lunedi' 28 maggio 2018 alle 16.30, in Aula Chisini, via Saldini 50,
California Institute of Technology
SPECTRAL THEORY, SUM RULES AND LARGE DEVIATIONS
ABSTRACT: After defining the spectral theory of orthogonal polynomials on the unit circle (OPUC) and real line (OPRL), I’ll describe Verblunsky’s version of Szego’s theorem as a sum rule for OPUC and the Killip–Simon sum rule for OPRL and their spectral consequences. Next I’ll explain the original proof of Killip– Simon using representation theorems for meromorphic Herglotz functions. Finally I’ll focus on recent work of Gamboa, Nagel and Rouault who obtain the sum rules using large deviations for random matrices.
Te': ore 16.00, Sala Rappresentanza
ABOUT THE SPEAKER: Barry Simon has been described as a “dynamo” in mathematical physics who requires “only five percent of the time ordinary mortals need” to write a research article. Author of more than 400 works including over 20 influential monographs, Simon’s fundamental research, exposition and mentoring of graduate students and postdocs has earned him a wealth or recognitions including the Henri Poincaré Prize in Mathematical Physics (2012), the AMS Leroy P. Steele for Lifetime Achievement (2016), the Hungarian Academy’s Bolyai Prize (2015) and the Dannie Heineman Prize for Mathematical Physics (2018). Simon has said of himself to have “the heart of a physicist, but the head of a mathematician” and his impact on mathematics and physics is difficult to underestimate. His fundamental contributions have been felt in quantum mechanics, quantum field theory, statistical mechanics, spectral theory, phase transitions and symmetry breaking in certain regimes fundamental to physics. Simon received his Ph.D in Physics at Princeton University in 1970 under the direction of Arthur S. Wightman and rose to the rank of Full Professor at Princeton within six years at the tender age of 30. In 1981, Simon moved to Caltech where he remains as the IBM Professor of Mathematics and Physics, Emeritus.
In collaborazione con il : SEMINARIO MATEMATICO E FISICO DI MILANO
Per ulteriore informazioni: http://www.mat.unimi.it/users/lezioleo/
K. Payne e B. Ruf
Dipartimento di Matematica "F. Enriques"
Universita' degli Studi di Milano
F. Cipriani e C.D. Pagani
Dipartimento di Matematica "F. Brioschi"
Politecnico di Milano
Dipartimento di Matematica e Applicazioni
Universita' di Milano Bicocca