Talks & Presentations
Selected conference talks, invited lecture series, and lecture notes covering surface braid groups, quasiconformal mappings, Teichmüller theory, group actions, and Several Complex Variables.
Geometric Representations of Surface Braid Groups
An exploration of classical braids $B_n$, the mapping class group, and geometric representations of surface braid groups $B_n(S)$ via Hodge theory and homology of cyclic branched covers.
Quasiconformal Mappings and Teichmüller Theory
Lecture notes from the invited lecture series delivered at IISER Kolkata. Topics include the Grötzsch problem, geometric and analytic definitions of quasiconformal mappings, extremal length, the Beltrami differential equation, and foundations of Teichmüller spaces.
Group Actions and Möbius Transformations
Lecture notes for the two-part lecture series given at the Department of Mathematics, University of Calicut. Covers group actions, orbits, stabilizers, symmetric groups, and the geometry and algebra of Möbius transformations on the Riemann sphere.
Applied Conformal & Quasiconformal Geometry
From the foundations of holomorphic functions and the Beltrami equation to cutting-edge real-world applications in medical imaging (CT/MRI scanners, virtual colonoscopy), Ricci flow, and surface parameterization.