanish on the points of X: I = { F(z)  (∀a ∈ X) (F(a) = 0) }. The primary example of interest is where the Gram matrix of X is proportional to the first idempotent in some Qpolynomial ordering of an association scheme (X, R) defined on X.
Title: Obstructions for matroids of pathwidth at most k and graphs of linear rankwidth at most k
Speaker: Sangil Oum Affiliation: Institute for Basic Science / KAIST Zoom: Join via http://matroidunion.org/?page_id=2477 or please email Shayla RedlinAbstract:
Every minorclosed class of matroids of bounded branchwidth can be characterized by a minimal list of excluded minors, but unlike graphs, this list could be infinite in general. However, for each fixed finite field $\mathbb F$, the list contains only finitely many $\mathbb F$representable matroids, due to the wellquasiordering of $\mathbb F$representable matroids of bounded branchwidth under taking matroid minors [J. F. Geelen, A. M. H. Gerards, and G. Whittle (2002)].
Title: “LatticeBased ZeroKnowledge Arguments for Integer Relations” by Benoit Libert, San Ling, Khoa Nguyen, and Huaxiong Wang
Speaker: Camryn Steckel Affiliation: University of Waterloo Zoom: Contact Jesse ElliottAbstract:
We provide latticebased protocols allowing to prove relations among committed integers. While the most general zeroknowledge proof techniques can handle arithmetic circuits in the lattice setting, adapting them to prove statements over the integers is nontrivial, at least if we want to handle exponentially large integers while working with a polynomial size modulus q.
Title: Type B qStirling numbers
Speaker: Joshua Swanson Affiliation: USC Location: MC 6029 or contact Logan Crew for Zoom linkAbstract:
The Stirling numbers of the first and second kind are classical objects in enumerative combinatorics which count the number of permutations or set partitions with a given number of blocks or cycles, respectively. Carlitz and Gould introduced qanalogues of the Stirling numbers of the first and second kinds, which have been further studied by many authors including Gessel, Garsia, Remmel, Wilson, and others, particularly in relation to certain statistics on ordered set partitions.
Title: Strongly nonexpansive mappings revisited: uniform monotonicity and operator splitting
Speaker: Walaa Moursi Affiliation: University of Waterloo Location: MC 5501 or please contact Emma Watson for Zoom linkAbstract:
The correspondence between the class of nonexpansive mappings and the class of maximally monotone operators via the reflected resolvents of the latter has played an instrumental role in the convergence analysis of the splitting methods. Indeed, the performance of some of these methods, e.g., Douglas–Rachford and Peaceman–Rachford methods hinges on iterating the socalled splitting operator associated with the individual operators.
Title: On packing dijoins in digraphs and weighted digraphs
Speaker: Ahmad Abdi Affiliation: LSE Zoom: http://matroidunion.org/?page_id=2477 or email shayla.redlin@uwaterloo.caAbstract:
Let D=(V,A) be a digraph. A dicut is the set of arcs in a cut where all the arcs cross in the same direction, and a dijoin is a set of arcs whose contraction makes D strongly connected. It is known that every dicut and dijoin intersect. Suppose every dicut has size at least k.
Title: A Multijection of Cokernels
Speaker: Alex McDonough Affiliation: UC Davis Zoom: Contact olya.mandelshtam@uwaterloo.caAbsract:
I discovered an intriguing linear algebra relationship which I call a multijection. I used this construction to solve an open problem about higherdimensional sandpile groups, but I think that it has more to say.
Title: Fixedsize schemes for certification of large quantum systems
Speaker: Laura Mancinska Affiliation: QMATH, University of Copenhagen Location: MC 5501 or please contact Emma Watson for Zoom linkAbstract:
In this talk I will introduce the concept of selftesting which aims to answer the fundamental question of how do we certify proper functioning of blackbox quantum devices. We will see that there is a close link between selftesting and representations of algebraic relations. We will leverage this link to propose a family of protocols capable of certifying quantum states and measurements of arbitrarily large dimension with just four binaryoutcome measurements.
This is a joint work with Chris Schafhauser and Jitendra Prakash.
Title: Decomposing graphs and hypergraphs into complete bipartite subgraphs
Speaker: Sebastian Cioaba Affiliation: University of Delaware Zoom: Contact Sabrina LatoAbstract:
The problem of decomposing (partitioning or covering) graphs into complete bipartite subgraphs (bicliques) has a long history. In this talk, I will describe the basic results including the use of spectral methods, the extension of the problem to hypergraphs and present some of the open problems in this area.
Title: Reduced bandwidth: a qualitative strengthening of twinwidth in minorclosed classes (and beyond)
Speaker: Ojoung Kwon Affiliation: Hanyang University Zoom: http://matroidunion.org/?page_id=2477 or contact Shayla RedlinAbstract:
In a reduction sequence of a graph, vertices are successively identified until the graph has one vertex. At each step, when identifying $u$ and $v$, each edge incident to exactly one of $u$ and $v$ is coloured red.
Title: Sorting probabilities for Young diagrams and beyond
Speaker: Greta Panova Affiliation: University of Southern California Zoom: Contact Logan Crew or Olya MandelshtamAbstract:
Sorting probability for a partially ordered set P is defined as the min Pr[x<y]  Pr[y<x] going over all pairs of elements x,y in P, where Pr[x<y] is the probability that in a uniformly random linear extension (extension to total order) x appears before y.
The celebrated 1/32/3 conjecture states that for every poset the sorting probability is at most 1/3, i.e. there are two elements x and y, such that 1/3\leq Pr[x<y] \leq 2/3.
Title: The chromatic number of trianglefree hypergraphs
Speaker: Lina Li Affiliation: University of Waterloo Location: MC 5501 or please contact Emma Watson for Zoom linkAbstract:
A classical result of Johansson showed that for any trianglefree graph $G$ with maximum degree $\Delta$, it chromatic number is $O(\Delta/\log\Delta)$. This result was later generalized to all rank 3 hypergraphs due to the work of Copper and Mubayi. In this talk, I will present a common generalization of the above results to all hypergraphs, and this is sharp apart from the constant.
Title: Oriented Cayley Graphs with all eigenvalues being integer multiples of $\sqrt{\Delta}$
Speaker: Xiaohong Zhang Affiliation: University of Waterloo Zoom: Contact Sabrina LatoAbstract:
Let $G$ be a finite abelian group. An oriented Cayley graph on $G$ is a Cayley digraph $X(G,C)$ such that $C \cap (C)=\emptyset$. Consider the $(0,1,1)$ skewsymmetric adjacency matrix of an oriented Cayley graph $X=X(G,C)$.
Title: Minimal induced subgraphs of two classes of 2connected nonHamiltonian graphs
Speaker: Zishen Qu Affiliation: University of Waterloo Zoom: http://matroidunion.org/?page_id=2477 or contact Shayla RedlinAbstract:
Finding sufficient conditions for a class of graphs to be Hamiltonian is an old problem, with a wide variety of conditions such as Dirac's degree condition and Whitney's theorem on 4connected planar triangulations. We discuss some past results on sufficient conditions for Hamiltonicity involving the exclusion of fixed induced subgraphs, and some properties of the graphs involved in such results.
Title: Multiplying quantum Schubert polynomials using combinatorics
Speaker: Laura Colmenarejo Affiliation: NC State University Zoom: Contact Logan Crew or Olya MandelshtamAbstract:
Schubert polynomials are a very interesting family of polynomials in algebraic geometry due to their relation with the cohomology of the flag variety. Moreover, they are also very interesting from a combinatorial point of view because they can be considered generalizations of Schur functions.
Combinatorics & Optimization
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 5198884567, ext 33038
PDF files require Adobe Acrobat Reader.
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.