David Penneys
Ohio State University, OH·Mathematics & Statistics
Symmetry is one of the main tools for understanding physical and mathematical systems. Classical symmetries, like rotations, can always be undone, and mathematicians describe them with structures called groups.
- Fields
Mathematics & Statistics
Physics
- Topics
operator algebras
von Neumann algebras
higher category theory
- Grants
- 1 known grant, through May 2029
What they work on
- Develop an operator-algebra description of topologically ordered quantum spin systems, using nets of von Neumann algebras to study superselection sectors, the distinct types of particle-like excitations.
- Connect superselection theory for topological order to the boundary-algebra approach from quantum information theory.
- Build new higher-dimensional quantum spin systems from higher fusion category data, and prove that topologically ordered spin systems naturally form higher categories.
- Develop fermionic and anyonic operator algebras to better describe topologically ordered phases of matter that occur in nature.
More about the research
Quantum systems can have richer "non-invertible" or quantum symmetries, which are described by higher categories. These are mathematical structures that track objects, the relationships between them, and relationships between those relationships. This project studies such symmetries in quantum spin systems. These are mathematical models of matter in which each atom's quantum state lives in a small vector space. Some spin systems have topological order, a robust collective quantum state that can serve as a quantum error-correcting code for quantum computers.
Why it matters
This is basic mathematics. It could deepen the rigorous understanding of topologically ordered quantum matter and its symmetries. Topologically ordered spin systems provide local quantum error-correcting codes, so this understanding could eventually inform the design of fault-tolerant quantum computers. It could also inform the study of topological phases of matter found in real materials.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
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.
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.
Yizhi You
Northeastern University, MA·Physics·Early-career
Construct microscopic models and hybrid fracton field theories to describe the collective behavior of fractons, particle-like excitations with restricted mobility, and the phases and phase transitions they form.
The school
Ohio State University: 71 labs on PI Pages, $1.6B a year on research, 882 research doctorates a year.
Reach out
A start for your email. Fill in the brackets.