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Noncommutative Geometry Seminar - Yang Liu

photo of Yang Liu
October 1, 2015
10:30AM - 11:30AM
Math Building 105

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2015-10-01 10:30:00 2015-10-01 11:30:00 Noncommutative Geometry Seminar - Yang Liu Title: Modular curvature for toric noncommutative manifoldsSpeaker: Yang Liu (OSU)Abstract: A general question behind the talk is to explore a good notion for intrinsic curvature in the framework of noncommutative geometry started by Alain Connes in the 80’s.  It has only recently begun (2014) to be comprehended via the intensive study of modular geometry on the noncommutative two tori.  In this talk, we extend recent results on the modular geometry on noncommutative two tori to a larger class of noncommutative manifolds: toric noncommutative manifolds.  The first contribution of my work is a pseudo differential calculus which is suitable  for spectral geometry on toric noncommutative manifolds.  As a main application, we derive a general expression for the modular curvature with respect to a conformal change of metric on toric noncommutative manifolds.  By specializing our results to the noncommutative two  and four tori,  we recovered the modular curvature functions  found in the previous works.  An important technical aspect of the computation is that it is free of computer assistance. Math Building 105 Department of Mathematics math@osu.edu America/New_York public

Title: Modular curvature for toric noncommutative manifolds

Speaker: Yang Liu (OSU)

Abstract: A general question behind the talk is to explore a good notion for intrinsic curvature in the framework of noncommutative geometry started by Alain Connes in the 80’s.  It has only recently begun (2014) to be comprehended via the intensive study of modular geometry on the noncommutative two tori.  In this talk, we extend recent results on the modular geometry on noncommutative two tori to a larger class of noncommutative manifolds: toric noncommutative manifolds.  The first contribution of my work is a pseudo differential calculus which is suitable  for spectral geometry on toric noncommutative manifolds.  As a main application, we derive a general expression for the modular curvature with respect to a conformal change of metric on toric noncommutative manifolds.  By specializing our results to the noncommutative two  and four tori,  we recovered the modular curvature functions  found in the previous works.  An important technical aspect of the computation is that it is free of computer assistance.

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