Docentes profile for Joseph Varilly

Curriculum Vitae

Life cycle

• Professor, Escuela de Matemática, Universidad de Costa Rica, since 1979. Catedrático (Full Professor) since 1991.
• Subdirector of the Centro de Investigaciones Matemáticas y Metamatemáticas (CIMM), Universidad de Costa Rica, 2012-2021.
• Visitante Distinguido. Universidad Complutense de Madrid, Spain, Spring 2007.
• Visiting Marie Curie Professor, Uniwersytet Warszawski, Poland, Fall 2005.
• Associate Member of the International Centre for Theoretical Physics (ICTP), Trieste, Italy, 1998-2005.
• Visiting Professor. CINVESTAV del IPN, México, DF, Fall 1991.
• Ph. D. (Mathematics), University of Rochester. USA, 1980. Advisor: Gérard G. Emch.
• B. Sc. (Mathematical Science) and M. Sc. (Mathematics), University College, Dublin, 1972-73.

Research

After doctoral work on quantum statistical mechanics, my research centred on phase-space quantization (1985-95) and from 1992 on noncommutative geometry and its physical applications. Since 2010, I have also worked on problems in quantum chemistry and quantum field theory.

Selected publications

• The chirality theorem (with José M. Gracia-Bondía and Jens Mund).
  Annales Henri Poincaré 19, 843-874 (2018).
• Stora's fine notion of divergent amplitudes (with José M. Gracia-Bondía).
  Nuclear Physics B 912, 28-37 (2016).
• Improved Epstein-Glaser renormalization in x-space versus differential renormalization (with José M. Gracia-Bondía and Heidy Gutiérrez).
  Nuclear Physics B 886, 824-869 (2014).
• Elementos de geometría plana, second edition. Editorial de la UCR, San José, 2014.
• Riemannian manifolds in noncommutative geometry (with Steven Lord and Adam Rennie).
  Journal of Geometry and Physics 62, 1611-1638 (2012).
• Density functional theory on phase space (with Philippe Blanchard and José M. Gracia-Bondía).
  International Journal of Quantum Chemistry 112, 1134-1164 (2012).
• Introduction to Noncommutative Geometry, EMS Publishing House, Zürich, 2006.
• The Dirac operator on SUq(2) (with Ludwik Dabrowski, Giovanni Landi, Andrzej Sitarz and Walter van Suijlekom).
  Communications in Mathematical Physics 259, 729-759 (2005).
• Elements of Noncommutative Geometry, Birkhäuser, Boston, 2001. With José M. Gracia-Bondía and Héctor Figueroa.
• The Standard Model as a noncommutative geometry: the low energy regime (with José M. Gracia-Bondía and Carmelo Pérez Martín).
  Physics Reports 294, 363-406 (1998).
• The Moyal representation for spin (with José M. Gracia-Bondía).
  Annals of Physics 190, 107-148 (1989).
• Algebras of distributions suitable for phase-space quantum mechanics (with José M. Gracia-Bondía).
  Journal of Mathematical Physics 29, 869-879 (1988).

Mini-courses

• Tres caminos hacia la geometría elemental.
  CANP Conference: Construcción de Capacidades en Matemáticas y Educación Matemática, San José, Costa Rica, 2012.
• Dirac operators in noncommutative geometry.
  Instytut Matematyczny Polskiej Akademii Nauk (IMPAN), Warszawa, Poland, 2005.
• Examples of noncommutative geometrical spaces
  Winter School on Noncommutative Geometry and Mathematical Physics, CIRM, Marseille, France, 2004.
• Some applications of noncommutative geometry to physics
  Clay Mathematics Institute Spring School on Noncommutative Geometry and its Applications, Vanderbilt University, Nashville, TN, USA, 2003.
• Cyclic cohomology, Hopf algebras and quantum theory
  CIMPA Summer School on Geometric and Topological Methods in Quantum Field Theory, Villa de Leyva, Colombia, 2001.
• Noncommutative geometry and quantization
  X Jorge André Swieca Summer School of the Sociedade Brasileira de Física, Aguas de Lindoia, SP, Brasil, 1999.
• Introduction to noncommutative geometry
  EMS Summer School on Noncommutative Geometry and Applications, Monsaraz, Portugal, 1997.

Teaching

Current teaching

• MA-870: Geometría diferencial

Past teaching

• SP-1311: Análisis funcional (2018).
• SP-1329: Álgebra homológica (2018).
• MA-505: Análisis I (2017).
• MA-370: Principios de geometría (2010, 2013, 2016).
• MA-455: Ecuaciones diferenciales ordinarias (2016).
• MA-729: Teoría de representaciones (2015).
• MA-870: Geometría diferencial (2014).
• MA-561: Grupos y anillos (2014).
• SP-1322: Análisis real II (2012).
• MA-702: Variable compleja (2012).
• MA-704: Topología (2011).
• MA-707: Seminario de geometría no conmutativa (2010).
• MA-860: Teoría de módulos (2008).
• MA-460: Algebra lineal II (2007).
• MA-660: Teoría de Galois (2006).
• SP-1313: Clifford geometry (1995).
• IPN-MX: Teoría de grupos en cuantización (1991, en el CINVESTAV del IPN).
• MA-700: TeX: Edición programable de matemáticas (1990).

Last modified: Sept 2018