COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Differential Geometry and Topology Seminar > Integrals over unitary groups, maps on surfaces, and Euler characteristics

## Integrals over unitary groups, maps on surfaces, and Euler characteristicsAdd to your list(s) Download to your calendar using vCal - Michael Magee, Durham
- Wednesday 31 January 2018, 16:00-17:00
- MR13.
If you have a question about this talk, please contact Ivan Smith. For a positive integer r, fix a word w in the free group on r generators. Let G be any group. The word w gives a `word map’ from G^r to G: we simply replace the generators in w by the corresponding elements of G. We again call this map w. The push forward of Haar measure under w is called the w-measure on G. We are interested in the case G = U(n), the compact Lie group of n-dimensional unitary matrices. A motivating question is: to what extent do the w-measures on U(n) determine algebraic properties of the word w? For example, we have proved that one can detect the ‘stable commutator length’ of w from the w-measures on U(n). Our main tool is a formula for the Fourier coefficients of w-measures; the coefficients are rational functions of the dimension n, for reasons coming from representation theory. We can now explain all the Laurent coefficients of these rational functions in terms of Euler characteristics of certain mapping class groups. I’ll explain all this in my talk, which should be broadly accessible and of general interest. Time permitting, I’ll also invite the audience to consider some remaining open questions. This is joint work with Doron Puder (Tel Aviv University). This talk is part of the Differential Geometry and Topology Seminar series. ## This talk is included in these lists:- All CMS events
- All Talks (aka the CURE list)
- CMS Events
- DPMMS Lists
- DPMMS Pure Maths Seminar
- DPMMS info aggregator
- DPMMS lists
- Differential Geometry and Topology Seminar
- MR13
- School of Physical Sciences
Note that ex-directory lists are not shown. |
## Other listsWorkshop "Formalism and Functionalism in Negation" Leica Scientific Forum talks## Other talksMaking Smart Decisions in Systems Design: How to Engineer Decisions in a Connected World? Primary liver tumor organoids: a new pre-clinical model for drug sensitivity analysis Cognition in the wild: foraging hummingbirds and building nests Computational Neuroscience Journal Club Flow Cytometry TODAY Foster Talk - Localised RNA-based mechanisms underlie neuronal wiring |