Alain Connes and NCG

One of the first things that I learned about Non-Commutative Geometry (NCG) was that Alain Connes is the founder of NCG. I  googled his name, and I found out that he has traveled to Iran. I download the PDF of the interview which had been done by Khosroshahi and Eaman Eftekhari at IPM. then by reading the interview, I found out that NCG has got roots in Operator Algebra (OA) and some other fields of mathematics, but mainly it is rooted in OA. I remember in some…

Convex functions

Whenever we talk about convex functions, an inequality suddenly arise that presents an algebraic definition for a geometric content. I mean we have an image of convexity and from that imagination to this definition there is something to explain. The only thing I never have understood is that “what does it come from?” “Why we define a convex function as something that satisfies in such inequality?” The below image is just an example of a mathematical book (Rudin, complex and real analysis) but you can…

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