“A Complex Ball Quotient and the Monster”

We shall talk about an arithmetic lattice M in PU(13,1) acting on the the unit ball B in thirteen dimensional complex vector space. Let X be the space obtained by removing the hypersurfaces in B that have nontrivial stabilizer in M and then quotienting the rest by M. The fundamental group G of the ball quotient X is a complex hyperbolic analog of the braid group. We shall state a conjecture that relates this fundamental group G and the monster simple group and describe our results (joint with D. Allcock) towards this conjecture. The discrete group M is related to the Leech lattice and has generators and relations analogous to Weyl groups. Time permitting, we shall give a second example in PU(9,1) related to the Barnes-Wall lattice for which there is a similar story.

### Details

Algebraic Geometry SeminarTathagata Basak (Iowa State University)

May 25, 2018

4:30 PM - 5:30 PM

More information available at:

http://mathematics.stanford.edu/algebraic-geometry-seminar/

### Location

Math 383-N450 Serra Mall

Bldg. 380

Room 383-N

Stanford CA 94305