REMINDER - MATHS Seminars this week at ICTP

[ICTP Math Section]

MATH EVENTS THIS WEEK AT ICTP


    _Today, Tuesday 5 December_

*at 14:00
in the ***Budinich Lecture Hall** (ICTP Leonardo da Vinci Building)

Second lecture of the _MINI-COURSE on __Quantum Black Holes for 
Mathematicians_

By Atish Dabholkar (ICTP, HECAP)

Description of the course:  Study of black holes in string theory has 
revealed a beautiful and precise connection between the physics of 
quantum black holes and topics in number theory and geometry. The aim of 
these lectures is to outline these connections through examples starting 
with basic concepts and motivations from physics.

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    **_Tomorrow, Wednesday 6 December _

*at 14:00 *
**in the Luigi Stasi Seminar Room **(ICTP Leonardo da Vinci Building, 
First floor)

_SEMINAR
_
by Pavel Putrov (IAS, USA)

Title:
Towards a categorification of WRT invariant of 3-manifolds Abstract: In 
my talk I will conjecture existence of certain new homological 
invariants of closed 3-manifolds. The invariants provide a 
categorification of the analytically continued Witten-Reshetikhin-Turaev 
(WRT) invariant, have some similarities with Heegaard/monopole Floer 
homology and generalize Khovanov homology of knots to compact 
3-manifolds. Physically such invariants can be defined as Hilbert spaces 
of M-theory in certain backgrounds. I will describe mathematical 
properties of such invariants, and how to calculate them for some 
specific types of 3-manifolds. The talk is mainly based on a joint work 
with S. Gukov, D. Pei and C. Vafa.




    _On Thursday 7 December_

*at 14:00*
*in the ***Budinich Lecture Hall** (ICTP Leonardo da Vinci Building)

First lecture of the MINI-COURSE 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.