Geometric PDE - Curvature and Regularity of Optimal Transport - Part I
Pseudorandomness - Randomness extractors
Pseudorandomness in Mathematics and Computer Science Mini-Workshop
In math, one often studies random aspects of deterministic systems and structures. In CS, one often tries to efficiently create structures and systems with specific random-like properties. Recent work has shown many connections between these two approaches through the concept of "pseudorandomness".
Lectures by Bourgain, Impagliazzo, Sarnak and Wigderson (schedule below), will explore some of the facets of pseudorandomness, with particular emphasis on research directions and open problems that connect the different viewpoints of this concept in math and CS.
Pseudorandomness - Exponential sums, equidistribution and pseudo-randomness
Pseudorandomness - When do sparse sets have dense models?
Pseudorandomness - Substitution sequences at primes
Compromises and Rotten Compromises
Geometric PDE - Optimal Transportation and Nonlinear Elliptic PDE - Part II
Geometric PDE - Optimal transportation and nonlinear elliptic PDE
http://www.math.ias.edu/sp/gpde
In these lectures we will describe the relationship between optimal transportation and nonlinear elliptic PDE of Monge-Ampere type, focusing on recent advances in characterizing costs and domains for which the Monge-Kantorovich problem has smooth diffeomorphism solutions.
Background references.
L.C Evans, PDE and Monge-Kantorovich mass transfer. Current developments in Mathematics, 1997. Int. Press, Boston, (1999).