In quantum mechanics, the momentum space and position space wave functions are related by the Fourier transform. We investigate how the Fourier transform arises in the context of geometric quantization. We consider a Hilbert space bundle H over the space J of compatible complex structures on a symplectic vector space. This bundle is equipped with a projectively flat connection. We show that par...

We show that noncongruence subgroups of SL2(Z) projectively equivalent to congruence subgroups are ubiquitous. More precisely, they always exist if the congruence subgroup in question is a principal congruence subgroup Γ(N) of level N > 2, and they exist in many cases also for Γ0(N). The motivation for asking this question is related to modular forms: projectively equivalent groups have the sam...

We investigate the action of semigroups of d× d matrices with entries in the max-plus semifield on the max-plus projective space. Recall that semigroups generated by one element with projectively bounded image are projectively finite and thus contain idempotent elements. In terms of orbits, our main result states that the image of a minimal orbit by an idempotent element of the semigroup with m...

Abstract. A function is exponentially concave if its exponential is concave. We consider exponentially concave functions on the unit simplex. It is known that gradient maps of exponentially concave functions are solutions of a MongeKantorovich optimal transport problem and allow for a better gradient approximation than those of ordinary concave functions. The approximation error, called L-diver...