| Start Date: | 6/1/2015 | Start Time: | 3:00 PM |
| End Date: | 6/1/2015 | End Time: | 4:00 PM |
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Event Description
Joseph A. Ball, Virginia Tech
Abstract: The Nevanlinna-Pick interpolation theorem, now approaching its centennial, characterizes when it is possible to find a holomorphic function _f _mapping the unit disk into the closed unit disk while satisfying some additional prescribed interpolation conditions in terms of the positivity of an associated Pick matrix constructed explicitly from the interpolation data. It was not until 1990 that Jim Agler found a parallel result for when it is possible to map the bidisk holomorphically into the closed disk while simultaneously satisfying a collection of prescribed interpolaton conditions; the criterion involves having to solve a matrix equation for a pair of positive Pick matrices rather than inspecting a single Pick matrix explicitly constructed from the data. We discuss recent generalizations of these ideas to the setting of so-called free noncommutative functions, a sort of quan- tization of classical function theory whereby one studies functions on tuples of square matrices of all possible sizes satisfying some additional compatibility properties rather than on tuples of complex numbers (see [KVV]). This talk reports on current joint work with Gregory Marx (Virginia Tech) and Victor Vinnikov (Ben Gurion University). |
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Location:
Korman Center, Room 245, 15 South 33rd Street, Philadelphia, PA 19104 |
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