My main interests are in Algebra, Metric Geometry, and Geometric Analysis.
- Algebra
- Combinatorial methods in algebra (especially ring theory)
- Ring commutativity conditions
- Metric geometry
- Gromov hyperbolicity
- CAT(0) and convexity
- Ptolemaic condition
- Geometric analysis
- Poincaré/Sobolev/Trudinger/Hardy inequalities
- Quasiconformal and quasisymmetric mappings
- The Heisenberg group and subriemannian geometry
- Other analysis
- Elliptic PDEs
- Doubling measures
- Muckenhoupt and reverse Hölder weights
- Classical complex function theory
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