Cesar Cuenca
Ohio State University, OH·Mathematics & Statistics
Large random systems are everywhere, from traffic flow to polymers to the arrangement of atoms in solids. Their behavior is often too complicated to analyze exactly.
- Fields
Mathematics & Statistics
Physics
- Topics
random matrices
random partitions
plane partitions
- Grants
- 1 known grant, through Jul 2027
What they work on
- Describe the large-scale behavior of continuous and discrete beta-ensembles (Boltzmann distributions generalizing random matrix eigenvalues and random partitions) at different temperature limits, using new versions of free probability.
- Develop the Dunkl transform, built from multivariate Bessel functions, as the main tool for analyzing the limits of random particle ensembles.
- Address infinite-dimensional versions of classifying irreducible representations and noncommutative harmonic analysis within asymptotic representation theory.
- Extend links between representations and discrete quantized beta-ensembles found through q-orthogonal multivariate polynomials, connecting them to the Boltzmann measures studied in the first part.
More about the research
So mathematicians and physicists study simplified "solvable" models that show the same large-scale behavior but can be worked out exactly. This project builds and studies such solvable models, which come from random matrices, plane partitions (three-dimensional stacks of cubes) and quantum algebras. It uses special functions, families of functions with rich algebraic structure, together with tools from representation theory and combinatorics.
Why it matters
This is basic mathematics. It adds exact results about how large random particle systems behave and how they connect to symmetry in infinite dimensions. Such solvable models serve as stand-ins for real random systems like polymers, percolation and the molecular structure of solids. The results could eventually inform how scientists predict the large-scale behavior of those systems.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Dimitri Shlyakhtenko
University of California-Los Angeles, CA·Mathematics & Statistics
Develop methods based on partial differential equations (equations describing change) for non-commutative settings, extending tools from classical analysis to von Neumann algebras using free probability.
Tao Mei
Texas A&M University-College Station, TX·Mathematics & Statistics
Determine the Lp-approximation properties of group von Neumann algebras, which are operator algebras built from discrete groups, that is, how well these infinite-dimensional objects can be approximated by simpler pieces.
Hugo Woerdeman
Drexel University, PA·Mathematics & Statistics
Resolve open problems on when noncommutative rational expressions in bounded operator variables become singular or vanish, combining complex analysis, representation theory and operator theory.
The school
Ohio State University: 71 labs on PI Pages, $1.6B a year on research, 882 research doctorates a year.
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