(My) math interests
My primary interests lie in the topics related to the analysis of manifolds and functions on it: be it through geometric, topological, dynamical or analytical perspectives/techniques.
- I have invested a lot of time on Riemann surfaces, hyperbolic manifolds and discrete subgroups of
during my MS thesis.
- Rigidity of discrete groups: Mostow-Prasad’s rigidity theorem, Tukia’s proof of quasiconformal rigidity, Sullivan’s proof of measurable rigidity using Patterson-Sullivan measures
- Deformations of discrete groups: quasiconformal deformations, space of discrete faithful representations
of finitely generated groups - Constructing such discrete subgroups for higher
which various (geometric/topological/algebraic) properties - Complex analysis, Riemann surfaces and complex geometry, holomorphic mappings, quasiconformal mappings on spheres
- Locally compact groups, geometric and analytic group theory/abstract harmonic analysis, amenable groups, ergodic theory of actions of amenable groups, representation theory of Lie groups and Lie algebras
- Geometric and analytic theory of finitely generated groups, Gromov hyperbolic groups, boundaries of Gromov hyperbolic groups, Cannon-Thurston maps
- Geometric topology of 2 and 3-manifolds
- Riemannian geometry
- Symplectic geometry and Hamiltonian flows
I wish to someday study more about several complex variables, complex manifolds and algebraic tools used in complex geometry.
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The events that I have coorganized are the following.
The events I attended include the following.
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