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