As we have seen, the technique used in our Main Theorem seems close to optimal, at least when restricted to the Lie groups SL(m,R). Nevertheless, the authors believe that for other families of symmetric spaces, there are likely to be improvements on…

We now establish the results on thermodynamic formalism and large deviations for CAT(−1) geodesic flows given in Theorem B. The results are proved for expansive flows with weak specification, and thus apply to geodesic flow on compact CAT(−1) spaces…

In this Section we complete the proof of Theorem 31, by showing that the S-extended I-function

In this paper we performed a detailed analysis of invariant measures on finite rank aperiodic Bratteli diagrams, both simple and non-simple. Here are some of the key findings:

In this section we compute the scattering matrix as well as the semiclassical spectral measure associated to H(ℏ). Thereby, we complete the proofs of Theorems 1.2 and 1.3. The most important step consists of computing the Wronskian W(f−(⋅,E;ℏ),f+(⋅,…

In the paper [GoPe] (see also [Go]) Goryachko and Petrov described all indecomposable characters on the group R of rational permutations of the unit interval [0,1). In this section we will apply Theorem 5.6 to get a new proof of their result.

The following construction generalizes that of (derdzinski-maschler-06, , §5) (in the case m=2), and gives rise to compact Kähler surfaces (M,g) with nonconstant Killing potentials τ, which have geodesic gradients, but need not be special Kähler-Ric…

Coates was supported in part by a Royal Society University Research Fellowship, ERC Starting Investigator Grant number 240123, and the Leverhulme Trust. Givental was supported in part by NSF grants DMS-0604705 and DMS-1007164. Tseng was supported in…

The resolvent trace, or equivalently the heat trace, expansion for second order Laplace type operators goes back at least to Minakshisundaram and Pleijel [MiPl49]. Via Karamata’s tauberian theorem there is a connection to the eigenvalue counting fun…

The regularity hypothesis in Theorem 1.3 can now be stated:

We now describe how, under appropriate hypotheses on the vector bundle E=E1⊕⋯⊕Er and the toric Deligne–Mumford stack X, Theorem 22 gives a mirror theorem for the complete intersection stack Y cut out by a generic section of E. Suppose that the vecto…

We describe here the SSRs which correspond to simple Heisenberg graded classical Lie algebras by Theorem 2.16.