# Summer Graduate School

Parent Program: |
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Location: |
Pacific Institute for Mathematical Sciences (PIMS), Vancouver, Canada |

## Show List of Lecturers

- Tom Hutchcroft (California Institute of Technology)
- Mathav Murugan (University of British Columbia)

## Show List of Speakers

- Nathanael Berestycki (University of Vienna)
- Nina Holden (ETH Zurich)
- Tianyi Zheng (University of California, San Diego)

The Summer Schools in Probability are a highlight of Canadian probability and are internationally significant. Launched by PIMS in 2004, the school takes the form of two main 4-week courses along with three mini-courses. The schools have played a major role in the development of an exceptionally strong community of young probabilist in Canada, North America and overseas. This will be the 13th time this school has run.

The two long courses (24 hours each) are:

- Tom Hutchcroft (Caltech),
**Topics in Percolation** - Matav Murugan (UBC),
**Heat Kernel Estimates, Harnack Inequalities, and Quasisymmetry**

The three minicourses (3 hours each) are:

- Nathanael Berestycki (U. Vienna),
**Spectral Geometry of Liouville Quantum Gravity** - Nina Holden (NYU),
**Random Surfaces** - Tianyi Zheng (UC San Diego),
**Poisson Boundary of Random Walks and Growth of Groups**

#### School Structure

There will be two long courses (24 lecture hours each), three minicourses (3 lecture hours each), and 15 hours reserved for short presentations by participants. The participant presentations are an important component of the school. They promote interaction amoung participants and provide a panorama of current research in probability. No talks are scheduled on Wednesdays. Instead, optional excursions are arranged by the organizers.

#### Prerequisites

A first year-long graduate course in measure-theoretic probability, roughly covering the material of Billingsley's Probability and Measure. Some familiarity with percolation or other statistical mechanical models would be useful but is not required.

#### Application Procedure

SLMath is only able to support a limited number of students to attend this school. Therefore, it is likely that only one student per institution will be funded by SLMath.

For **eligibility** and **how to apply**, see the **Summer Graduate Schools homepage.**

#### Venue

The summer school will take place at the Pacific Institute for Mathematical Sciences (PIMS) on the campus of the University of British Columbia in Vancouver, Canada. Participants will be housed in shared accommodation within the Gage residences at UBC, in six-bedroom suites with shared facilities including kitchen. The interactions between students facilitated by this accommodation style provides important networking opportunities.

**Keywords and Mathematics Subject Classification (MSC)**

**Tags/Keywords**

percolation

phase transition

critical phenomena

critical exponents

mean-field theory

heat kernel

Harnack inequality

symmetric Markov process

Dirichlet form

harmonic measure

Liouville Brownian motion

Liouville quantum gravity and conformal field theory

Gaussian free field

Selberg trace formula

heat kernel asymptotics

Weyl law

Liouville Quantum Gravity

random planar maps

gaussian multiplicative chaos

Schramm-Loewner evolution

Liouville conformal field theory

Poisson boundary

speed

entropy

random walk on group

growth rate of groups

**Primary Mathematics Subject Classification**

05C80 - Random graphs (graph-theoretic aspects) [See also 60B20]

82B27 - Critical phenomena in equilibrium statistical mechanics

11F72 - Spectral theory; trace formulas (e.g., that of Selberg)

81T40 - Two-dimensional field theories, conformal field theories, etc. in quantum mechanics

58J50 - Spectral problems; spectral geometry; scattering theory on manifolds [See also 35Pxx]

60D05 - Geometric probability and stochastic geometry [See also 52A22, 53C65]

**Secondary Mathematics Subject Classification**No Secondary AMS MSC