Mathematical Sciences: Heat Flow Estimates and Berezin-Toeplitz Algebras

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9500716 Coburn Coburn will continue studies of heat flow estimates and Berezin-Toeplitz algebras in several directions. Efforts will be continued to develop "backward heat estimates", obtained for the usual heat equation in earlier work with C. A. Berger, to more general parabolic equations. Another focus will be to follow-up recent work with J. Xia on "Toeplitz algebras and Rieffel deformations" to check whether Toeplitz algebras on bounded domains are generally "strict deformation quantizations" of the corresponding algebras of continuous functions. Coburn and Berger will also follow-up Coburn's work on "Deformation estimates for the Berezin-Toeplitz quantization" to obtain isomorphism invariants for the algebras of (boson) canonical commutation relations. These invariants arise from an appropriate extension of the index theorem to pseudo-differential operators with "eventually slowly varying" symbols. ***