Events - October 2022

Title: The ADMM:  Past, Present, and Future

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.

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: Hadamard’s Maximal Determinant Problem and Generalisations

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

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: Approximate Counting via Lorentzian Polynomials and Entropy Optimization

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: On the Adaptivity Gap of Stochastic Orienteering

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.