Department of Mathematics and Computer Science

At this research seminar, researchers and students from FNUG present updates from their current research. Beforehand, there will be a potluck lunch.

Speaker: Elise Lepage (​Columbia University).Abstract: Quantum groups and their representations admit categorifications, in which vector spaces and linear maps are replaced by categories and functors. I will describe a construction of these categorifications using Fukaya-Seidel categories of Coulomb branches. This construction realizes categorifications of irreducible representations, Verma modules, and arbitrary tensor products of these representations. A key feature of this construction is a differential relating categorified Verma modules to categorified irreducible representations. I will show how this differential arises geometrically.

Speaker: ​Guglielmo Lockhart (University of Bonn).​Abstract: General principles suggest that the spectrum of excitations of quantum gravity theories includes not just pointlike particles, but also higher-dimensional membranes. In this talk I will focus on a specific class of one-dimensional membranes, the faithful strings, whose properties can be described using the language of vertex operator algebras. I will discuss how this mathematical structure encodes symmetries of quantum gravity theories, and makes it possible to determine refined information like gauge group topology. Moreover, I will show that modular invariance of the faithful string torus partition function is a powerful tool to detect inconsistencies in a candidate quantum gravity theory, or conversely to identify apparently consistent quantum gravities and study their properties. This provides an exciting opportunity to study exotic quantum gravity models that do not admit any known weakly coupled realization within string theory, in supersymmetric as well as non-supersymmetric settings.

Meet the critically acclaimed British author Zadie Smith at SDU on Monday, October 5, for a discussion about her writing and a reading from selected works.

The Wilder Garden has soon been part of SDU for a year, and we’d like to mark the occasion with you.

FNUG and NAFA invite to a NiSE Webinar

Speaker: Ben Brown (​IBM).Abstract: TBA

Speaker: Ben Brown (​IBM).Abstract:In seminal work Alexei Kitaev proposed topological quantum computing, whereby logic gates of a quantum computer are conducted by creating, braiding and fusing anyonic particles on a two-dimensional plane. Furthermore, he showed the proposal is inherently robust to local perturbations when anyons are created as quasiparticle excitations of a topologically ordered lattice model prepared at zero temperature. Over the decades following this proposal there have been considerable technological developments towards the construction of a fault-tolerant quantum computer. Rather than maintaining some target ground state at zero temperature, a modern approach is to actively correct the errors a target state experiences, where we use noisy quantum circuit elements to identify and subsequently correct for deviations from the ideal state. We present an error-correction scheme that enables us to carry out robust universal quantum computation by braiding anyons. We show that our scheme can be carried out on a suitably large device with an arbitrarily small failure rate assuming circuit elements are below some threshold level of local noise. The error-corrected scheme we have developed therefore enables us to carry out fault-tolerant topological quantum computation using modern quantum hardware that is now under development.

Poster Session and presentation

TBA