3 papers
math.DG2024
Minimal Submanifolds and Waists of Locally Symmetric Spaces
Mikolaj Fraczyk, Ben Lowe
We study the higher expansion properties of locally symmetric spaces, with a particular focus on octonionic hyperbolic manifolds. We show that codimension two minimal submanifolds…
math.PR2024
Spectral non-concentration near the top for unimodular random graphs
Mikolaj Fraczyk, Ben Hayes, Madhu Sudan +1
In recent work on equiangular lines, Jiang, Tidor, Yuan, Zhang, and Zhao showed that a connected bounded degree graph has sublinear second eigenvalue multiplicity. More generally t…
math.GT2022
Bottom of the Length Spectrum of Arithmetic Orbifolds
Mikolaj Fraczyk, Lam L. Pham
We prove that cocompact arithmetic lattices in a simple Lie group are uniformly discrete if and only if the Salem numbers are uniformly bounded away from . We also prove an anal…