Florentiu Daniel Cibotaru

Visiting Assistant Professor

Ph.D., University of Notre Dame, 2009

M.S., University of Notre Dame, 2006

For additional information see Daniel Cibotaru's Personal Page.

Research Interests

My main areas of interest are Global Analysis and Algebraic Topology. Specifically, I am interested in the role that geometric methods play in developing a good understanding of elliptic boundary value problems. This has both functional analytic and index theoretic implications.

 In my recent work, I  use symplectic topology methods to give an intersection theoretic interpretation of the odd Chern character and how that implies localization formulae for the index of a family of self-adjoint, Fredholm operators, the easiest example of which is the well-known  case of the spectral flow. In a different direction, in collaboration with L. Nicolaescu we investigate 1-parameter families of elliptic operators in the case of a non-cylindrical cobordism and derive an index correction formula in the spirit of the gluing formula for the eta invariant.

Selected Publications

• Localization formulae in odd K-theory, PhD thesis, http://arxiv.org/abs/0901.2563
• Joint with L. Nicolaescu, Dirac Operators on Cobordisms:  Degenerations and Surgery, http://arxiv.org/abs/0908.3236
  

Please direct questions and comments to: dcibotar@nd.edu