MPLW Multiple Zeta Values, Recent Developments (2012)

About the Speaker :

Professor Joseph Osterle  is a number theorist at the University of Paris VI, where he has been a professor for well over two and half decades. He has made  a number of well-known contributions to number theory among other things  to the  formulation of the fundamental abc conjecture. He is also a widely acclaimed  expositor of mathematics in general and number theory in particular.

Abstract of Lectures:

Multiple zeta values satisfy various polynomial relations over the field of rational numbers, some of them already known to Euler and some others only discovered quite recently. Last year Francis Brown proved that they are all rational linear combinations of those for which the exponents $k_i$ belong to $\{2,3\}$; these latter ones are believed to be linearly independent over rational numbers. The lectures in the first two weeks are part of the Panorama lecture series meant for a general audience. In these two weeks, Professor Oesterlé will describe the history of the subject and state the main results.

The lectures in the later weeks will be an attempt to provide the relevant details of Brown's work. As we will see, Brown's method consists in constructing motivic analogues of the multiple zeta values for which he is able to prove the analogous results. This construction involves Hopf algebras, iterated integrals, unipotent group schemes, cohomology and periods, motivic versions of the fundamental group, mixed Tate motives. Describing these tools and giving the proofs will be the main task of the course.

List of Selected participants of Panorama Lectures

https://www.imsc.res.in/getting_imsc