** Random Geometry and Topology Minisymposium at SIAM AG 2019**

This is the website for the minisymposium on Random Geometry and Topology to be held at the SIAM Conference on Applied Algebraic Geometry 2019.

Location: University of Bern, Bern, Switzerland.

This minisymposium is meant to report on the recent activity in the field of random geometry and topology. The idea behind the field is summarized as follows: take a geometric or topological quantity associated to a set of instances, endow the space of instances with a probability distribution and compute the expected value, the variance or deviation inequalities of the quantity. The most prominent example of this is probably Kostlan, Shub and Smales celebrated result on the expected number of real zeros of a real polynomial. Random geometry and topology offers a fresh view on classical mathematical problems. At the same time, since randomness is inherent to models of the physical, biological, and social world, the field comes with a direct link to applications.

### Organizers

Paul Breiding, Max-Planck-Institute for Mathematics in the Sciences Leipzig.

Khazhgali Kozhasov, Max-Planck-Institute for Mathematics in the Sciences Leipzig.

Antonio Lerario, SISSA.

Erik Lundberg, Florida Atlantic University.

### Speakers, Titles and Abstracts

Peter Bürgisser: The real tau-conjecture is true on average

Koiran's real tau-conjecture claims that the number of real zeros of a structured polynomial given as a sum of m products of k real sparse polynomials, each with at most t monomials, is bounded by a polynomial in mkt. This conjecture has a major consequence in complexity theory since it would lead to superpolynomial bounds for the arithmetic circuit size of the permanent. We confirm the conjecture in a probabilistic sense by proving that if the coefficients involved in the description of f are independent standard Gaussian random variables, then the expected number of real zeros of f is O(mkt), which is linear in the number of parameters.

Chris Peterson: TBA

Emil Horobet: TBA

Michele Ancona: TBA

Federico Dalmao: TBA

Leo Mathis: TBA

Michele Stecconi: TBA

Andrew Newman: TBA

Orlando Marigliano: TBA

Christian Lehn: TBA

### Information for speakers

- The rules of SIAM do not allow a speaker to present multiple
talks at this conference.
Here is a list of other proposed
sessions.
- Talks will be 19-21 minutes plus 4 minutes for questions. (At 17
minutes, a signal will be given if desired).
- The minisymposium number is to be determined.
- Students can apply for travel support
here.

See also the website of the

SIAM AG Activity Group.