15 citations · 17 across the 2 of their papers we have counts for
13 papers
Dirac Operator in Matrix Geometry
Ivan G. Avramidi
We review the construction of the Dirac operator and its properties in Riemannian geometry and show how the asymptotic expansion of the trace of the heat kernel determines the spec…
A Noncommutative Deformation of General Relativity
Ivan Avramidi
We develop a novel approach to gravity in which gravity is described by a matrix-valued symmetric two-tensor field and construct an invariant functional that reduces to the standar…
Heat Kernel Asymptotics of Zaremba Boundary Value Problem
Ivan Avramidi
The Zaremba boundary-value problem is a boundary value problem for Laplace-type second-order partial differential operators acting on smooth sections of a vector bundle over a smoo…
A discrete leading symbol and spectral asymptotics for natural differential operators
Ivan Avramidi, Thomas Branson
We initiate a systematic study of natural differential operators in Riemannian geometry whose leading symbols are not of Laplace type. In particular, we define a discrete leading s…
Foundational Problems in Quantum Gravity
Ivan G. Avramidi, Giampiero Esposito
Boundary conditions play a crucial role in the path-integral approach to quantum gravity and quantum cosmology, as well as in the current attempts to understand the one-loop semicl…
A new explicit expression for the Korteweg-De Vries hierarchy
Ivan G. Avramidi, Rainer Schimming
We derive an improved fully explicit expression for the right-hand sides of the matrix KdV hierarchy using the relation to the heat kernel of the one-dimensional Schrödinger operat…