BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Memento EPFL//
BEGIN:VEVENT
SUMMARY:Quantum differential operators\, and the torus T^2
DTSTART:20131104T151500
DTEND:20131104T170000
DTSTAMP:20260406T102129Z
UID:af7a01a9fde1f01fcab2c5409d155c4cc70e9325a0b9a097f27c6ce9
CATEGORIES:Conferences - Seminars
DESCRIPTION:David Jordan (Edinburgh)\nThe algebra Dq(G) is a q-deformation
  of the algebra D(G) of differential operators on a semi-simple algebraic 
 group. In this talk\, I will explain an intimate relationship between Dq(G
 ) and the torus T^2: namely\, Dq(G) carries an action by algebra automorph
 isms of the torus mapping class group SL2(Z)\, and also yields representat
 ions of the torus braid group extending the well-known action of the plana
 r braid group on tensor powers of quantum group representations. Finally\,
  the so-called Hamiltonian reduction of Dq(G) quantizes the moduli space L
 oc_G(T^2) of G-local systems on T^2\, or equivalently\, homomorphisms π_1
 (T^2)→G\,and this observation allows us to generalize the construction o
 f D_q(G) to quantize Loc_G(Σ_g\,r)\, for an arbitrary surface with genus 
 g and r punctures.\nTime permitting\, I will outline work in progress with
  David Ben-Zvi and Adrien Brochier putting all of the above into the conte
 xt of topological field theories.
LOCATION:MA A110 http://plan.epfl.ch/?lang=fr&room=MA+110
STATUS:CONFIRMED
END:VEVENT
END:VCALENDAR