A birthday conference about two problems that have intrigued Jim Simons and many others.

## Gallavotti’s challenge:

Given a general volume preserving initial velocity field, construct for a given accuracy, an algorithm for determining the volume preserving fluid velocity at one point one second later in an explicit amount of computer time. And prove it. This is open for 3D and is discussed for 2D in section 3.2 of Gallavotti’s book “Foundations of fluid mechanics” 2^{nd} edition, Springer-Verlag.

## Yau’s challenge:

Construct a closed manifold V of complex dimension at least three and

a) Prove V does not admit a complex structure.

b) Show the tangent vector bundle to V does admit a complex structure.

Decades ago Yau found such a V in complex dimension two.

A few surveys, suggestions, ideas and speculations animated by Gregory Falkovich (fluids) and Jean-Pierre DeMailly (complex manifolds) and confirmed remarks by J. Glimm, Y.T. Siu, T. Drivas, J. Torres, D. Angella, A. Milivoyevic, B. Ferlengez, S. Wilson, D. Sullivan.

The Graduate Center of the City University of New York

April 23 (full day), 24 (full day) and 25 (morning) of 2018

Organizer: Dennis Sullivan.

This conference is made possible by support from