University of Colorado at Boulder

Seminar on 

Deformation Theory

   Spring 2011:  Tuesdays 3-4 PM in MATH 350

This is a working seminar meant to introdruce deformation theory.  The seminar will be held in MATH 350.  The mathematics department is at the corner of Colorado Ave and Folsom St.  For a map of the campus, click here.  This could loosely be considered a continuation of last spring's seminar on  Stacks and Groupoids (although the material from that seminar is not a prerequisite).

Schedule of upcoming talks:

January 18
 Markus Pflaum and Sebastian Casalaina-Martin
 Organizational meeting
January 25
 Markus Pflaum
 An introduction to deformations
February 1 Markus Pflaum
 An introduction to deformations, part II
February 8
 Markus Pflaum
 An introduction to deformations, part III
February 15
 NO SEMINAR
 NO SEMINAR
February 22
 Sebastian Casalaina-Martin
 An elementary introduction to deformations from the perspective of algebraic geometry
March 1
 Sebastian Casalaina-Martin
 Tangent spaces and first order deformations
March 8
 Sebastian Casalaina-Martin
 Introduction to sheaves
March 15
 Eitan Angel
 Introduction to sheaves and cohomology: the Cech cohomology.
March 22
 NO SEMINAR
 NO SEMINAR
March 29
 Eitan Angel
 Sheaves and cohomology continued: derived functors.
April 5
 Eitan Angel
 Sheaves and cohomology: Riemann-Roch and Serre duality.
April 12
 Graeme Wilkin Holomorphic vector bundles and the Kodaira-Spencer map
April 19
 Graeme Wilkin
 Holomorphic vector bundles and the Kodaira-Spencer map, part II
April 26
 Graeme Wilkin Holomorphic vector bundles and the Kodaira-Spencer map, part III


This seminar is being continued in the fall.

References: 
  • M.J. Pflaum, Deformation Theory, in "Encyclopedia in Mathematical Physics" (J.-P. Francoise, G.L. Naber, T.S. Tsun, Eds.), Elsevier (2006) (pdf).
  • Kodaira, Complex manifolds and deformation of complex structures.
  • Sernesi, Deformations of algebraic schemes.
  • Fundamental Algebraic Geometry, Grothendiek's FGA explained, Fantechi et al.
  • There are some nice lecture notes on the website http://math.stanford.edu/~vakil/defthy/
  • Complexe Cotangent et Déformations I, II Lecture Notes in Mathematics, Illusie. (pdf from springer, free on campus)
  • For a little background on the physics related to deformation quantization: Mathematical methods in quantum physics, Teschl (pdf)



This seminar is being organized by Sebastian Casalaina-Martin and Markus Pflaum.  The web page is maintained by Sebastian Caslaina-Martin; it is yet another example of a shameless (indirect) copying of a webpage of Pasha Belorousski's at the University of Michigan.