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Please note: The University of Waterloo is closed for all events until further notice.

Friday, June 12, 2020 — 1:30 PM EDT

**Title:** One Dollar Each Eliminates Envy

Speaker: | Vishnu V. Narayan |

Affiliation: | McGill University |

Zoom: | Contact Sharat Ibrahimpur |

**Abstract:**

We study the fair division of a collection of $m$ indivisible goods amongst a set of $n$ agents. Whilst envy-free allocations typically do not exist in the indivisible goods setting, envy-freeness can be achieved if some amount of a divisible good (money) is introduced.

Thursday, June 11, 2020 — 2:30 PM EDT

**Title: **An Upper Bound on Graphical Partitions

Speaker: | Steve Melczer |

Affiliation: | UQAM/CRM |

Zoom | Contact Karen Yeats |

**Abstract**:

An integer partition is called graphical if it can be realized as the size-ordered degree sequence of a simple graph (with no loops or multiple edges). In his 1736 paper on the Königsberg bridge problem, arguably the origin of graph theory, Euler gave a necessary condition for a partition to be graphical: its sum must be even.

Friday, June 5, 2020 — 3:30 PM EDT

**Title:** Matroids, tropical geometry, and positivity

Speaker: | Lauren K. Williams |

Affiliation: | Harvard University & Radcliffe Institute |

Zoom: | Please email Emma Watson. |

**Abstract:**

The theory of matroids -- a class of combinatorial objects which simultaneously generalize graphs as well as vectors in a vector space -- was pioneered by William Tutte in his 1948 PhD thesis. Matroids are also closely connected to the Grassmannian and the tropical Grassmannian. In recent years, mathematicians and physicists have been exploring positive notions of all of these objects, finding applications to scattering amplitudes and shallow water waves. In my talk I will give an introduction to matroids, tropical geometry, and positivity, and survey some of the beautiful results and applications.

Friday, June 5, 2020 — 1:00 PM EDT

**Title: **A Strongly Polynomial Label-Correcting Algorithm for Linear Systems with Two Variables per Inequality

Speaker: | Cedric Koh |

Affiliation: | London School of Economics and Political Science |

Zoom: | Contact Sharat Ibrahimpur |

**Abstract:**

In this talk, I will present a strongly polynomial label-correcting algorithm for solving the feasibility of linear systems with two variables per inequality. The algorithm is based on the Newton–Dinkelbach method for fractional combinatorial optimization, and extends previous work of Madani (2002).

Thursday, June 4, 2020 — 2:30 PM EDT

**Title: **Weighted generating functions for weighted chord diagrams

Speaker: | Lukas Nabergall |

Affiliation: | University of Waterloo |

Zoom: | Contact Karen Yeats |

**Abstract****:**

Motivated by the universal property of the Connes-Kreimer Hopf algebra of rooted trees and Hopf subalgebras arising from so-called combinatorial Dyson-Schwinger equations, we introduce a class of two-variable recursive functional equations involving Hochschild 1-cocycle operators.

Friday, May 29, 2020 — 3:30 PM EDT

**Title:** Symmetry of random graphs

Speaker: | Jane Gao |

Affiliation: | University of Waterloo |

Zoom: | Please email Emma Watson |

**Abstract:**

A graph is said asymmetric if its automorphism group contains only the identity permutation. Otherwise, it is said symmetric. In this talk we will survey symmetry of Erdos-Renyi random graphs, of random regular graphs, and of random graphs with moderate degree sequences.

Thursday, May 28, 2020 — 2:30 PM EDT

**Title:** The e-positivity of chromatic symmetric functions

Speaker: | Steph van Willigenburg |

Affiliation: | University of British Columbia |

Zoom: | Contact Karen Yeats |

**Abstract:**

The chromatic polynomial was generalized to the chromatic symmetric function by Stanley in his seminal 1995 paper. This function is currently experiencing a flourishing renaissance, in particular the study of the positivity of chromatic symmetric functions when expanded into the basis of elementary symmetric functions, that is, e-positivity.

Thursday, May 21, 2020 — 2:30 PM EDT

**Title:** Nakajima quiver varietites and irreducible components of Springer fibers

Speaker: | Mee Seong |

Affiliation: | United States Military Academy and Army Research Laboratory |

Zoom: | Contact Karen Yeats |

**Abstract:**

Springer fibers and Nakajima quiver varieties are amongst the most important objects in geometric representation theory. While Springer fibers can be used to geometrically construct and classify irreducible representations of Weyl groups, Nakajima quiver varieties play a key role in the geometric representation theory of Kac--Moody Lie algebras.

Friday, May 15, 2020 — 3:30 PM EDT

Zoom (for information email emma.watson@uwaterloo.ca)

**Title:** Permanent Hardness from Linear Optics

Speaker: | Daniel Grier |

Affiliation: | University of Waterloo |

Location: | Online (Zoom) |

**Abstract:**

One of the great accomplishments in complexity theory was Valiant's 1979 proof that the permanent of a matrix is #P-hard to compute. Subsequent work simplified Valiant's ideas and even began to recast them as problems in quantum computing. In 2011, this culminated in a striking proof by Aaronson, based solely on quantum linear optics, of the #P-hardness of the permanent.

Thursday, May 14, 2020 — 10:00 AM EDT

**Title:** Combinatorial masters in QED

Speaker: | Oliver Schnetz |

Affiliation: | Friedrich-Alexander Universität Erlangen |

Zoom: | Contact Karen Yeats |

**Abstract:**

Calculations in perturbative QED (and also in QCD) use a reduction from Feynman integrals to `master integrals'. In general, the reduction to master integrals is performed by excessive use of computer power.

Friday, May 8, 2020 — 3:30 PM EDT

Zoom (for information email emma.watson@uwaterloo.ca)

**Title:** Hardness of set-partitioning formulation for the vehicle routing problem with stochastic demands

Speaker: | Ricardo Fukasawa |

Affiliation: | University of Waterloo |

Location: | Online (Zoom) |

**Abstract:**

The vehicle routing problem considers the cheapest way to serve a set of customers using a fixed set of vehicles. When a vehicle serves a customer, it picks up its demand which is given as an input, and the total demand picked up cannot exceed the vehicle’s capacity. This classical combinatorial optimization problem combines aspects of routing (like a traveling salesman problem) and packing (like a knapsack problem).

Friday, March 13, 2020 — 3:30 PM EDT

**Title:** Widths in even-hole-free graphs

Speaker: | Nicolas Trotignon |

Affiliation: | École Normale Supérieure de Lyon |

Room: | MC 5501 |

**Abstract:**

Historically, the study of even-hole-free graphs is motivated by the analogy with perfect graphs. The decomposition theorems that are known for even-hole-free graphs are seemingly more powerful than the ones for perfect graphs: the basic classes and the decompositions are more restricted.

Friday, March 13, 2020 — 1:00 PM EDT

**Title**:

Speaker: | Harry Sivasubramaniam |

Affiliation: | University of Waterloo |

Room: | MC 5417 |

**Abstract:**

Differential privacy is about preserving an individuals privacy while maintaining utility in the context of data analysis.

Thursday, March 12, 2020 — 4:00 PM EDT

**Title:** Improving the general upper bound for Hadwiger's conjecture

Speaker: | Luke Postle |

Affiliation: | University of Waterloo |

Room: | MC 5479 |

**Abstract:**

In 1943, Hadwiger conjectured that every K_t-minor-free graph has chromatic number at most t-1.

Thursday, March 12, 2020 — 2:30 PM EDT

**Title:** Proof of the monotone column permanent conjecture

Speaker: | David Wagner |

Affiliation: | University of Waterloo |

Room: | MC 5417 |

**Abstract:**

In 1993, Jim Haglund conjectured the following. If A is a square matrix of real numbers which are weakly decreasing down each column, and J is the all-ones matrix of the same size, then the permanent of the matrix xJ+A is a polynomial with only real roots.

Tuesday, March 10, 2020 — 8:42 AM EDT

**Title:** Rectangular Catalan Algebraic Combinatorics

Speaker | François Bergeron |

Affiliation | LACIM - Université du Québec à Montréal |

Room | MC 5501 |

**Abstract:**

The enumeration of Dyck-like lattice paths in a m x n rectangle has a long and fruitful history culminating in Bizley-Grossman’s formula (1954). We will discuss how it is natural to extend this formula to weighted enumeration, with parameters accounting for such statistics as area; and to consider parking-function analogs.

Friday, March 6, 2020 — 3:30 PM EST

**Title:** Binary Submatroids

Speaker: | Peter Nelson |

Affiliation: | University of Waterloo |

Room: | MC 5501 |

**Abstract:**

A binary matroid can be thought of as a set of nonzero binary vectors.

Friday, March 6, 2020 — 1:00 PM EST

**Title:** Recognizing slack matrices

Speaker: | Matt Gerstbrein |

Affiliation: | University of Waterloo |

Room: | MC 5417 |

**Abstract:**

This week, we will be discussing the topic of slack matrices. Slack matrices arise in the context of lifts of polytopes, where, given a polytope P, we can characterize the existence of a lift of P of a given size in terms of properties of an associated slack matrix.

Thursday, March 5, 2020 — 2:30 PM EST

**Title: **Combinatorial Hall algebras

Speaker: | Matt Szczesny |

Affiliation: | Boston University |

Room: | MC 5417 |

**Abstract:**

The Hall algebra of a finitary category is an associative (and sometimes Hopf) algebra whose structure constants count the number of extensions between objects.

Thursday, March 5, 2020 — 1:00 PM EST

**Title:** Strongly cospectral vertices in cubelike graphs

Speaker: | Soffia Arnadottir |

Affiliation: | University of Waterloo |

Room: | MC 5417 |

**Abstract:**

A cubelike graph is a Cayley graph of the elementary abelian 2-group. Two vertices in a graph are strongly copsectral if they are cospectral and parallel.

Wednesday, March 4, 2020 — 2:00 PM EST

**Title:** Vertex-minors and sparsity

Speaker: | Rose McCarty |

Affiliation: | University of Waterloo |

Room: | MC 5479 |

**Abstract:**

We discuss an ongoing project with Jim Geelen and Paul Wollan to describe the structure of graph classes excluding a vertex-minor.

Tuesday, March 3, 2020 — 1:15 PM EST

**Title:** Introduction to Monotone Operators

Speaker: | Naomi Graham |

Affiliation: | University of Waterloo |

Room: | MC 5501 |

**Abstract: **

This talk will be an entry level introduction to the theory of monotone operators as they are presented in Bauschke and Combette’s *Convex Analysis and Monotone Operator Theory in Hilbert Spaces.*

Friday, February 28, 2020 — 3:30 PM EST

**Title:** Parallel strategies for SIDH: towards computing SIDH twice as fast

Speaker: | Francisco Rodríguez-Henríquez |

Affiliation: | CINVESTAV-IPN |

Room: | MC 5501 |

**Abstrtact:**

Over the last ten years, there has been an intense research effort to find hard mathematical problems that would be presumably hard to solve by a quantum attacker and at the same time could be used to build reasonably efficient public-key cryptoschemes.

Friday, February 28, 2020 — 1:00 PM EST

**Title:** An Introduction to the Circuits of Polyhedra, The Circuit Diameter, and Their Applications

Speaker: | Sean Kafer |

Affiliation: | University of Waterloo |

Room: | MC 5417 |

**Abstract:**

The combinatorial diameter of a polyhedron P is the maximum value of a shortest path between two vertices of P, where the path moves along edges of P. Its study is motivated largely by its implications on the running time of the Simplex algorithm.

Thursday, February 27, 2020 — 4:00 PM EST

**Title:** Excluding an asymmetric group labelled graph

Speaker: | Farbod Yadegarian |

Affiliation: | University of Waterloo |

Room: | MC 5479 |

**Abstract:**

There are several models of group labelled graphs. In the simpler, undirected model, for an abelian group Γ, every edge e receives a label γ(e) in Γ.

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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 Indigenous Initiatives Office.