Events Calendar - Viewing Details

Events Calendar - Viewing Details

THURSDAY Dec. 07 : FIFTY-SEVENTH WILLIAM J. SPENCER LECTURE
Title: Homological Stability and Beyond
Søren Galatius
Stanford University and University of Copenhagen

Abstract: The most important algebraic topological invariant of a space \(X\) is perhaps its homology groups \(H_i(X)\). Much effort has been devoted to its calculation in the case \(X = \mathcal{M}_g\), the moduli space of Riemann surfaces. In 1985, John Harer proved that these homology groups are independent of genus as long as \(g \gg i\). This phenomenon, known as homological stability, is the basis of many future developments, eventually leading to an essentially complete understanding of \(H_i(\mathcal{M}_g)\) when \(g\) is large compared to \(i\). Outside this range of degrees, known as the stable range, we know very little about the homology of \(\mathcal{M}_g\). I will explain joint work with A. Kupers and O. Randal-Williams on a "metastable range" in which a secondary homological stability phenomenon happens. The method is based on so-called Quillen homology, or derived indecomposables, and applies to other situations in which homological stability results have been established classically, such as general linear groups of fields.
Time and Place: 02:30 PM Burt 114