From MFO (Oberwolfach)

Andrew Ranicki has died. Ranicki was a topologist, with particular expertise in algebraic surgery.  Indeed, Ranicki had the unusual title of Professor of Algebraic Surgery at the University of Edinburgh.  (Andrew was a special case for almost everything.)  His two papers on surgery in Proc. London Math. Soc. [MR0560997 and MR0566491 (*)] were among his most cited papers.   He was also familiar to many for his work in $K$-theory, including his work as an editor for leading journals in the subject.  Continue reading →

Maryam Mirzakhani is known for her work on moduli spaces of Riemann surfaces.  Some of her most cited work looks at the moduli space of a genus $g$ Riemann surface with $n$ geodesic boundary components.  In two of her papers, she computes the volume of these moduli spaces, with respect to the Weil-Petersson metric (see below).  In another, she provides a means for counting the number of simple closed geodesics of length at most $L$. Mirzakhani is also known for her work on billiards (see the review of her paper with Eskin and Mohammadi below), a subject closely related to moduli space questions.  Teichmüller theory and the geometry of moduli spaces are famously deep subjects.  Making progress requires mastering large areas of analysis, dynamical systems, differential geometry, algebraic geometry, and topology.  I can only appreciate Mirzakhani’s work superficially, as I have not mastered those subjects.   Instead, some reviews of her work are reproduced below.   Continue reading →