Prakash Belkale

from Wikipedia, the free encyclopedia

Prakash Belkale is an Indian-American mathematician who studies algebraic geometry .

life and work

Belkale received his PhD from the University of Chicago in 1999 with Madhav Nori . He is a professor at the University of North Carolina at Chapel Hill .

He is best known for rebutting the Spanning Tree Conjecture by Maxim Kontsevich (1997) in 2003 with Patrick Brosnan . It concerns the number-theoretical properties of Feynman graphs of a simple model theory of quantum field theory, the theory. It was part of a theory of the mathematical properties of Feynman graphs developed by David Broadhurst and Dirk Kreimer from the perturbative treatment of quantum field theories. Kontsevich hypothesized that the function which gives the number of points on the hypersurface belonging to the Feynman graph over finite fields (with , p prim) is a polynomial in q. The conjecture was numerically well confirmed (and it applies to lower order Feynman graphs) and the rebuttal came as a surprise at the time. The conjecture would have led to another conjecture that the Feynman amplitudes could have been represented as rational multiples of multiple zeta functions and the refutation by Brosnan and Belkale showed that the relationships were much more complex, which was later worked out more precisely by Francis Brown and others .

He deals with counting algebraic geometry (Schubert calculus) and connection to intersection theory and representation theory, with quantum cohomology and with modular spaces of vector space bundles on curves (conformal blocks, strange duality).

In 2010 he was invited speaker at the International Congress of Mathematicians in Hyderabad (The tangent space to an enumerative problem).

Fonts

  • Transformation formulas in quantum cohomology, Composition Math., 140, 2004, pp. 778-792, Arxiv
  • Strange duality and the Hitchin / WZW connection, J. Diff. Geom., Vol. 82, 2009, pp. 229-465, Arxiv
  • Unitarity of the KZ / Hitchin connection on conformal blocks in genus 0 for arbitrary Lie algebras, J. Math. Pures Appl., Volume 98, 2012, 367-398 Arxiv
  • Geometric Proofs of Horn and Saturation Conjectures, J. of Algebraic Geometry, Arxiv
  • Invariant Theory of GL (n) and intersection theory of Grassmannians, Internat. Math. Research Notes, Vol. 69, 2004, pp. 3709-3721
  • with Brosnan: Periods and Igusa local zeta functions, Int. Math. Res. Not., Vol. 49, 2003, pp. 2655-2670, Arxiv

literature

  • Michel Brion: Restriction de représentations et projection d'orbites coadjointes, d'après Belkale, Kumar et Ressayre, Bourbaki Seminar 1043, 2011
  • Christian Pauly: La dualité étrange, d'après P. Belkale, A. Marian et D. Oprea, Bourbaki Seminar 994, 2008

Web links

Individual evidence

  1. ↑ Prakash Belkale in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. ↑ Belkale, Brosnan Matroids motives, and a conjecture of Kontsevich , Duke Math. J., Volume 116, 2003, pp. 1-188, Arxiv
personal data
SURNAME Belkale, Prakash
BRIEF DESCRIPTION Indian-American mathematician
DATE OF BIRTH 20th century