Visiting assistant professor at University of Cincinnati (Ohio, USA). Analysis and geometry (on metric space) are my areas of research. My goal is to advertise these subjects to advanced students and experts that are new to the field.
Toics covered so far @YoungMeasures:
(1) Hausdorff measures (5 videos)
(2) Area Formula (13 videos): Lipschitz maps, Rademacher’s theorem, Jacobians
(3) Coarea Formula (14 videos): Fubini’s theorem
(4) Curves in Euclidean and metric space (12 videos): rectifiable curves, arclength parameterizations
(5) Geometric Measure theory (29 videos): Cantorsets and fractals and their various dimension, Densities of Hausdorff measures
(6) Analysis on Metric Spaces (55 videos): Hajlasz-Sobolev and Newtonian-Sobolev functions, upper gradients, Poincare inequality, Modulus of Path Families
(7) Heisenberg, sub-Riemannian manifolds
Future plans: Lipschitz Maps into Metric Spaces: metric differentiability
PLEASE SUBSCRIBE!