ICTP Mini Course by Professor Don B. Zagier (IMP, Bonn and ICTP) - December 2017 - ICTP (Budinich Lecture Hall)

[ICTP Math Section]

M A T H E M A T I C S   S E M I N A R S  2017



Professor Don B. Zagier (MPI, Bonn/ICTP)


will give a mini-course (3 lectures) on

Knot invariants, units, K-theory and modular forms


Description of the course:
  I will present joint work with Frank Calegari and Stavros Garoufalidis 
in which elements of the Bloch group of a number field (a more 
elementary version of algebraic   K-theory that will be explained in 
detail in the lectures) produce units in cyclotomic extensions of this 
field.  The result was motivated by experimental discoveries relating to 
quantum invariants (specifically, Jones polynomials and the Kashaev 
invariant) of knots, and had an unexpected application to a proof of a 
well-known conjecture of Werner Nahm relating the modularity of certain 
q-hypergeometric series to the vanishing of a certain invariant in the 
Bloch group.


Lectures are scheduled as follows:


•	Thursday, 7 December, at 14:00

•	Tuesday, 12 December at 16:00

•	Thursday, 14 December at 16:00




VENUE:  Budinich Lecture Hall (ICTP Leonardo da Vinci Building)