Two-Dimensional Random Geometry

Description

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This workshop will focus on random geometric objects whose definitions are motivated by theoretical physics. In many cases, these objects are known or expected to describe the large-scale behavior of natural discrete random objects. Some of the most important examples are the following.

• Schramm-Loewner evolution (SLE): random fractal curves which describe the large-scale behavior of discrete random curves which arise in statistical mechanics. For example, if one considers the critical Ising model on the square grid, then re-scales so that the size of the squares goes to zero, the interfaces between regions of positive and negative spin will converge to SLE₃ curves.
• Liouville quantum gravity (LQG): random fractal surfaces which are connected to string theory and conformal field theory. These surfaces describe the large-scale behavior of random planar maps. For example, uniform random triangulations of the sphere converge, in a certain sense, to $\sqrt{8/3}$-LQG as the number of triangles tends to infinity.

There has been a huge number of exciting mathematical developments in this subject in recent years. Such developments include rigorous proofs of results which were originally justified heuristically in the physics literature, proofs of new results which were not predicted by physicists, and applications to new and unexpected topics. These developments have opened up an abundance of interesting research directions.

Organizers

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E G

N H

X S

Speakers

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T A

M A

J A

N B

J B

T B

T B

D C

N C

B D

C G

X L

K K

G M

M P

E P

W Q

R R

E S

L S

S S

J S

H W

Registration

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IMSI is committed to making all of our programs and events inclusive and accessible. Contact to request accommodations.

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