Organized by Robert Berman, Semyon Klevtsov, Paul Wiegmann, and Steve Zelditch

Dates: June 15 – 19, 2015

Attendee List Download Talk ScheduleView Videos

This workshop is devoted to random surfaces, shapes and fields, in both physics and geometry. In statistical mechanics in two spatial dimensions random fields are associated with critical fluctuations of random geometric objects such as curves and surfaces. Recently similar mathematical structures have been observed in the theory of quantum Hall effect. These problems call for a quest of further and deeper understanding of measures of random geometrical objects. In higher dimensions, the natural generalization of stochastic conformal geometry is to Kahler manifolds. Correlation functions of random fields on general Kahler manifolds are related to Bergman kernels. In general dimensions, Bergman kernels arise as covariance kernels of Gaussian holomorphic random fields, whose zeros and critical points are of interest both in mathematics and physics. Bergman kernels give an alternative approach to random surfaces by way of random Bergman metrics, defined by random holomorphic embeddings into projective space. The workshop will include talks by physicists and mathematicians on each topic.

This workshop is a part of the Spring 2015 program, Large N limit problems in Kahler Geometry, which is organized by Robert Berman, Semyon Klevtsov, Paul Wiegmann, and Steve Zelditch. This program takes place from April 20 – June 19, 2015.

#### Quantum Geometry, Stochastic Geometry, Random Geometry, you name it Schedule

Time | Title | Presenters | Video |

9:30am | Liouville quantum field theory on Riemann surfaces I, Part 1 | Vincent Vargas | video slides |

10:30am | Coffee Break | SCGP Cafe | |

11:00am | Random nodal portraits: few results and many questions, Part 1 | Misha Sodin | video slides |

12:00pm | Lunch | SCGP Cafe | |

1:30pm | Universal components of random real algebraic hypersurfaces, Part 1 | Damien Gayet | video |

2:30pm | On the structure of the zero set of monochromatic random waves. | Yaiza Canzani | video slides |

3:30pm | Coffee | SCGP Cafe | |

4:00pm | Nodal Sets of Random Eigenfunctions of the Harmonic Oscillator | Boris Hanin | video |

Time | Title | Presenters | Video |

9:30am | Liouville quantum field theory on Riemann surfaces I, Part 2 | Vincent Vargas | video |

10:30am | Coffee Break | SCGP Cafe | |

11:00am | Universal components of random real algebraic hypersurfaces, Part 2 | Damien Gayet | video |

12:00pm | Lunch | SCGP Cafe | |

1:00pm | SCGP Weekly talk: Kahler geometry in physics and probability | Semyon Klevtsov | video slides |

2:00pm | Random nodal portraits: few results and many questions, Part 2 | Misha Sodin | video slides |

3:30pm | Coffee | SCGP Cafe | |

4:00pm | Probability measures on manifolds of Riemannian metric | Dmitry Jakobson | video slides |

Time | Title | Presenters | Video |

9:30am | Liouville quantum field theory on Riemann surfaces II, Part 1 | Remi Rhodes | video slides |

10:30am | Coffee Break | SCGP Cafe | |

11:00am | Collective Field Theory of Quantum Hall States as Random Geometry | Tankut Can | video slides |

12:00pm | Lunch | SCGP Cafe | |

1:30pm | Uniqueness in geometric quantization | Laszlo Lempert | video |

2:30pm | Kaehler geometries of conformal maps | Leon Takhtajan | video slides |

3:30pm | Coffee | SCGP Cafe | |

4:00pm | Balanced embedding of pairs and logarithmic K-stability | Song Sun | video |

Time | Title | Presenters | Video |

9:30am | Liouville quantum field theory on Riemann surfaces II, Part 2 | Remi Rhodes | video slides |

10:30am | Coffee Break | SCGP Cafe | |

11:00am | Brownian motion on the space of Kahler metrics | Steven Morris Zelditch | video |

12:00pm | Lunch | SCGP Cafe | |

1:30pm | Equdistribution for zeros of holomorphic sections of singular Hermitian line bundles | Xiaonan Ma | video slides |

2:30pm | Holography and operator traces | Michael Douglas | video |

3:30pm | Coffee | SCGP Cafe | |

4:00pm | Bose-Einstein Condensation, Irreversibility, large N and Quantum Black Holes | Frank Ferrari | video |

Time | Title | Presenters | Video |

9:30am | Which fluid dynamics models the Quantum Hall Effect? | Vincent Pasquier | video |

10:30am | Coffee Break | SCGP Cafe | |

11:00am | Large degree asymptotics of characteristic polynomials in 2D Coulomb gas | Seung Yeop Lee | video slides |

11:30am | 2D quantum gravity on Kahler manifolds: a first-principles computation | Laetitia Leduc | video slides |

12:00pm | Multifractality in the quantum Hall effect revisited | Roberto Bondesan | video slides |

12:30pm | Lunch | SCGP Cafe | |

3:30pm | Coffee | SCGP Cafe |