Events by month

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}.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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).