PhD Defense Tommaso Aschieri
Title: Sharp Quantization with Symmetry
Abstract:
This thesis studies Berezin-Toeplitz quantization of complex projective spaces. We establish optimal remainder bounds for the asymptotic expansion of the Berezin transform. Our estimates require minimal regularity conditions on functions and achieve asymptotically sharp constants.
We also derive the complete asymptotic expansion for products of Toeplitz operators under weaker regularity assumptions than previously known. The results are optimal in regularity requirements and the constants obtained are sharp. The remainder terms exhibit a striking feature: they have a sign and are operator-bounded by the next term in the expansion.
Finally, we study semiclassical approximations of quantum channels, proving entropy estimates for SU(2)-equivariant channels in terms of generalized Wehrl entropies. We discuss partial extensions to SU(d).
Advisor: Jan Philip Solovej, MATH, University of Copenhagen
Assessment committee:
Albert Werner (chair), MATH, University of Copenhagen
Mariá Ángeles Garcia-Ferrero, Instituto de Ciencias Matematicas (ICMAT), Madrid, Spain
Eric Anders Carlen, Rutgers University, Piscataway NJ, USA