Gábor Francsics

Research Interests

Partial differential equations, several complex variables, complex hyperbolic spaces, microlocal analysis, scattering theory. I am also interested in financial mathematics..

In the Fall of 2008 I was on sabbatical leave at the Mathematical Sciences Research Institute in Berkeley. I was a research member of the Analysis on Singular Spaces Program.

Teaching

• Spring 2013:
  • Introduction to Financial Mathematics, MTH 457-001.
• Fall 2012:
  • PDE's in Financial Mathematics, MTH 890-002.
  • Theory of Mathematical Interest, MTH 360, MWF 11:30-12:20.
• Spring 2012:
  • Introduction to Financial Mathematics, MTH 457-001.
• Fall 2011:
  • Linear Algebra, MTH 309-002, MTH 309-006.
• Spring 2011:
  • Introduction to Financial Mathematics, MTH 457-001.
• Fall 2010:
  • PDE's in Financial Mathematics, MTH 890-001.
  • Multivariable Calculus, MTH 234, MWF 12:40-13:30.
• Spring 2010:
  • Introduction to Financial Mathematics, MTH 457-001.
• Fall 2009:
  • PDE's in Financial Mathematics, MTH 890-001.
  • Multivariable Calculus, MTH 234, MWF 12:40-13:30.

Publications

My research area is partial differential equations, several complex variables, complex hyperbolic spaces, microlocal analysis, scattering theory. I am also interested in financial mathematics. This is a link to the webpage of the MSU PDE seminar.

Some of my recent papers:

• "Analytic regularity for the Bergman kernel" (joint work with N. Hanges), Journees Equations aux derivees partielles, Saint-Jean-de-Monts, 1998, Expose V.
• Treves curves and the Szego Kernel (joint work with N. Hanges), Indiana Univ. Math. Journal, 47(1998) 995-1009.
• "The Bergman kernel for convex tubes" (joint work with N. Hanges), Schrödinger Institute Preprint, ESI 808 (1999) 1-39, December 1999.
• "Analytic singularities of the Bergman kernel for tubes" (joint work with N. Hanges), Duke Mathematical Journal, 108(2001) 539--580.
• "A fundamental domain for the Picard modular group" (joint work with P. Lax), Schrödinger Institute Preprint, ESI 1273 (2003) 1-19, January 2003.
• "A semi-explicit fundamental domain for the Picard modular group in complex hyperbolic space" (joint work with P. Lax), Contemporary Mathematics, 368 (2005) 211-226.
• "An explicit fundamental domain for the Picard modular group in two complex dimensions" (joint work with P. Lax), Preprint 2005, (pdf version here ).
• "Spectral analysis on complex hyperbolic spaces" (joint work with P. Lax), Proceedings of Hayama Symposium on Complex analysis in Several Variables, 2005.
• "Analysis of a Picard modular group" (joint work with P. Lax), Proceedings of National Academy of Sciences, 103(2006), 11103-11105.
• "Generators of a Picard modular group in two complex dimensions" (joint work with E. Falbel, P. Lax and John R. Parker), Preprint 2009, to appear in Proceedings of the American Mathematical Society.
• "Geometry of the Gauss-Picard modular group" (joint work with E. Falbel, and John R. Parker), Mathematische Annalen, 349(2011), Number 2, 459-508.

Interesting Conferences

A Conference Celebrating the Mathematics and 75th Birthday of Francois Treves
April 8-10, 2005, Rutgers University, New Jersey.

Phase Space Analysis and related topics
September 15-18, 2004, Grado, Italy.

Workshop on Geometric Analysis of PDE and Several Complex Variables Serra Negra, S. Paulo, Brazil August 04-09, 2004

Program in Complex Analysis
November 2000, Schrödinger Institute for Mathematical Physics, Vienna.

Conference on Microlocal Analysis and Partial Differential Equation
April 6-9, 2000 University of Notre Dame, Notre Dame
Here is the postscript version of the abstract of my talk "Waves on complex hyperbolic spaces".