REMINDER: Two Special Lectures "From knots to number theory" - Tuesday 26 October and Friday 29 October, at 16:30 (Don ZAGIER)

[ICTP Math Section]

the Institute of the Mathematical Sciences of the Americas (IMSA)

Two Special Lectures (Zoom/Presence Meeting)


1) Special Lecture "From knots to number theory" I

Starts 26 Oct 2021 16:30
Ends 26 Oct 2021 18:00
Central European Time

/and/

2) Special Lecture "From knots to number theory" II

Starts 29 Oct 2021 16:30
Ends 29 Oct 2021 18:00
Central European Time
_
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*Don Zagier* (ICTP Ramanujan Chair) will be giving two lectures, at 
4:30p.m. on Tuesday 26 and Friday 29, October 2021, for the Institute of 
the Mathematical Sciences of the Americas (IMSA). The lectures will be 
given in person in the Budinich Lecture Hall, and streamed to Miami. All 
who are interested are warmly invited and even encouraged to attend in 
person, since it is much nicer to give a lecture with a physical audience.

*Abstract:* During the course of the last few years a number of 
startling connections between quantum invariants of knots and 
3-manifolds and high-level number theory have emerged. Already the 
rigidity theorems of 3-dimensional hyperbolic topology, which have been 
known for many years, had a quite non-trivial arithmetic content, with 
the volume of every hyperbolic 3-manifold being linked via the 
dilogarithm to the so-called Bloch group and algebraic K-theory, and 
another connection comes from the Kashaev invariant, which is linked via 
his famous conjecture to the hyperbolic volume but also belongs to the 
so-called Habiro ring, which is a beautiful number-theoretical object 
that is not yet well known to number theorists. The more recent 
developments that I will describe concern even deeper links to algebraic 
number theory (construction of non-trivial units) and algebraic 
K-theory, to a generalization of the classical Habiro ring to Habiro 
rings associated to arbitraryy algebraic number fields, and above all to 
surprising "quantum modularity" properties of the Kashaev invariant and 
its generalizations leading to a new type of object in the theory of 
modular forms. All of the work that will be reported on is joint with 
Stavros Garoufalidis, and some of it also with Rinat Kashaev and with 
Peter Scholze. The lectures are intended for a general mathematical 
audience and do not require any prior knowledge of knot theory, 
K-theory, modular forms theory, or any other theory.

_/*Light refreshments will be served after the 1st lecture, on Tuesday 
26 October, at 18:00, Terrace Level of the ICTP Leonardo da Vinci 
Building */_

All are most welcome to attend.

http://indico.ictp.it/event/9735/

http://indico.ictp.it/event/9736/

-- 
Koutou Mabilo
ICTP Mathematics Group
Leonardo Da Vinci Building
Strada Costiera no. 11
34151 Trieste, Italy
Tel. no.: +39-040-2240455

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