at the

American Institute of Mathematics, Palo Alto, California

organized by

Amir Dembo, J. Maurice Rojas, Bernard Shiffman, and Steve Zelditch

This workshop, sponsored by AIM and the NSF, will be devoted to advancing the theory of random functions and surfaces. This theory, ranging from polynomials to analytic functions to holomorphic sections to algebraic varieties, has advanced tremendously over the last decade and grown to encompass quite general analytic objects of interest in contemporary geometry and algebra. Physics provides another vital source of problems and intuitions. Random functions are fundamental in such areas of applied mathematics and physics as in the numerical solutions of intractable problems from optimization, in quantum chaos, in astrophysics and (more recently) in string theory and quantum gravity.

The main topics for the workshop are:

- the distribution of zeroes of random analytic functions (including statistical fewnomial theory and random matrix ensembles)
- discrete random analytic functions (e.g., the connections between dimers, tilings, and quantum gravity)
- random analogues of Hilbert's Sixteenth Problem (i.e., the topology of random real zero sets)

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and working sessions.

The deadline to apply for support to participate in this workshop has passed.

For more information email *workshops@aimath.org*

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