K. Ilinski: Key results in physics and mathematics

New explicit relationship between analytical properties of meromorphic functions on Riemann surfaces and differential-geometric characteristics of these surfaces

Next step after Riemann-Roch Theorem.  Application of Supersymmetrical Quantum Field Theory brings new unexpected results in 150-years old branch of mathematics. Generalization from Riemann to Klein surfaces.

First index theorem for differential operators on Klein surfaces. N.V. Borisov, K.N. Illinski and G.V. Kalinin, “New Index Formulas as a Meromorphic Generalization of the Chern-Gauss-Bonnet Theorem”, Lett.Math.Phys. 43 (1998), 249-262

Resulting from

N.V. Borisov and K.N. Ilinski “N=2 Supersymmetric Quantum Mechanics on Riemann Surfaces with Meromorphic Superpotentials”, Commun.Math.Phys. 161 (1994), 177-194

A.D. Dolgallo and K.N. Ilinski “Generalised supersymmetric quantum mechanics on Riemann Surfaces with meromorphic superpotentials”, J.Math.Phys. 35(5) (1994), 2074-2082

N.V. Borisov and K.N. Il'inskii, “Supersymmetry on noncompact manifolds and complex geometry”, Journal of Mathematical Sciences, Vol. 85, No 1 (1997), 1605-1618

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