Contact Info
Combinatorics & Optimization
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 5198884567, ext 33038
PDF files require Adobe Acrobat Reader.
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Title: Chromatic structure in locally sparse graphs
Speaker: Ross Kang Affiliation: Radboud University Nijmegen Zoom: Please email Emma WatsonAbstract:
Efforts to understand the structure of trianglefree 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 InstituteAbstract:
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 InstituteAbstract:
The success of operator splitting techniques for convex optimization has led to an explosion of methods for solving largescale 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.
Title: On solving bilevel programming problems
Speaker: Jane Ye Affiliation: University of Victoria Zoom: Please email Emma WatsonAbstract:
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 twolevel 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.
Title: Tails and Chains
Speaker: Chris Godsil Affiliation: University of Waterloo Zoom: Contact Soffia ArnadottirAbstract:
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 01matrix with D_{i,i}=1 if i is in C.
Title: Approximation Algorithms for Matchings in Big Graphs
Speaker: Alex Pothen Affiliation: Purdue University Zoom: Please email Emma WatsonAbstract:
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.
Title: Spectral Properties of the exponential distance matrix
Speaker: Kate Lorenzen Affiliation: Linfield University Zoom: Contact Soffia ArnadottirAbstract:
Given a graph $G$, the exponential distance matrix is defined entrywise 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.
Title: TightlySecure Digital Signatures
Speaker: Tibor Jager Affiliation: University of Wuppertal, Germany Zoom: Please email Emma WatsonAbstract:
This talk will cover two recent results on tightlysecure digital signature schemes from PKC 2021 and ASIACRYPT 2021.
The first part will consider a strong multiuser 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 ORproofs.
Title: Graph Continued Fractions
Speaker: Thomás Spier Affiliation: Matemática Pura e Aplicada (IMPA) Zoom: Contact Soffia ArnadottirAbstract:
This talk is about a connection between matching polynomials and continued fractions. For the matching polynomials: we prove a refinement of a theorem by Ku and Wong, which extends the classical GallaiEdmonds decomposition;
Title: Semidefinite Optimization Approaches for Reactive Optimal Power Flow Problems
Speaker: Miguel Anjos Affiliation: University of Edinburgh Zoom: Register through The Fields InstituteAbstract:
The Reactive Optimal Power Flow (ROPF) problem consists in computing an optimal power generation dispatch for an alternating current transmission network that respects power flow equations and operational constraints. Some means of voltage control are modelled in ROPF such as the possible activation of shunts, and these controls are modelled using discrete variables. The ROPF problem belongs to the class of nonconvex MINLPs, which are NPhard problems. We consider semidefinite optimization approaches for solving ROPF problems and their integration into a branchandbound algorithm.
Title: Structured (In)Feasibility: Nonmonotone Operator Splitting in Nonlinear Spaces
Speaker: Bissan Ghaddar Affiliation: Western University Zoom: Register through The Fields InstituteAbstract:
Several challenging optimization problems in power networks involve operational decisions, nonlinear models of the underlying physics described by the network as well as uncertainty in the system parameters. However, these networks exhibit a nice structure. This talk provides an overview of approaches that combine recent advances in robust optimization and conic relaxations of polynomial optimization problems along with exploiting the structure of the underlying problem. These approaches are demonstrated on applications arising in power networks.
Title: Forcing Quasirandomness in Permutations
Speaker: John Noel Affiliation: University of Victoria Zoom: Contact Steve MelczerAbstract:
A striking result in graph theory is that the property of a graph being quasirandom (i.e. resembling a random graph) is characterized by the number of edges and the number of 4cycles being close to the expected number in a random graph. Král’ and Pikhurko (2013) proved an analogous result for permutations; i.e. that quasirandom permutations are characterized by the densities of all permutations of length 4.
Combinatorics & Optimization
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 5198884567, ext 33038
PDF files require Adobe Acrobat Reader.
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.