Abstract
For a scheme one has a notion of cohomological excess. The speaker first defines and discusses this notion and then he states the main result which says that the universal curve of genus g > 0 has cohomological excess at most g-1. The speaker shows that this is an algebro-geometric strengthening of Harer’s theorems on the virtual cohomological dimension of the mapping class group and implies a theorem of Diaz on the maximal dimension of a complete subvariety of a moduli space of curves. He also discusses some ingredients of the proof.
About the speaker
Prof Eduard Looijenga received his PhD from the University of Amsterdam in 1974. He served as a Professor at the University of Nijmegen from 1975 to 1987, and at the University of Amsterdam from 1987 to 1990. He was a Visiting Professor at the University of Michigan and the University of Utah. He has been a Professor at Utrecht University since 1991.
Prof Looijenga's research started in singularity theory, but migrated via Torelli problems to locally symmetric varieties, then to mapping class groups and moduli spaces of curves, while his recent work is concerned with automorphic forms with poles along Heegner divisors. One of his major works is a solution of the Zucker conjecture concerning identification of the L2 cohomology of an arithmetic Hermitian locally symmetric space and the intersection cohomology of the Baily-Borel compactification of the space.
Prof Looijenga was a Distinguished International Lecturer at the International Congress of Chinese Mathematicians in 2010. He was also an invited speaker at the International Congress of Mathematicians in 1978 and at the First European Congress of Mathematicians in 1992. He was editor of Journal of Computational Mathematics, and is currently editor of Michigan Mathematics Journal and the Journal of the European Mathematics Society.
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Free and open to the public. Seating is on a first-come first-served basis.
Institute for Advanced Study
Enquiries ias@ust.hk / 2358 5912
http://ias.ust.hk
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