Morris Ang
University of California-San Diego, CA·Mathematics & Statistics
Randomness can produce shapes, not just numbers. Random curves and random surfaces appear when physicists model fluctuating interfaces, critical phenomena and the strings of string theory.
- Fields
Mathematics & Statistics
Physics
- Topics
probability theory
mathematical physics
random geometry
- Grants
- 1 known grant, through Jun 2028
What they work on
- Determine the probability law of the random modulus, a number describing conformal shape, of Brownian surfaces for each topology, verifying a conjecture from bosonic string theory using Liouville quantum gravity (LQG).
- Derive exact formulas for three-point functions of the conformal loop ensemble, a collection of Schramm-Loewner evolution (SLE) loops arising from critical lattice loop models, and connect them to conformal field theories.
- Give a mathematical construction of the bosonic string, a loop moving in space and tracing a random LQG surface, and prove that its time evolution is Markovian.
More about the research
This mathematics project studies two such objects: Schramm-Loewner evolution (SLE), a family of random fractal curves, and Liouville quantum gravity (LQG), a model of random two-dimensional surfaces. The goal is to resolve long-standing problems that come from theoretical physics, specifically bosonic string theory and conformal field theory, by further developing the deep links between SLE and LQG.
Why it matters
This is pure mathematics. It aims to put predictions from string theory and conformal field theory on rigorous footing using random geometry. The methods developed for linking SLE and LQG are expected to apply to related problems in probability and mathematical physics, and could eventually inform how physicists model random surfaces and critical systems.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Jacopo Borga
Massachusetts Institute of Technology, MA·Mathematics & Statistics
Link the longest increasing subsequence of random permutations to directed distances on random planar maps, aiming to build a 'quantum version' of the Kardar-Parisi-Zhang directed landscape.
Igor Klebanov
Princeton University, NJ·Physics
Develop new methods for quantum field theories with defects or boundaries, where interactions are confined to a surface or edge, and identify the new critical phenomena and renormalization group flows they produce.
Ron Donagi
University of Pennsylvania, PA·Mathematics & Statistics
Attack the geometric Langlands conjecture, a proposed deep link between areas of mathematics, using non-abelian Hodge theory and ideas from quantum field theory.
The school
University of California-San Diego: 84 labs on PI Pages, $1.9B a year on research, 637 research doctorates a year.
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