Professor David Preiss, RNDR, CSC, FRS
Astor Professor of Pure Mathematics

Geometric measure theory in the broad sense: from problems of rectifiability and other regularity of currents, measures or sets to mathematical theory of fractals (cf P Mörters and D Preiss, Tangent measure distributions of fractal measures, Math Ann 312, 1998, 53-99) or Lipschitz solutions of partial differential equations.

Non-linear geometric functional analysis, in particular questions of differentiability (cf J Lindenstrauss and D Preiss, Almost Frechet differentiability of finitely many Lipschitz functions, Mathematika, 86, 1996, 393-412), isomorphism problem - are two (super-)reflexive Lipschitz isomorphic separable Banach spaces linearly isomorphic? - measures of size of sets in infinitely dimensional spaces (cf D Preiss and J Tiser, Two unexpected examples concerning differentiability of Lipschitz functions on Banach spaces, Operator Theory: Advances and Applications, 77 (1995), 219-238).

Classical real analysis: Differentiability problems, description of derivatives (cf D Preiss and M Tartaglia, On characterizing derivatives, Proc Amer Math Soc 123, 1995, 2417-2420), generalized integrals, structure of subsets of the real line - does every set of positive measure contain a similar copy of a single infinite set?

This page was last modified on February 8, 2007 by Helen Higgins