Srivatsav Kunnawalkam Elayavalli
University of Maryland, MD·Mathematics & Statistics
Von Neumann algebras began in the 1930s as a mathematical foundation for quantum physics. They are now a rich area of functional analysis, the study of infinite-dimensional spaces and the operators acting on them.
- Fields
Mathematics & Statistics
- Topics
von Neumann algebras
operator algebras
functional analysis
- Grants
- 1 known grant, through Jun 2028
What they work on
- Apply Voiculescu's free entropy theory, a measure of size for noncommuting variables, to determine the structure of free products and ultrapowers of finite von Neumann algebras.
- Develop the small-at-infinity compactification and use it to study the structure of von Neumann algebras arising from relatively properly proximal groups.
- Study rigidity and indecomposability of von Neumann algebras by combining free entropy, Popa's deformation/rigidity theory and Ozawa's boundary and amenable action methods.
More about the research
They also show up in dynamical systems, ergodic theory, group theory, model theory, topology and knot theory, as well as in quantum physics, quantum computation and cryptography. A central goal is classification: understanding exactly how these algebras are built and when they can or cannot be broken into simpler pieces.
Why it matters
This is pure mathematics. It aims to resolve open structural questions about von Neumann algebras by joining entropy and boundary techniques. Better understanding of these algebras could eventually inform areas where they appear, including quantum physics, quantum computation, group theory and ergodic theory.
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.
Denis Osin
Vanderbilt University, TN·Mathematics & Statistics
Study rigidity properties of acylindrically hyperbolic groups by addressing auxiliary questions and conjectures connecting analytic and geometric properties, motivated by open problems on quasi-isometric and measure equivalence rigidity.
The school
University of Maryland: 49 labs on PI Pages, $1.5B a year on research, 602 research doctorates a year.
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