Tao Mei
Texas A&M University-College Station, TX·Mathematics & Statistics
A common strategy in mathematics is to understand a complicated object by approximating it with simpler ones and then taking a limit. A space with infinitely many dimensions, for example, might be approximated by spaces with finitely many dimensions.
- Fields
Mathematics & Statistics
- Topics
Lp-approximation properties
von Neumann algebras
operator algebras
- Grants
- 1 known grant, through Jun 2027
What they work on
- 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.
- Connect Lp-approximation properties to von Neumann rigidity, which asks how much of a discrete group's structure is preserved by its operator algebra.
- Relate Lp-approximation properties to Connes's quantized calculus, a version of calculus for settings where quantities do not commute.
- Rebuild the classical theory of Fourier multipliers, which are operators that rescale frequency components, for noncommutative settings that lack geometric or metric structure and a commutative product.
More about the research
Whether, and how well, such approximations work is the subject of approximation properties. These properties are central to quantum probability, noncommutative geometry and quantized calculus, which is a calculus adapted to settings where quantities do not commute.
Why it matters
This is basic research in pure mathematics. It adds an understanding of how operator algebras built from groups can be approximated, and how the classical theory of Fourier multipliers can be extended to settings without commutativity or geometry. The project states that these results could inform noncommutative geometry and its applications to quantum information theory.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Srivatsav Kunnawalkam Elayavalli
University of Maryland, MD·Mathematics & Statistics
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.
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.
Corey Jones
North Carolina State University, NC·Mathematics & Statistics
Classify approximately finite-dimensional actions of amenable tensor categories on approximately finite-dimensional C*-algebras using K-theoretic invariants, extending earlier results for fusion categories.
The school
Texas A&M University-College Station: 23 labs on PI Pages, $1.4B a year on research, 768 research doctorates a year.
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