Events

Title: On the complexity of quantum partition functions

Abstract: Quantum complexity theory has been intertwined with the study of quantum many-body systems ever since Kitaev's insight that computing their ground energies is an intractable quantum constraint satisfaction problem that is complete for a quantum generalization of NP.

Title: Approximation algorithms for dense quantum Hamiltonians using convex relaxations

Abstract: Computing ground-state energy and partition functions for quantum Hamiltonian systems are problems of broad applicability in physics. These are also natural generalizations of well-studied classical computational tasks such as maximum constraint satisfaction and computing partition functions of Ising models. In this talk, I will present new classical approximation algorithms for these problems in the case of dense quantum Hamiltonians.

Title: Online Unrelated-Machine Load Balancing and Generalized Flow with Recourse

Abstract: I will present the online algorithms for unrelated-machine load balancing problem with recourse.  First, we shall present a (2+\epsilon)-competitive algorithm for the problem with O_\epsilon(\log n) amortized recourse per job.

Title: Research in Applications

Abstract: In this talk I will present my personal experiences in doing research involving applications. I will go over some of my work, presenting some of the key aspects that are involved, and trying to take stock of a few lessons learned.

Title: Error bounds for conic feasibility problems: case studies on the exponential cone

Abstract: Conic feasibility problems naturally arise from linear conic programming problems. An understanding of error bounds for these problems is instrumental in the design of termination criteria for conic solvers and the study of convergence rate of algorithms.

Title: An invitation to monotone operators and their applications in optimization

Abstract: In this talk, I give an overview of the theory of monotone operators and its connection to optimization algorithms. This talk is a good introduction to how abstract theoretical results serve as bases for successful algorithms in practice.  

Title: The rank of sparse symmetric matrices over arbitrary fields

Abstract: Consider a sequence of sparse Erdös-Rényi random graphs (G_{n,d/n})_n on n vertices with edge probability d/n. Moreover, we equip the edges of G_{n,d/n} with prescribed non-zero edge weights chosen from an arbitrary field F.

Title: Restricted Intersections and the Sunflower Problem

Abstract: A sunflower with $r$ petals is a collection of $r$ sets over a ground set $X$ such that every element in $X$ is in no set, every set, or exactly one set. Erdos and Rado showed that a family of sets of size $n$ contains a sunflower if there are more than $n!(r-1)^n$ sets in the family. Alweiss et al. and subsequently Rao improved this bound to $(O(r \log(rn))^n$.

Title: Ramsey degrees, big and small

Abstract: Many of the seminal results in finite Ramsey theory can be phrased by saying that a certain class of finite structures has the Ramsey property, such as the ordinary finite Ramsey theorem (the class of finite linear orders), the dual Ramsey theorem (the class of finite lex-ordered Boolean algebras), the Graham-Leeb-Rothschild theorem (the class of lex-ordered, finite-dimensional vector spaces over a fixed finite field), and the Nesetril-Rodl theorem (the class of finite ordered triangle-free graphs, among many others).

Title: Douglas–Rachford Algorithm for Control- and State-constrained Optimal Control Problems

Abstract: The Douglas - Rachford algorithm has been applied to many optimization problems due to its simplicity and efficiency but the application of this algorithm to optimal control is less common. In this talk we utilize this method to solve state- and control-constrained linear-quadratic optimal control problems.