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Wednesday, August 11, 2021 11:00 am - 11:00 am EDT (GMT -04:00)

Optimization: Theory, Algorithms, Applications Lecture Series

Title: HiGHS: Theory, software and Impact

Speaker: Julian Hall
Affiliation: University of Edinburgh
Zoom: Register through The Fields Institute

Abstract:

Since Dantzig formulated the simplex algorithm in 1947, the widespread need to solve linear optimization problems drove the development of algorithmic and computational techniques for decades, yielding several high performance commercial and open source software systems. This talk will focus on the Edinburgh-based work on solving large scale sparse linear programming problems that underpins the high performance open source linear optimization software, HiGHS, the challenges of developing such software, and the Impact that it has achieved.

Monday, August 16, 2021 11:30 am - 11:30 am EDT (GMT -04:00)

Algebraic Graph Theory Seminar - Lavanya Selvaganesh

Title: Spectral Properties of the eccentricity matrix for special classes of graphs

Speaker: Lavanya Selvaganesh
Affiliation: Indian Institute of Technology (BHU) Varanasi
Zoom Contact Soffia Arnadottir

Abstract:

Eccentricity matrix, another graph matrix, was originally proposed, as $D_{MAX}$ matrix, by Randi\'c in 2013 and redefined by Wang et al. in 2018 by using the concept of the eccentricities of vertices.

Friday, September 3, 2021 3:30 pm - 3:30 pm EDT (GMT -04:00)

Tutte Colloquium - Ross Kang

Title: Chromatic structure in locally sparse graphs

Speaker: Ross Kang
Affiliation: Radboud University Nijmegen
Zoom: Please email Emma Watson

Abstract:

Efforts to understand the structure of triangle-free graphs have long played a central role in the development of combinatorial mathematics. Classic results of Mantel (1907), Ramsey (1930), Blanche Descartes (1948) produce global structure from the local property of having no edges in any neighbourhood. Despite the scrutiny it has sustained over the decades, study of this topic, and its close relatives, continues to uncover surprisingly basic challenges, insights and connections. I will give a brief overview of the history as well as the focus of current/recent momentum.

Title: Factorization of completely positive matrices using iterative projected gradient steps

Speaker: Radu Ioan Bot
Affiliation: University of Vienna
Zoom: Register through The Fields Institute

Abstract:

We aim to factorize a completely positive matrix by using an optimization approach which consists in the minimization of a nonconvex smooth function over a convex and compact set. To solve this problem we propose a projected gradient algorithm with parameters that take into account the effects of relaxation and inertia. Both projection and gradient steps are simple in the sense that they have explicit formulas and do not require inner loops. We show that the sequence of generated iterates

Title: Structured (In)Feasibility: Nonmonotone Operator Splitting in Nonlinear Spaces

Speaker: Russell Luke
Affiliation: University of Goettingen
Zoom: Register through The Fields Institute

Abstract:

The success of operator splitting techniques for convex optimization has led to an explosion of methods for solving large-scale and nonconvex optimization problems via convex relaxation. This success is at the cost of overlooking direct approaches to operator splitting that embrace some of the more inconvenient aspects of many model problems, namely nonconvexity, nonsmoothness, and infeasibility.

Friday, September 10, 2021 3:30 pm - 3:30 pm EDT (GMT -04:00)

Tutte Colloquium - Jane Ye

Title: On solving bilevel programming problems

Speaker: Jane Ye
Affiliation: University of Victoria
Zoom: Please email Emma Watson

Abstract:

A bilevel programming problem is a sequence of two optimization problems where the constraint region of the upper level problem is determined implicitly by the solution set to the lower level problem. It can be used to model a two-level hierarchical system where the two decision makers have different objectives and make their decisions on different levels of hierarchy. Recently more and more applications including those in machine learning have been modelled as bilevel optimization problems. In this talk, I will report some recent developments in optimality conditions and numerical algorithms for solving this class of very difficult optimization problems.

Monday, September 13, 2021 11:30 am - 11:30 am EDT (GMT -04:00)

Algebraic Graph Theory Seminar - Chris Godsil

Title: Tails and Chains

Speaker: Chris Godsil
Affiliation: University of Waterloo
Zoom: Contact Soffia Arnadottir

Abstract:

Physicists are interested in "graphs with tails"; these are constructed by choosing a graph X and a subset C of its vertices, then attaching a path of length n to each vertex in C. We ask what is the spectrum of such graph? What happen if n increases? We will see that the answer reduces to questions about the matrix

\[ M(\zeta) := (\zeta_\zeta^{-1})I - A -\zeta D \]

where D is the diagonal 01-matrix with D_{i,i}=1 if i is in C.

Friday, September 17, 2021 3:30 pm - 3:30 pm EDT (GMT -04:00)

Tutte Colloquium - Alex Pothen

Title: Approximation Algorithms for Matchings in Big Graphs

Speaker: Alex Pothen
Affiliation: Purdue University
Zoom: Please email Emma Watson

Abstract:

Matchings in graphs are classical problems in combinatorial optimization and computer science, significant due to their theoretical importance and relevance to applications. Polynomial time algorithms for several variant matching problems with linear objective functions have been known for fifty years, with important contributions from Tutte, Edmonds, Cunningham, and Pulleyblank (all with Waterloo associations), and they are discussed in the textbook literature.

Monday, September 20, 2021 11:03 am - 11:03 am EDT (GMT -04:00)

Algebraic Graph Theory Seminar - Kate Lorenzen

Title: Spectral Properties of the exponential distance matrix

Speaker: Kate Lorenzen
Affiliation: Linfield University
Zoom: Contact Soffia Arnadottir

Abstract:

Given a graph $G$, the exponential distance matrix is defined entry-wise by letting the $(u,v)$-entry be $q^{dist(u,v)}$ where $dist(u,v)$ is the distance between the vertices $u$ and $v$ with the convention that if vertices are in different components, then $q^{dist(u,v)}=0$. We establish several properties of the characteristic polynomial (spectrum) for this matrix and the inertia of some graph families.

Friday, September 24, 2021 3:30 pm - 3:30 pm EDT (GMT -04:00)

Tutte Colloquium - Tibor Jager

Title: Tightly-Secure Digital Signatures

Speaker: Tibor Jager
Affiliation: University of Wuppertal, Germany
Zoom: Please email Emma Watson

Abstract:

This talk will cover two recent results on tightly-secure digital signature schemes from PKC 2021 and ASIACRYPT 2021.

The first part will consider a strong multi-user security definition for signatures with adaptive corruptions of secret keys, discuss its applications, and the technical challenges of constructing signatures with tight security in this setting. Then we will show a quite simple and efficient construction, based on sequential OR-proofs.