# Overview

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### Nicolas Bergeron Aisenstadt Chair Lecture Series

#### Nicolas Bergeron: October 2020

Nicolas Bergeron will give a series of six conferences, the first of which will take place on October 16, 2020, as part of the Quebec Mathematical Sciences Colloquium. The following lectures will take place from 9:30 a.m. to 10:30 a.m. in the week of October 19 to 23, 2020 as part of the workshop: Arithmetic quotients of locally symmetric spaces and their cohomology.

**Topic discussed during the week of October 19-23: Sczech cocycles and hyperplane arrangements**

**Abstract:**

Many authors, among which Nori, Sczech, Solomon, Stevens, or more recently Beilinson-Kings-Levin and Charollois-Dasgupta-Greenberg, have constructed different, but related, linear groups cocycles that are usually referred to as « Eisenstein cocycles. » In these series of lectures I will explain a topological construction that is a common source for all these cocycles. One interesting feature of this construction is that starting from a purely topological class it leads to the algebraic world of meromorphic forms on hyperplane complements in n-fold products of either the (complex) additive group, the multiplicative group or a (family of) elliptic curve(s). We will see that eventually our construction reveals hidden relations between products of elementary (rational, trigonometric or elliptic) functions) governed by relations between classes in the homology of linear groups.

This is based on a work-in-progress with Pierre Charollois, Luis Garcia and Akshay Venkatesh.

**Biography :**

Nicolas Bergeron is a French mathematician. He works in the Département de Mathématiques et Applications at the École normale supérieure (ENS) in Paris, of which he is the current director. He obtained his doctorate at ENS Lyon in 2000 under the supervision of Jean-Pierre Otal with a thesis entitled Geodesic cycles in hyperbolic varieties. He did his postdoctoral studies in Zurich and Neuchâtel. In 2001, he became Research Fellow at the Université de Paris Sud, where he completed his accreditation in 2005 (On cohomology and the spectrum of locally symmetrical varieties) and in 2005 at the École normale supérieure de Paris. Several of his publications show an interest in the Oulipo: reference to Tentative d'épuisement d'un lieu parisien, by Georges Perec, article devoted to Jacques Roubaud.

**Prizes and awards:**

He won the CNRS Bronze Medal in 2007.

He became a junior member of the Institut universitaire de France in 2010.

**Areas of interest:**

His areas of interest are the geometry and topology of locally symmetrical spaces, arithmetic groups, their cohomology.