Quantum Algebra & Quantum Topology - Dror Bar-Natan Part I

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Quantum Algebra & Quantum Topology Seminar
January 29, 2019
1:45PM - 3:00PM
Location
Cockins Hall 240

Date Range
Add to Calendar 2019-01-29 13:45:00 2019-01-29 15:00:00 Quantum Algebra & Quantum Topology - Dror Bar-Natan Part I Title: Computation without Representation Speaker: Dror Bar-Natan (University of Toronto) Abstract: A major part of "quantum topology" (you don't have to know what's that) is the definition and computation of various knot invariants by carrying out computations in quantum groups (you don't have to know what are these). Traditionally these computations are carried out "in a representation", but this is very slow: one has to use tensor powers of these representations, and the dimensions of powers grow exponentially fast. In my talk I will describe a direct-participation method for carrying out these computations without having to choose a representation and explain why in many ways the results are better and faster. The two key points we use are a technique for composing infinite-order "perturbed Gaussian" differential operators, and the little-known fact that every semi-simple Lie algebra can be approximated by solvable Lie algebras, where computations are easier. This is joint work with Roland van der Veen and continues work by Rozansky and Overbay Note: This talk is continued from 3:00 - 5:00pm in Mathematics Build 105. Seminar URL: https://www.coreyjonesmath.com/qaqt-seminar-osu Cockins Hall 240 Department of Mathematics math@osu.edu America/New_York public
Description

Title: Computation without Representation

SpeakerDror Bar-Natan (University of Toronto)

Abstract: A major part of "quantum topology" (you don't have to know what's that) is the definition and computation of various knot invariants by carrying out computations in quantum groups (you don't have to know what are these). Traditionally these computations are carried out "in a representation", but this is very slow: one has to use tensor powers of these representations, and the dimensions of powers grow exponentially fast.

In my talk I will describe a direct-participation method for carrying out these computations without having to choose a representation and explain why in many ways the results are better and faster. The two key points we use are a technique for composing infinite-order "perturbed Gaussian" differential operators, and the little-known fact that every semi-simple Lie algebra can be approximated by solvable Lie algebras, where computations are easier.

This is joint work with Roland van der Veen and continues work by Rozansky and Overbay

Note: This talk is continued from 3:00 - 5:00pm in Mathematics Build 105.

Seminar URLhttps://www.coreyjonesmath.com/qaqt-seminar-osu

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