BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Discrete Vector Bundles with Connection and the First Chern Class 
 - Anil  Hirani (University of Illinois at Urbana-Champaign)
DTSTART:20191002T083000Z
DTEND:20191002T093000Z
UID:TALK130654@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The use of differential forms in general relativity requires i
 ngredients like the covariant exterior derivative and curvature. One poten
 tial approach to numerical relativity would require discretizations of the
 se ingredients. I will describe a discrete combinatorial theory of vector 
 bundles with connections. The main operator we develop is a discrete covar
 iant exterior derivative that generalizes the coboundary operator and yiel
 ds a discrete curvature and a discrete Bianchi identity. We test this theo
 ry by defining a discrete first Chern class\, a topological invariant of v
 ector bundles.  This discrete theory is built by generalizing discrete ext
 erior calculus (DEC) which is a discretization of exterior calculus on man
 ifolds for real-valued differential forms. In the first part of the talk I
  will describe DEC and its applications to the Hodge-Laplace problem and N
 avier-Stokes equations on surfaces\, and then I will develop the discrete 
 covariant exterior derivative and its implications. This is joint work wit
 h Daniel Berwick-Evans and Mark Schubel.
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR