#
Random analytic functions

January 16 to January 20, 2006
at the

American Institute of Mathematics,
Palo Alto, California

organized by

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

## Original Announcement

This workshop 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)

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.

Papers arising from the workshop: