Events

Title: Quantum Algorithms and Mutually Unbiased Bases

Abstract: Mutually unbiased bases are fundamental to quantum information theory, showing up in quantum key distribution, quantum error correction, and quantum entanglement measures. They likewise might be familiar to algebraic graph theorists, thanks to their connection to equiangular lines and association schemes.

Title: Sets that Support a Joint Distribution

Abstract: Given a closed set on the plane and two probability distributions on the real line, when are there random variables with the given distributions whose joint distribution is supported by the given set?

Title: A brief introduction to lattice-based cryptography

Abstract: A brief introduction to lattice-based cryptography, one of the leading candidates for building quantum-resistant cryptosystems.

Title: Lorentzian polynomials

Abstract: Lorentzian polynomials on cones are intimately connected to Hodge theory, matroid theory and the geometry of zeros of polynomials.

Title: Breaking the Supersingular Isogeny Diffie-Hellman protocol

Abstract: Finding an explicit isogeny between two given isogenous elliptic curves over a finite field is considered a hard problem, even for quantum computers.

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: 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: 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: 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: 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).