Movshev minicourse on pure spinors

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Title: Beta gamma systems on affine cones and local cohomology: Computation of pure spinor correlation functions

Lecturer: Mikhail Movshev (SUNY at Stony Brook, USA)

Start time: December 2, 2016, 14h

Lecture 1: December 2 (friday), 14h00

Lecture 2: December 5 (monday), 14h00

Lecture 3: December 7 (wednesday), 16h00

Lecture 4: December 9 (friday), 14h00

Lecture 5: January 25 (wednesday), 14h00

Lecture 6: January 27 (friday), 14h00

Lecture 7: February 1 (wednesday), 14h00

Lecture 8: February 3 (friday), 14h00

Place: Third floor of IFT-UNESP – Room 3

Beta gamma system on pure spinors is a central object in the covariant formulation of the super string theory. To give an accurate mathematical description of this beta gamma system turned to be a nontrivial task due to singularity of the cone of pure spinors. In this course I will explain how this can be overcome by using machinery of local algebra. No prior knowledge of it is assumed. In particular we will compute the full partition function and I explain the method of computing the correlators.


0. Overview of the approach and principal results including computation of the full partition function for pure spinors.
1. Computation of Poincare series for spaces of Drinfeld’s quasimaps. Reduction to a problem of combinatorics.Gorenstein property.
2 Overview of local cohomology. Local cohomology as a space of states of a free system with finite number degrees of freedom.
3. Space of beta gamma system as a semi-infinite local cohomology. Importance of the Gorenstein condition.
4. Numerical analysis of the full partition function of the beta-gamma system on pure spinors.
5. An approach to computation of correlators of the beta-gamma system on pure spinors.

A “Certificate of Attendance” will be offered by the IFT Graduate Program to those participants attending the lectures.

There will be no application form for this activity and everyone is welcome to participate. For more information, send email to