Final Report Summary - ARIPHYHIMO (Arithmetic and physics of Higgs moduli spaces)
The project concerns with the geometry and topology of moduli spaces of Higgs bundles on a Riemann surface motivated by parallel considerations in number theory and mathematical physics. In this way the proposal bridges various duality theories in theoretical physics with the Langlands program in number theory.
The results of the work done in this project include discoveries of refined knot invariants, numerical invariants of the Cosmic Galois Group,
Eulerian polynomials of permutahedra, new proofs of Kac's conjectures from 1982 in the representation theory of quivers, asymptotically locally flat complete hyperkähler metrics on irregular open de Rhams spaces, and p-adic integration for Hitchin fibrations; all in studies of arithmetic, representation theory, geometry and topology of moduli spaces of Higgs bundles and related hyperkähler spaces.
The results of the work done in this project include discoveries of refined knot invariants, numerical invariants of the Cosmic Galois Group,
Eulerian polynomials of permutahedra, new proofs of Kac's conjectures from 1982 in the representation theory of quivers, asymptotically locally flat complete hyperkähler metrics on irregular open de Rhams spaces, and p-adic integration for Hitchin fibrations; all in studies of arithmetic, representation theory, geometry and topology of moduli spaces of Higgs bundles and related hyperkähler spaces.