Jacopo Borga
Massachusetts Institute of Technology, MA·Mathematics & Statistics
Shuffle a deck of cards and ask about the order. Then picture a randomly shaped surface or curve, of the kind physicists use to model quantum gravity and phase transitions.
- Fields
Mathematics & Statistics
Physics
- Topics
probability theory
combinatorics
mathematical physics
- Grants
- 1 known grant, through May 2027
What they work on
- 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.
- Determine the large-scale limit of uniform random meanders and meandric permutations, a long-standing open problem, by studying crossing fully packed loop models on planar maps.
- Connect limits of d-dimensional permutations to new scale-invariant random geometries from physics, beginning a higher-dimensional theory of permutons and random geometry.
More about the research
These seem unrelated, but recent work suggests deep links. This project connects random permutations, studied through permutons (the limiting shapes of very large random permutations), with random geometry. In this project, random geometry includes Schramm–Loewner evolution curves, a family of random fractal curves, and Liouville quantum gravity surfaces, random surfaces from physics. The work combines probability, combinatorics and mathematical physics.
Why it matters
This is basic mathematics. It aims to unify random permutations and the random geometries used in quantum physics and statistical mechanics. It would also settle long-open questions about meanders and give new tools for understanding universal random shapes. Over time these results could inform mathematical models in statistical physics.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Morris Ang
University of California-San Diego, CA·Mathematics & Statistics
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).
Xuan Wu
University of Illinois Urbana-Champaign, IL·Mathematics & Statistics
Establish connections between the KPZ equation, a model of random interface growth, and the KPZ line ensemble, a family of interacting random curves, using their shared Gibbs properties.
Le Chen
Auburn University, AL·Mathematics & Statistics·Early-career
Prove the existence of nontrivial invariant measures for the stochastic heat equation and the parabolic Anderson model, arising from the interaction between noise structure and rough initial data.
The school
Massachusetts Institute of Technology: 25 labs on PI Pages, $1.1B a year on research, 692 research doctorates a year.
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