# Events - 2022

Friday, December 16, 2022 — 3:30 PM EST

## Tutte Colloquium - Daniel Panario

Title: Probabilistic root finding in code-based cryptography

 Speaker: Daniel Panario Affiliation: School of Mathematics and Statistics, Carleton University Location: MC 5501 or contact Eva Lee for Zoom link

Abstract: Factorization of polynomials over finite fields, and the particular subproblem of finding roots of polynomials, have many applications in diverse areas such as computer algebra, cryptography and coding theory, among many others. In practice, fast factorization algorithms are probabilistic.

Tuesday, December 13, 2022 — 3:30 PM EST

## IQC MATH CS Seminar - Mario Szegedy

Title: Generating k EPR-pairs from an n-party resource state

 Speaker: Mario Szegedy Affiliation: Rutgers University Location: QNC 0101 or contact Eva Lee for Zoom lin

Abstract: Motivated by quantum network applications over classical channels, we initiate the study of n-party resource states from which LOCC protocols can create EPR-pairs between any k disjoint pairs of parties.

Monday, December 12, 2022 — 3:00 PM EST

## Graphs and Matroid Seminar - Cléophée Robin

Title: When all holes have the same length

 Speaker: Cléophée Robin Affiliation: University of Waterloo Location: MC 6029

Abstract: A hole is an induced cycle of length at least 4. For an integer k ≥ 4, we denote by Ck, the class of graphs where every hole has length k. We have defined a new class of graphs named blowup of ℓ-templates whose all holes have length 2ℓ + 1. Using earlier results on other related classes of graphs, we did obtain the following structural theorem :

Monday, December 12, 2022 — 11:30 AM EST

## Algebraic Graph Theory Seminar - Venkata Raghu Tej Pantangi

Title: Cameron-Liebler Sets in Permutation Groups

 Speaker: Venkata Raghu Tej Pantangi Affiliation: University of Regina Location: Contact Sabrina Lato for Zoom link

Abstract: Let $G \leq S_{n}$ be a transitive permutation group. Given $i,j \in [n]$, by $x_{i\to j}$, denote the characteristic function of the set $\{g \in G\ :\ g(i)=j\}$. A Cameron-Liebler set (CL set) in $G$ is a set which is represented by a Boolean function in the linear span of $\{x_{i\to j} \ :\ (i,j)\in [n]^2\}$. These are analogous to Boolean degree 1 functions on the hypercube and to Cameron-Liebler line classes in $PG(3,q)$. Sets of the form $\{g\ : g(i)\in X\}$ and $\{g\ : \ i \in g(X)\}$ (for $i \in [n]$ and $X \subset [n]$) are canonically occurring examples of CL sets. A result of Ellis et.al, shows that all CL sets in the $S_{n}$ are canonnical. In this talk, we will demonstrate many examples with exotic'' CL sets. Of special interest is an exotic CL set in $PSL(2,q)$ (with $q \equiv 3 \pmod{4}$), a 2-transitive group, just like $S_{n}$. The talk is based on ongoing joint work with Jozefien D'haeseleer and Karen Meagher.

Friday, December 9, 2022 — 3:30 PM EST

## Tutte Colloquium - Vijay Bhattiprolu

Titile: Global geometric reductions for some bottleneck questions in hardness of approximation

 Speaker: Vijay Bhattiprolu Affiliation: University of Waterloo Location: MC 5501 or contact Eva Lee for Zoom link

Abstract: I will describe the classical "local gadget reduction" paradigm for proving hardness of approximation results and then list some important optimization problems that resist all such attacks. With a focus on problems that can be cast as quadratic maximization over convex sets, I will describe some successes in bypassing the aforementioned bottleneck using ideas from geometry. Time permitting I will also describe some compelling new frontiers where answering some questions in convex geometry could be the path forward.

Friday, December 9, 2022 — 12:00 PM EST

## Combinatorial Optimization Reading Group - David Aleman

Title: Approximation algorithm for stochastic k-TSP

 Speaker: David Aleman Affiliation: University of Waterloo Location: MC 6029 or contact Rian Neogi for Zoom link

Abstract: The input of the deterministic k-TSP problem consists of a metric complete graph with root p in which the nodes are assigned a fixed non-negative reward. The objective is to construct a p-rooted path of minimum length that collects total reward at least k. In this talk we will explore a stochastic variant of this problem in which the rewards assigned to the nodes are independent random variables, and the objective is to derive a policy that minimizes the expected length of a p-rooted path that collects total reward at least k. We will discuss approximation algorithms for this problem proposed in a paper by Ene, Nagarajan and Saket, and a paper by Jiang, Li, Liu and Singla.

Friday, December 2, 2022 — 12:00 PM EST

## Combinatorial Optimization Reading Group - Jacob Skitsko

Title: Boosted Sampling

 Speaker: Jacob Skitsko Affiliation: University of Waterloo Location: MC 6029 or contact Rian Neogi for Zoom link

Abstract: We will discuss the boosted sampling technique introduced by Gupta et al. which approximates the stochastic version of problems by using nice approximation algorithms for the deterministic version of the problem. We will focus on rooted stochastic Steiner trees as an example, though other problems are covered by this approach (such as vertex cover and facility location). The problem is given to us in two stages: in the first stage we may choose some elements at a cheaper cost, and in the second stage our actual requirements are revealed to us, and we can buy remaining needed elements at a more expensive cost (where costs get scaled by some factor in the second stage). We will see that if our problem is sub-additive, and we have an alpha-approximation algorithm for the deterministic version of our problem with a beta-strict cost-sharing function then we can get an (alpha + beta)-approximation for the stochastic version of our problem. We also discuss related problems, for example the (not sub-additive!) unrooted stochastic Steiner tree problem.

Thursday, December 1, 2022 — 1:00 PM EST

## Algebraic Combinatorics - Sergey Yurkevich

Title: Algebraicity of solutions of functional equations with one catalytic variable

 Speaker: Sergey Yurkevich Affiliation: University Paris-Saclay Location: MC 5479 or contact Olya Mandelshtam for Zoom link

Abstract: Abstract: Numerous combinatorial enumeration problems reduce to the study of functional equations which can be solved by a uniform method introduced by Bousquet-Mélou and Jehanne in 2006. In my talk, I will first briefly explain this result and its proof. Then I will present a new generalization of it to the case of systems of functional equations with one catalytic variable. The method is constructive and yields an algorithm for computing the minimal polynomials of interest.

Monday, November 28, 2022 — 3:00 PM EST

## Graphs and Matroid Seminar - Hidde Koerts

Title: k-Connectedness and k-Factors in the Semi-Random Graph Process

 Speaker: Hidde Koerts Affiliation: University of Waterloo Location: MC 6029

Abstract: The semi-random graph process is a single player graph game where the player is initially presented an edgeless graph with n vertices. In each round, the player is offered a vertex u uniformly at random and subsequently chooses a second vertex v deterministically according to some strategy, and adds edge uv to the graph. The objective for the player is then to ensure that the graph fulfils some specified property as fast as possible.

Monday, November 28, 2022 — 11:30 AM EST

## Algebraic Graph Theory Seminar - Bogdan Nica

Title: A recursive spectral bound for independence

 Speaker: Bogdan Nica Affiliation: Indiana University-Purdue University Indianapolis Location: Contact Sabrina Lato for Zoom link

Abstract: We discuss an upper bound for the independence number of a graph, in the spirit of the well-known Hoffman bound. Our bound involves the largest Laplacian eigenvalue of the graph; more surprisingly, it also involves the independence number of a certain induced graph. We illustrate the bound on several examples.

Friday, November 25, 2022 — 3:30 PM EST

## Tutte Colloquium - Stefan Weltge

Title: Integer programs with bounded subdeterminants and two nonzeros per row

 Speaker: Stefan Weltge Affiliation: Technical University of Munich Location: MC 5501 or contact Eva Lee for Zoom link

Abstract: Determining the complexity of integer linear programs with integer coefficient matrices whose subdeterminants are bounded by a constant is currently a very actively discussed question in the field. In this talk, I will present a strongly polynomial-time algorithm for such integer programs with the further requirement that every constraint contains at most two variables. The core of our approach is the first polynomial-time algorithm for the weighted stable set problem on graphs that do not contain more than k vertex-disjoint odd cycles, where k is any constant. Previously, polynomial-time algorithms were only known for k = 0 (bipartite graphs) and for k = 1.

This is joint work with Samuel Fiorini, Gwenaël Joret, and Yelena Yuditsky, which recently appeared at FOCS this year.

Friday, November 25, 2022 — 12:00 PM EST

## Combinatorial Optimization Reading Group - Ian DeHaan

Title: Greedy algorithm for stochastic matching is a 2-approximatio

 Speaker: Ian DeHaan Affiliation: University of Waterloo Location: MC 6029 or contact Rian Neogi for Zoom link

Abstract: We will discuss the greedy algorithm for the stochastic matching problem. In this problem, we are given an undirected graph where each edge is assigned a probability p_e in [0, 1] and each vertex is assigned a patience t_v in Z+. We begin each step by probing an edge e which is not adjacent to any edges in our matching. The probe will succeed with probability p_e, and if it does, we add e to our matching. Otherwise, we may not probe e again. We also may not probe edges adjacent to a vertex v more than t_v times. The goal is to maximize the number of edges we add to our matching.

Thursday, November 24, 2022 — 1:00 PM EST

## Algebraic Combinatorics - Michael Borinsky

Title: Asymptotics of the Euler characteristic of Kontsevich's commutative graph complex

 Speaker: Michael Borinsky Affiliation: ETH, Zurich Location: MC 5479 or contact Olya Mandelshtam for Zoom link

Abstract: I will present results on the asymptotic growth rate of the Euler characteristic of Kontsevich's commutative graph complex. By a work of Chan-Galatius-Payne, these results imply the same asymptotic growth rate for the top-weight Euler characteristic of M_g, the moduli
space of curves, and establish the existence of large amounts of unexplained cohomology in this space. This asymptotic growth rate
follows from new generating functions for the edge-alternating sum of graphs without odd automorphisms. I will give an overview on this
interaction between topology and combinatorics and illustrate the combinatorial and analytical tools that were needed to obtain these
generating functions.

Monday, November 21, 2022 — 6:00 PM EST

## Algebraic Graph Theory - Daniel Horsley

Title: Exact Zarankiewicz numbers through linear hypergraphs

 Speaker: Daniel Horsley Affiliation: Monash University Location: Contact Sabrina Lato for Zoom link

Abstract: The \emph{Zarankiewicz number} $Z_{2,2}(m,n)$ is usually defined as the maximum number of edges in a bipartite graph with parts of sizes $m$ and $n$ that has no $K_{2,2}$ subgraph. An equivalent definition is that $Z_{2,2}(m,n)$ is the greatest total degree of a linear hypergraph with $m$ vertices and $n$ edges. A hypergraph is \emph{linear} if each pair of vertices appear together in at most one edge. The equivalence of the two definitions can be seen by considering the bipartite incidence graph of the linear hypergraph.

Friday, November 18, 2022 — 3:30 PM EST

## Tutte Colloquium - Vera Traub

Title: Approximating Weighted Connectivity Augmentation below Factor 2

 Speaker: Vera Traub Affiliation: Research Institute for Discrete Mathematics, University of Bonn Location: MC 5501 or contact Melissa Cambridge for Zoom link

Abstract:  The Weighted Connectivity Augmentation Problem (WCAP) asks to increase the edge-connectivity of a graph in the cheapest possible way by adding edges from a given set. It is one of the most elementary network design problems for which no better-than-2 approximation algorithm has been known, whereas 2-approximations can be easily obtained through a variety of well-known techniques.

Friday, November 18, 2022 — 12:00 PM EST

## Combinatorial Optimization Reading Group - Madison Van Dyk

Title: Approximation algorithms for stochastic orienteering

 Speaker: Madison Van Dyk Affiliation: University of Waterloo Location: MC 6029 or contact Rian Neogi for Zoom link

Abstract: This week we revisit the stochastic orienteering problem in which we are given a metric graph where each node has a deterministic reward and a random size. The goal is to adaptively decide on which nodes to visit to maximize the expected reward, while not exceeding the budget B on the distance plus the size of jobs processed.

Thursday, November 17, 2022 — 1:00 PM EST

## Algebraic Graph Theory Seminar - Josip Smolcic

Title: Algorithms for Analytic Combinatorics in Several Variables

 Speaker: Josip Smolcic Affiliation: University of Waterloo Location: MC 5479

Abstract: In this presentation we will see how to apply the theory of complex analysis to study multivariate generating series by looking at several examples. Specifically, given a rational bivariate generating function G(x, y)/H(x, y) with coefficients f_{i, j} the objective is algorithmically determine asymptotic formulas to approximate f_{rn, sn} as n goes to infinity, for fixed positive integers r and s.

Monday, November 14, 2022 — 3:00 PM EST

## Graphs and Matroids Seminar - Jeremy Chizewer

Title: The Hat Guessing Number of Graphs

 Speaker: Jeremy Chizewer Affiliation: University of Waterloo Location: MC 6029

Abstract:  The hat guessing number HG(G) of a graph G on n vertices is defined in terms of the following game: n players are placed on the n vertices of G, each wearing a hat whose color is arbitrarily chosen from a set of q possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number HG(G) is the largest integer q such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of q possible colors.

Monday, November 14, 2022 — 11:30 AM EST

## Algebraic Graph Theory Seminar - Paul Horn

Title: Graphs, curvature, and local discrepancy

 Speaker: Paul Horn Affiliation: University of Denver Location: contact Sabrina Lato for Zoom link

Abstract: Spectral graph theory, the use of eigenvalues to study graphs, gives an important window into many properties of graphs.  One of the reasons for this is that the eigenvalues can be used to certify the `pseudo-randomness' of the edge set of a graph.  In recent years, several notions of discrete curvature have been introduced that gives a 'local' way (depending on the neighborhood structure of vertices) to study some of the same properties that eigenvalues can capture.

Friday, November 11, 2022 — 3:30 PM EST

## Tutte Colloquium - Linda Cook

Title: Forbidding some induced cycles in a graph

 Speaker: Linda Cook Affiliation: Institute for Basic Science, South Korea Location: MC 5501 or contact Melissa Cambridge for Zoom link

Abstract:  We call an induced cycle of length at least four a hole. The parity of a hole is the parity of its length. Forbidding holes of certain lengths in a graph has deep structural implications. In 2006, Chudnovksy, Seymour, Robertson, and Thomas famously proved that a graph is perfect if and only if it does not contain an odd hole or a complement of an odd hole. In 2002, Conforti, Cornuéjols, Kapoor, and Vušković provided a structural description of the class of even-hole-free graphs.

Friday, November 11, 2022 — 12:00 PM EST

## Combinatorial Optimization Reading Group - Sharat Ibrahimpur

Title: Stochastic Minimum Norm Combinatorial Optimization

 Speaker: Sharat Ibrahimpur Affiliation: Location: MC 6029 or contact Rian Neogi for Zoom link

Abstract:  In this work, we introduce and study stochastic minimum-norm optimization. We have an underlying combinatorial optimization problem where the costs involved are random variables with given distributions; each feasible solution induces a random multidimensional cost vector. The goal is to find a solution that minimizes the expected norm of the induced cost vector, for a given monotone, symmetric norm. We give a framework for designing approximation algorithms for stochastic minimum-norm optimization and apply it to give approximation algorithms for stochastic minimum-norm versions of load balancing and spanning tree problems.

Thursday, November 10, 2022 — 1:00 PM EST

## Algebraic Combinatorics Seminar - Theo Douvropoulos

Title: Recursions and Proofs in Coxeter-Catalan combinatorics

 Speaker: Theo Douvropoulos Affiliations: U Mass Amherst Location: MC 5479 or contact Olya Mandelshtam for Zoom link

Abstract:  The collection of parking functions under a natural Sn-action (which has Catalan-many orbits) has been a central object in Algebraic Combinatorics since the work of Haiman more than 30 years ago. One of the lines of research spawned around it was towards defining and studying analogous objects for real and complex reflection groups W; the main candidates are known as the W-non-nesting and W-non-crossing parking functions.

Monday, November 7, 2022 — 11:00 AM EST

## Algebraic Graph Theory - Soffía Árnadóttir

Title: Cayley graphs, association schemes and state transfer

 Speaker: Soffía Árnadóttir Affiliation: Technical University of Denmark Location: contact Sabrina Lato for Zoom link

Abstract: The aim of this talk is to give some examples of how association schemes can be used as a tool to study certain properties of Cayley graphs. In particular, they contribute to our long-term goal of characterizing perfect state transfer in Cayley graphs. The talk is based on the following paper https://arxiv.org/abs/2204.09802.

Friday, November 4, 2022 — 3:30 PM EDT

## Tutte Colloquium - Jim Geelen

Title: Sylvester, Gallai, and their complex relatives

 Speaker: Jim Geelen Affiliation: University of Waterloo Location: MC 5501 or contact Melissa Cambridge for Zoom link

Abstract: Given any finite set of points in the real plane, not all collinear, there is a line in the plane that contains exactly two of them. This pretty result was conjectured by Sylvester in 1893 and proved by Gallai in 1944. We will present an extension of the result to higher dimensional complex spaces and discuss some related conjectures. This is joint work with Matthew Kroeker.

Friday, November 4, 2022 — 12:00 PM EDT

## Combinatorial Optimization Reading Group - David Aleman

Title: Approximation Algorithms for Stochastic Knapsack

 Speaker: David Aleman Affiliation: University of Waterloo Location: MC 6029 or contact Rian Ne

Abstract: The classical Knapsack problem takes as input a set of items with some fixed nonnegative values and weights. The goal is to compute a subset of items of maximum total value, subject to the constraint that the total weight of these elements is at most a given limit. In this talk we review a paper by Gupta, Krishnaswamy, Molinaro and Ravi, in which the following stochastic variation of this problem is considered: the value and weight of each item are correlated random variables with known, arbitrary distributions.

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