#### Contact Info

Combinatorics & Optimization

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext 33038

PDF files require Adobe Acrobat Reader.

Monday, October 31, 2022 — 11:30 PM EDT

**Title**: Equiangular lines and algebraic number theory

Speaker: | Ingemar Bengtsson |

Affiliation: | Stockholm University |

Location: | contact Sabrina Lato for Zoom link |

**Abstract**: It is believed that SICs, that is maximal equiangular tight frames, exist in all complex vector spaces. To construct them we use the Weyl-Heisenberg groups, and hence the cyclotomic numbers (roots of unity).

Monday, October 31, 2022 — 3:00 PM EDT

**Title**: Cliques in dense matroids

Speaker: | Fernanda Rivera |

Affiliation: | University of Waterloo |

Location: | MC 6029 |

**Abstract**: We will give a singly exponential bound on the number of points a $U_{2,q+2}$-minor-free matroid can have without containing $M(K_{q+2})$ as a minor.

Friday, October 28, 2022 — 3:30 PM EDT

**Title:** The ADMM: Past, Present, and Future

Speaker: | Jonathan Eckstein |

Affiliation: | Rutgers University |

Location: | MC 5501 or contact Melissa Cambrdige for Zoom link |

**Abstract:** Over the past 15 years, the alternating direction method of multipliers (ADMM) has become a standard optimization method. This talk will cover the origins of the ADMM, its subsequent development, and what to expect in the future.

Friday, October 28, 2022 — 12:00 PM EDT

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.

Friday, October 28, 2022 — 9:00 AM to Saturday, October 29, 2022 — 5:00 PM EDT

Optimization is an important area of applied mathematics that bridges mathematical theory with applications in diverse fields. This Twenty Fourth Annual Midwest Optimization Meeting provides opportunities for researchers in this region with different backgrounds to come together to share their research and teaching experiences, forge collaborations with colleagues from different institutions, and to expose students to applications of mathematical theory. This workshop will focus on bringing together several of the diverse communities working on large scale optimization models that arise from variational problems.

Registration information, schedule, and abstracts click here

Thursday, October 27, 2022 — 1:00 PM EDT

Title: A raising operator formula for Macdonald polynomials

Speaker: | Anna Pun |

Affiliation: | CUNY- Baruch College |

Location: | MC 5479 or contact Olya Mandelshtam for Zoom |

Abstract: In this talk, I will give a brief introduction on Catalanimal, a tool that helps us to prove the shuffle theorem under any line, the extended delta conjecture and the Loehr- Warrington conjecture. I will then focus on its variant "Macanimal" which gives us an explicit raising operator formula for the modified Macdonald polynomials. Our method just as easily yields a formula for an infinite series of $GL_l$ characters which truncates to the modified Macdonald polynomials.

Monday, October 24, 2022 — 11:30 AM EDT

**Title:** Hadamard’s Maximal Determinant Problem and Generalisations

Speaker: | Guillermo Nunez Ponasso |

Affiliation: | Worcester Polytechnic Institute |

Location: | Please contact Sabrina Lato for Zoom link |

**Abstract:** Any matrix $M$ of order $n$ with entries taken from the complex unit disk satisfies Hadamard’s determinantal inequality $|\det M|\leq n^{n/2}$. Matrices meeting this bound with equality have pairwise orthogonal rows and columns. Such matrices are known as Hadamard matrices, and character tables of finite abelian groups give examples at every order.

Friday, October 21, 2022 — 12:00 PM EDT

Title: The Probabilistic Set-Covering Problem

Speaker: | Noah Weninger |

Affiliation: | University of Waterloo |

Location: | MC 6026 or contact Rian Neogi for Zoom link |

Abstract: In the classical set-covering problem, we have a set of items and a set S of subsets of the items. The objective is to find a min-cost subset C of S which covers every item, i.e., where every item is contained in at least one of the subsets in C. The probabilistic set-covering problem (PSC) generalizes this to a stochastic setting where the objective is to find a min-cost covering which covers a random subset of the items with probability at least p. We will discuss some structural properties of this problem which lead to a branch-and-bound algorithm for solving it.

Thursday, October 20, 2022 — 1:00 PM EDT

**Title:** Quasisymmetric functions, descent sets, immaculate tableaux, and 0-Hecke modules

Speaker: | Shelia Sundaram |

Affiliation: | |

Location: | MC 5479 or contact Olya Mandelshtam for Zoom link |

**Abstract: **

The first half of this talk will be expository and devoted to a discussion of (quasi)symmetric functions and tableaux.

We define new families of quasisymmetric functions, in particular the new basis of row-strict dual immaculate functions, with an associated cyclic, indecomposable 0-Hecke algebra module. Our row-strict immaculate functions are related to the dual immaculate functions of Berg-Bergeron-Saliola-Serrano-Zabrocki (2014-15) by the involution \psi on the ring Qsym of quasisymmetric functions. We uncover the remarkable properties of the immaculate Hecke poset induced by the 0-Hecke action on standard immaculate tableaux, revealing other submodules and quotient modules, often cyclic and indecomposable.

Monday, October 17, 2022 — 11:30 AM EDT

**Title:** An introduction to discrete quantum walks

Speaker: | Harmony Zhan |

Affiliation: | Simon Fraser University |

Location: | please contact Sabrina Lato for Zoom link |

**Abstract:** A discrete quantum walk is determined by a unitary matrix representation of a graph. In this talk, I will give an overview of different quantum walks, and show how the spectral information of the unitary matrix representation links properties of the walks to properties of the graphs. Part of this talk will be based on the book, Discrete Quantum Walks on Graphs and Digraphs, by Chris and me.

Friday, October 14, 2022 — 3:30 PM EDT

**Title:** Approximate Counting via Lorentzian Polynomials and Entropy Optimization

Speaker: | Jonathan Leake |

Affiliation: | University of Waterloo |

Location: | MC 5501 or contact Melissa Cambridge for Zoom link |

**Abstract:** Over the past 20 years, Lorentzian and real stable polynomials have been used to derive a number of combinatorial theorems, from log-concavity statements to counting and volume bounds. One significant thread of this research lies in the utilization of entropy optimization methods to approximately count certain combinatorial objects, such as the matchings of a bipartite graph, the intersection of the sets of bases of two matroids, and the integer points of various polytopes in general. In this talk, we will discuss various results one can achieve using such methods.

Friday, October 7, 2022 — 3:30 PM EDT

**Title:** Bipartite Matching in Almost-Linear Time and More

Speaker: | Yang Peng |

Affiliation: | University of Waterloo |

Location: | MC 5501, please contact Amanda Lutz for Zoom link |

**Abstract:** This talk will present an algorithm that computes maximum bipartite matchings in m^{1 + o(1)} time, and discuss its connections with optimization, graph algorithms, and data structures.

Friday, October 7, 2022 — 12:00 PM EDT

**Title:** On the Adaptivity Gap of Stochastic Orienteering

Speaker: | Paul Lawrence |

Affiliation: | University of Waterloo |

Location: | MC 6029 or contact Rian Neogi for the Zoom link |

**Abstract: **This talk highlights the *stochastic orienteering* problem, in which we are given a budget B and a graph G=(V,E) with edge distances *d(u,v) *and a starting vertex *x.* Each vertex *v* represents a job with a deterministic reward and a random processing time, drawn from a known distribution.

Thursday, October 6, 2022 — 1:00 PM EDT

Title: Lineup polytopes and applications in quantum physics

Speaker: | Jean-Philippe Labbé |

Affiliation: | Université du Québec |

Location: | MC 5479 contact Olya Mandelshtam for Zoom link |

Abstract: To put it simply, Pauli's exclusion principle is the reason why we can't walk through walls without getting hurt. Pauli won the Nobel Prize in Physics in 1945 for the formulation of this principle. A few years later, this principle received a geometrical formulation that is still overlooked today. This formulation uses the eigenvalues of certain matrices (which represent a system of elementary particles, for example electrons). These eigenvalues form a symmetric geometric object obtained by cutting a hypercube: it is a hypersimplex.

Monday, October 3, 2022 — 11:30 AM EDT

Title: Jack Derangements

Speaker: | Nathan Lindzey |

Affiliation: | Technion |

Location: | Contact Sabrina Lato for Zoom link |

Abstract: For each integer partition $\lambda \vdash n$ we give a simple combinatorial formula for the sum of the Jack character $\theta^\lambda_\alpha$ over the integer partitions of $n$ with no singleton parts. For $\alpha = 1,2$ this gives closed forms for the eigenvalues of the permutation and perfect matching derangement graphs, resolving an open question in algebraic graph theory. Our proofs center around a Jack analogue of a hook product related to Cayley's $\Omega$--process in classical invariant theory, which we call \emph{the principal lower hook product}.

Combinatorics & Optimization

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext 33038

PDF files require Adobe Acrobat Reader.

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

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.