In recent years there has been a great deal of activity in both the theoretical and applied aspects of partial differential equations, with emphasis on realistic engineering applications, which usually involve lack of smoothness. On March 21-25, 1990, the University of Chicago hosted a workshop that brought together approximately fortyfive experts in theoretical and applied aspects of these subjects. The workshop was a vehicle for summarizing the current status of research in these areas, and for defining new directions for future progress - this volume contains articles from participants of the workshop.

This volume presents five papers based on selected lectures given at the Current Developments in Mathematics conference, held in November 2019 at Harvard University.

Papers based on selected lectures given at the Current Development Mathematics Conference, held in November 2017 at Harvard University.

This volume presents five papers based on selected lectures given at the Current Developments in Mathematics conference, held in November 2018 at Harvard University.

Papers based on selected lectures given at the Current Development Mathematics Conference, held in November 2015 at Harvard University.

Papers based on selected lectures given at the Current Development Mathematics Conference, held in November 2011 at Harvard University. Contents: The Laplacian on planar graphs and graphs on surfaces (Richard Kenyon); Hyperbolicity and stable polynomials in combinatorics and probability (Robin Pemantle); Introduction to KPZ (Jeremy Quastel)

Papers based on selected lectures given at the Current Development Mathematics Conference, held in November 2010 at Harvard University.

Papers based on selected lectures given at the Current Development Mathematics Conference, held in November 2009 at Harvard University.

These are the proceedings of the joint seminar by M.I.T. and Harvard on the current Developments in mathematics for the year 2001. Established in 1995, this seminar has been continued on the third weekend of November every year. The organizing committee for the seminar consisted of distinguished mathematicians from the mathematics departments of both institutions: Barry Mazur, Wilfried Schmid, and Shing-Tung Yau from Harvard, and David Jerison, A. J. de Jong and George Lustig from M.I.T.. We trust that these proceedings will be of interest to many mathematicians, and will inspire future developments and research pursuits in mathematics.