Carolina Neira

Contact: cneiraj@unal.edu.co

Research interests

Research interests: Pseudodifferential Operators. Global Analysis. Symplectic Geometry. Mathematical Physics. Noncommutative Geometry.

Publications

1. Nonsmooth Pseudodifferential Boundary Value Problems on Manifolds. With Helmut Abels. Journal of Pseudodifferential Operators. 2018, DOI: 10.1007/s11868-018-0268-6. arXiv:1709.04157

2. The canonical trace and the noncommutative residue on the noncommutative torus. With Cyril Levy and Sylvie Paycha. Trans. Amer. Math. Soc. 368 (2016), 1051-1095. arXiv:1303.0241

3. Traces of Holomorphic Families of Operators on the Noncommutative Torus and on Hilbert Modules. With Sara Azzali, Cyril Levy and Sylvie Paycha. Geometric Methods in Physics. Trends in Mathematics, pp 3-38. Birkhäuser Basel 2015. arXiv:1501.06338

4. Classification of traces and associated determinants on odd-class operators in odd dimensions. With Marie Françoise Ouedraogo. SIGMA Symmetry, Integrability and Geometry: Methods and Applications 8 (2012), Paper 023. arXiv:1111.6750

5. Semiclassical measures and Weyl's law. Oberwolfach Reports. Report No. 49/2011. Volume 8, Issue 4, 2011. Pages: 2789-2791. Arbeitsgemeinschaft in Quantum Ergodicity. Oberwolfach, Germany.

6. Classification of traces and hypertraces on spaces of classical pseudodifferential operators. With Matthias Lesch. J. Noncommut. Geom. 7 (2013), no. 2, 457-498. arXiv:1011.3238

7. A mathematical interpretation of the point splitting procedure in quantum field theory. Lecturas Matemáticas. 27 (2006), no. 2, 83-104.

Students

Master

  • 2019-1: Spectral Action and its Applications. Coadvisor. (Current). Juan Daniel López Castaño

Undergraduate

  • 2019-2: Estudio de la característica de Euler como invariante topológico para la clasificación de superficies (Current). Iván Andrés Orozco Macana
  • 2018-2: Theory of Lie Groups and Some Applications in Theoretical Physics. Jaime Junior Cuervo Cardenas
  • 2017-2: A Mathematical Interpretation of Feynman Diagrams and Dimensional Regularization via Hopf Algebras. Daniel Camilo Padilla González
  • 2017-2: Potencias Complejas de Operadores Pseudodiferenciales Elípticos. Juan Daniel López Castaño