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Quantum Geometry, Stochastic Geometry, Random Geometry, you name it: June 15 – 19, 2015

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