# Regulators, Mahler measures, and special values of L-functions

## February 16-20, 2015

**Organizers ** : Henri Darmon (McGill), Matilde Lalin (Montréal), Wadim Zudilin (Newcastle)

In *1979*, Deligne formulated a far-reaching body of conjectures relating special values of *L*-functions arising in arithmetic geometry (more precisely, pieces of the cohomology of algebraic variety cut out by correspondences, the so-called *motives* of Grothendieck) to associated *periods* — ostensibly transcendental quantities which encode the difference between natural rational structures on DeRham and Betti cohomology. These conjectures, which applied to integer points that are *critical* in the sense of Deligne, were later extended by Bloch and Beilinson to non-critical points (building on the earlier insights of Borel in the case of the Riemann zeta-function and Dirichlet *L*-functions) expressing these special values in terms of certain *regulators* on Higher Chow groups and *K*-groups that are naturally associated to the relevant motive. In the last decade, David Boyd discovered a number of tantalising and appealingly concrete identities relating Mahler Measures to similar special values of *L*-functions, which were then extended by a host of other mathematicians. One goal of this workshop will be to integrate these identities more solidly within the overarching but largely conjectural framework governing the behaviour of special values of *L*-functions.

**Tentative list of participants (not yet confirmed):** : Jennifer Balakrishnan (MIT), Marie-Josée Bertin (Paris), Amnon Besser (Negev), David Boyd (UBC), Francis Brown (Jussieu), Francois Brunault (Lyon), Jose Ignacio Burgos (Madrid), David Burns (Kings College London), , Pierre Charollois (Paris), Samit Dasgupta (Santa Cruz), Christophe Deninger (Munster), David Dummit (Vermont), Gerard Freixas (Jussieu), Jenny Fuselier (High Point University), Herbert Gangl (Jussieu), Matthew Greenberg (Calgary), Annette Huber (Freiburg), Guido Kings (Regensburg), Manfred Kolster (McMaster), James Lewis (Alberta), Vincent Maillot (Paris), Michelle Manes (University of Hawaii), Anton Mellit (Köln), Matthew Papanikolas (Texas), Cristian Popescu (UCSD), Fernando Rodriguez-Villegas (Trieste), Matthew Rogers (CRM), Detchat Samart (Texas), Jonathan Sands (Vermont), Ander Steele (Calgary), Akshay Venkatesh (Stanford), M. Vlasenko (Dublin), Don Bernard Zagier (Bonn & Collège de France)