© | << < ? > >> |
Dror Bar-Natan:
Talks:

# Computation without Representation

###
Ohio State University Quantum Topology Seminar, January 29, 2019

**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.

**Handout:**
CWOR.html,
CWOR.pdf,
CWOR.png.

**Talk Video**
(in Toronto, November 2018).

**Links:**
Full
Ov
Za
Zip
kc
kiw
talks

**Sources:** pensieve.