Summary of Research

Ivan G. Avramidi

 

• Heat kernel asymptotic expansion
• Leading derivatives in the heat kernel and the nonlocal structure of the functional determinants
• Algebraic methods for the `low-energy' heat kernel
• Korteweg-de Vries hierarchy
• Second-order operators with a non-scalar leading symbol (non-Laplace type operators)
• Higher-order differential operators
• Oblique (Grubb-Gilkey-Smith) boundary value problem in gauge theories and quantum gravity on manifolds with boundary
• Non-smooth (Zaremba) boundary value problem
• Effective potential in Yang-Mills theory
• Higher derivative quantum gravity
• Higher spin fields in curved spacetime
• Propagation of radio-waves
• Review papers and books
• References
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