From symplectic geometry to combinatorics and back - Cristofaro Gardiner 01:05:27 Free group Cayley graph and measure decompositions - Yong Hou 58:44 Diophantine properties of Markoff numbers - Jean Bourgain 01:01:15 A frontal view on Lefschetz fibrations I - Emmy Murphy 01:01:02 A fro...
On some aspects of the geometry of differential equations in physics”, Int - Gràcia, Muñoz-Lecanda, et al.X. Gràcia, M. C. Muñoz-Lecanda, and N. Román-Roy, “On some aspects of the geometry of differential equations in physics,” Int. J. Geometric Methods Mod. Phys. , 1 ,...
Cycles on the moduli of Shtukas and Taylor coefficients of L-functions - Zhang 01:04:32 Geometric structures and thin groups II - Darren Long 40:52 Geometric structures and thin groups I - Alan Reid 44:36 From symplectic geometry to combinatorics and back - Cristofaro Gardiner 01:05:27...
The Schlfli identity, which is important in Regge calculus and loop quantum gravity, is examined from a symplectic and semiclassical standpoint in the special case of flat, three-dimensional space. In this case a proof is given, based on symplectic geometry. A series of symplectic and Lagrangian...
RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS Vol. 16 No. 3 2009 ALGEBRAIC ASPECTS OF THE HIRZEBRUCH SIGNATURE OPERATOR 419 Example 3.5 [classical]. Let (V, G) be a real N -dimensional oriented Euclidean space with an inner product G : positive ON basis V of × V V ). → We R and the ...
The purpose of these lectures is to give an introduction to the topological aspect s of the loop space ΩG when G is a compact Lie group. We will give a direct method of computing the cohomology of ΩG from very geometric and group theoretic data, usuall
Mathematical PhysicsGeneral Relativity and Quantum CosmologyThe Schlfli identity, which is important in Regge calculus and loop quantum gravity, is examined from a symplectic and semiclassical standpoint in the special case of flat, three-dimensional space. In this case a proof is given, based on ...
Journal of Geometry & PhysicsN.J. Hitchin. Geometrical aspects of Schlesinger's equation. J. Geom. Physics, 23(3-4):287-300, 1997.N. Hitchin, Geometrical aspects of Schlesinger's equation. J. Geom. Phys. 23 (1997), no. 3-4, 287-300....
(Recall, for instance, the symplectic structure of phase space and Liouville's theorem.) To what extent mechanics is of geometric nature is illustrated by the fact that, historically, it gave important impulses to the development of differential geometry. In turn, the modern formulation of ...
differential geometryFaddeev and Vershik proposed the Hamiltonian and Lagrangian formulations of constrained mechanical systems that are invariant from the differential geometry standpoint. In both formulations, the description is based on a nondegenerate symplectic 2 -form defined on a cotangent bundle T*...