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Prakash Belkale

{{Short description|Indian-American mathematician}}

{{Use dmy dates|date=December 2018}}

{{Use Indian English|date=December 2018}}

Prakash Belkale (born May 1973, Bangalore) is an Indian-American mathematician, specializing in algebraic geometry and representation theory.{{cite book|first=Michel |last=Brion|title=Restriction de représentations et projection d'orbites coadjointes, d'après Belkale, Kumar et Ressayre|series=Bourbaki Seminar 1043|year=2011}}{{cite book|author=Christian Pauly|title=La dualité étrange, d'après P. Belkale, A. Marian et D. Oprea|series=Bourbaki Seminar 994|year=2008}}

Education and career

Belkale received his Ph.D. in 1999 from the University of Chicago with thesis advisor Madhav Nori.{{MathGenealogy|id=38253}}

In 2003, together with Patrick Brosnan, Belkale disproved Maxim Kontsevich's Spanning-Tree Conjecture (first published in 1997).{{cite journal|last1=Belkale|first1=Prakash|last2=Brosnan|first2= Patrick|authorlink2=Patrick Brosnan|title=Matroids, motives and a conjecture of Kontsevich|journal=Duke Mathematical Journal |volume=116|year=2003|issue=1 |pages=1–188|doi=10.1215/s0012-7094-03-11615-4|arxiv=math/0012198|s2cid=7966214}}

{{quotation|Let G be a finite connected graph. The Kirchhoff polynomial of G is a certain homogeneous polynomial whose degree is equal to the first betti number of G. These polynomials appear in the study of electrical circuits and in the evaluation of Feynman amplitudes. Motivated by work of D. Kreimer and D. J. Broadhurst associating multiple zeta values to certain Feynman integrals, Kontsevich conjectured that the number of zeros of a Kirchhoff polynomial over the field with q elements is always a polynomial function of q. We show that this conjecture is false by relating the schemes defined by Kirchhoff polynomials to the representation spaces of matroids. Moreover, using Mnev's universality theorem, we show that these schemes essentially generate all arithmetic of schemes of finite type over the integers.}}

Belkale works on enumerative algebraic geometry, quantum cohomology and moduli spaces of vector bundles on curves (conformal blocks and strange duality), and the Schubert calculus and its connections to intersection theory and representation theory. He is a professor at the University of North Carolina at Chapel Hill.

In 2010 he was an invited speaker at the International Congress of Mathematicians in Hyderabad and gave a talk The tangent space to an enumerative problem. In December 2014 he was elected a Fellow of the American Mathematical Society.

Selected publications

  • {{cite journal|title=Local systems on \mathbb{P}^{1} – S for S a finite set|journal=Compositio Mathematica|volume=129|issue=1|year=2001|pages=67–86|doi=10.1023/A:1013195625868|last1=Belkale|first1=Prakash|doi-broken-date=1 November 2024 |doi-access=free}}
  • {{cite journal|title=Invariant Theory of GL(n) and intersection theory of Grassmannians|journal=Int. Math. Res. Not.|volume=2004|year=2004|pages=3709–3721|last1=Belkale|first1=Prakash|issue=69|doi=10.1155/S107379280414155X|doi-access=}}
  • {{cite journal|title=Periods and Igusa Local Zeta functions|journal=Int. Math. Res. Not.|volume=2003|year=2003|pages=2655–2670|last1=Belkale|first1=Prakash|last2=Brosnan|first2=Patrick|issue=49|doi=10.1155/S107379280313142X|doi-access=}}
  • {{cite journal|title=Eigenvalue problem and a new product on cohomology of flag varieties|journal=Invent. Math.|volume=166|issue=1|year=2006|pages=185–228|doi=10.1007/s00222-006-0516-x|arxiv=math/0407034|bibcode=2006InMat.166..185B|last1=Belkale|first1=Prakash|last2=Kumar|first2=Shrawan|s2cid=1825694}}
  • {{cite journal|title=The strange duality conjecture for generic curves|journal=J. Amer. Math. Soc.|volume=21|issue=1|year=2008|pages=235–258|mr=2350055|doi=10.1090/S0894-0347-07-00569-3|arxiv=math/0602018|bibcode=2008JAMS...21..235B|last1=Belkale|first1=Prakash|s2cid=3096761}}
  • {{cite journal|title=Quantum generalization of the Horn conjecture|journal=J. Amer. Math. Soc.|volume=21|issue=2|year=2008|pages=365–408|url=https://www.ams.org/journals/jams/2008-21-02/S0894-0347-07-00584-X/S0894-0347-07-00584-X.pdf|doi=10.1090/S0894-0347-07-00584-X|bibcode=2008JAMS...21..365B|arxiv=math/0303013|last1=Belkale|first1=Prakash|s2cid=407064}}
  • {{cite journal|title=The tangent space to an enumerative problem|journal=Proceedings of the International Congress of Mathematicians|year=2010|url=http://www.mathunion.org/ICM/ICM2010.2/Main/icm2010.2.0405.0426.pdf|last1=Belkale|first1=Prakash}}
  • {{cite journal|title=Unitarity of the KZ/Hitchin connection on conformal blocks in genus 0 for arbitrary Lie algebras|journal= J. Math. Pures Appl.|volume=98|issue= 4|year=2012|pages=367–398|doi=10.1016/j.matpur.2012.02.008 |arxiv=1101.5846|last1= Belkale|first1= Prakash|s2cid= 119138383}}

References

{{reflist}}

External links

  • [http://www.unc.edu/~belkale/ Homepage]

{{Authority control}}

{{DEFAULTSORT:Belkale, Prakash}}

Category:1973 births

Category:Living people

Category:Algebraic geometers

Category:University of Chicago alumni

Category:University of North Carolina alumni

Category:American people of Kannada descent

Category:20th-century Indian mathematicians

Category:21st-century Indian mathematicians

Category:Fellows of the American Mathematical Society

Category:Scientists from Bengaluru