Speaker: 1.Prof. Jeu-Liang Sheu (University of Kansas) 2.Prof. Mourad Ismail (University of Central Florida)
Title: 1.Rosenberg's noncommutative Gauss-Bonnet theorem 2.Approximation by exponential operators.
Time: 2015-06-11 (Thu.)  15:00 - 17:15
Place: Auditorium, 6 Floor, Institute of Mathematics (NTU Campus)
Abstract: 1.Based on the concept of connections in noncommutative geometry introduced by Connes and used in Connes and Rieffel's successful classification of Yang-Mills moduli for the noncommutative two-torus, Jonathan Rosenberg proposed a simple framework extending the classical notion of Levi-Civita connections in Riemannian geometry to the noncommutative tori, proving its existence and uniqueness and establishing an analogue of the Gauss-Bonnet theorem for the noncommutative two-torus with a conformal deformation of the flat metric. In this talk, we present some relevant observations and the finding that the Gauss-Bonnet theorem still holds for a class of non-commuting and hence non-conformal scalings along the principal directions of a two-torus. (This is a joint work with Mira A. Peterka.)

2.We survey some of the work on approximation of continuous functions by positive linear operators. We will mention in some detail the exponential operators associated with exponential families of probability distributions.

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