Dr. Miroslav Engliš of the Mathematics Institute at the Czech Academy of Sciences in Prague, will visit campus for the Shoemaker Lecture Series, which will take place Monday through Wednesday, Sept. 11-13.
Each talk will begin at 4 p.m.Engliš’ first lecture, “An Excursion Into Berezin-Toeplitz Quantization and Related Topics,” will be held Monday, Sept. 11, in Gillham Hall Room 5300.
“This talk will discuss an elegant quantization procedure that is based on methods from analysis of several complex variables,” he said. “Further highlights will include connections to Lie group representations or related developments for harmonic functions.”
The second lecture titled “Arveson-Douglas Conjecture and Toeplitz Operators” will take place Tuesday, Sept. 12, in Memorial Field House Room 1270.
“A basic problem in multivariable operator theory is finding appropriate ‘models’ for tuples of operators. For the case of commuting tuples, this is resolved by a nice theory developed by William Arveson, and the question of the size of the commutators of the model operators with their adjoints is the subject of the Arveson-Douglas conjecture,” Engliš said. “Though the latter is still open in full generality at the moment, we give a proof of the conjecture in a special case, using methods verging on microlocal analysis and complex analysis of several variables.”
The final lecture on “Reproducing Kernels and Distinguished Metrics” will be held Wednesday, Sept. 13, in Gillham Hall Room 5300.
“I will discuss the questions of existence and uniqueness of balanced metrics on noncompact complex domains, where some answers are yet unknown nowadays even for the simplest case of the unit disc,” Engliš said.
His free, public talks are made possible by the Richard Shoemaker Funds and are sponsored by the Mathematics and Statistics Department, as well as the College of Natural Sciences and Mathematics.
For more information, go to math.utoledo.edu/shoemaker.html.