Lior Silberman

Associate Professor

Research Classification

Mathematics

Research Interests

Metric geometry
Number theory
Automorphic forms
Analysis on manifolds
Topology
Homogenous dynamics
Representation Theory
Group Theory

Relevant Degree Programs

 

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Master's students
Doctoral students
Postdoctoral Fellows
2019
2020

Mathematics, almost any field

Graduate Student Supervision

Doctoral Student Supervision (Jan 2008 - May 2019)
The topology of representation varieties (2016)

The goal of this thesis is to understand the topology of representation varieties. To be more precise, let G be a complex reductive linear algebraic group and let K ⊂ G be a maximal compact subgroup. Given a finitely generated nilpotent group Γ, we consider the representation spaces Hom(Γ,G) and Hom(Γ,K) endowed with the compact-open topology. Our main result shows that there is a strong deformation retraction of Hom(Γ,G) onto Hom(Γ,K). We also obtain a strong deformation retraction of the geometric invariant theory quotient Hom(Γ,G)//G onto the ordinary quotient Hom(Γ,K)/K. Using these deformations, we then describe the topology of these spaces.

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Master's Student Supervision (2010 - 2018)
Sup-norm problem of certain eigenfunctions on arithmetic hyperbolic manifolds (2015)

We prove a power saving over the local bound for the L∞ norm of uniformly non-tempered Hecke-Maass forms on arithmetic hyperbolic manifolds of dimension 4and 5. We use accidental isomorphism and use the Hecke theory of the correspond-ing groups to show that if the automorphic form is non-tempered at positive densityof finite places then the Hecke eigenvalues are large; amplifying the saving comingfrom the non temperedness we get a power saving.

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Geometric retracts of Siegel's upper half space (2013)

The purpose of this thesis is to construct a codimension 1 cocompact Sp₂gℤ-equivariant strong deformation retract Wg of Siegel's upper half space hg . This yields a partial contribution towards the problem of constructing a strong spine for the real linear symplectic group Sp₂gℝ.

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Escape of Mass on Hibter Modular Varieties (2012)

No abstract available.

 
 

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