Noncommutative geometry and number theory: Where arithmetic meets geometry and physics

Front Matter....Pages i-viii
The Hecke algebra of a reductive p -adic group: a geometric conjecture....Pages 1-34
Hilbert modular forms and the Ramanujan conjecture....Pages 35-56
Farey fractions and two-dimensional tori....Pages 57-77
Transgressions of the Godbillon-Vey Class and Rademacher functions....Pages 79-107
Archimedean cohomology revisited....Pages 109-140
A twisted Burnside theorem for countable groups and Reidemeister numbers....Pages 141-154
Introduction to Hopf-Cyclic Cohomology....Pages 155-178
The non-abelian (or non-linear) method of Chabauty....Pages 179-185
The residues of quantum field theory - numbers we should know....Pages 187-203
Phase transitions with spontaneous symmetry breaking on Hecke C * -algebras from number fields....Pages 205-216
On harmonic maps in noncommutative geometry....Pages 217-234
Towards the fractional quantum Hall effect: a noncommutative geometry perspective....Pages 235-261
Homological algebra for Schwartz algebras of reductive p-adic groups....Pages 263-300
A non-commutative geometry approach to the representation theory of reductive p -adic groups: Homology of Hecke algebras, a survey and some new results....Pages 301-321
Three examples of non-commutative boundaries of Shimura varieties....Pages 323-340
Holomorphic bundles on 2-dimensional noncommutative toric orbifolds....Pages 341-359
A New short proof of the local index formula of Atiyah-Singer....Pages 361-372