FoCM 2014 conference

Workshop B6 - Random Matrices

December 17, 15:00 ~ 15:25 - Room B12

## Gap probabilities and applications to geometry and random topology

### Antonio Lerario

### Institut Camille Jordan, Lyon, France - anto.lerario@gmail.com

What is the volume of the set of singular symmetric matrices of norm one? What is the probability that a random plane misses this set? What is the expected "topology" of the intersection of random quadric hypersurfaces? In this talk I will combine classical techniques form algebraic topology ("spectral sequences") with ideas from Random Matrix Theory and show how these problems can be solved using a local analysis of the "gap probability" at zero (the probability that a random matrix has a gap in its spectrum close to zero).

Joint work with Erik Lundberg (Florida Atlantic University).