Event From Date
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Event Title
SPS organises a seminar by Sameer Chavan
Event Details
Mathematics Seminar TODAY, TUESDAY MARCH 5, 2019 at 4PM at SPS, JNU
with details as below and in the attached poster:
Title: Brown-Douglas-Fillmore Theorem
Speakar: Sameer Chavan, Department of Mathematics, Indian Institute of Technology Kanpur
Date: March 5, 2019 (TUESDAY)
Time: 4PM
Venue: Seminar Room, SPS, JNU
Time: 4PM
Venue: Seminar Room, SPS, JNU
Abstract: A bounded linear operator is essentially normal if its self-commutator is com- pact. By essential equivalence of two operators, we mean unitary equivalence modulo compact operators. The celebrated Brown-Douglas-Fillmore Theorem (or the BDF theorem) classifi\u000Ces
all essentially normal operators up to essential equivalence by means of the essential spectrum and index data. The original proof of the BDF theorem relies on the idea of associating to every compact Hausdor space X the group Ext(X) of -monomorphisms from the contin-
uous functions on X into the Calkin algebra. It turns out that for planar sets, this group is isomorphic to the group of homomorphisms from the \u000Cfirst cohomotopy group into the set of integers. We will discuss two special cases of this theorem. The fir\u000Cst of which, usually known as Weyl-von Neumann theorem, says that two self-adjoint operators are essentially equivalent
if and only they have same essential spectrum. In terms of the extension group, this result says that Ext(X) must be trivial for any compact subset X of the real line. The second interesting case identi\u000Cfies the extension group of the unit circle with the group of integers.
The talk will be accessible to a wider audience.
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Seminar Co-ordinator, SPS, JNU
