Event Detail

Event Type: 
Analysis Seminar
Date/Time: 
Monday, May 11, 2015 - 12:00 to 13:00
Location: 
BAT 250

Speaker Info

Institution: 
Higher School of Economics, Moscow, Undergraduate Student
Abstract: 

In study of geometrical objects it is often useful to look at their spaces of functions. In most cases these spaces turn out to be commutative algebras with certain properties. Moreover, it is quite usual that correspondence between geometrical objects and spaces is bijective (Nullstellensatz for affine algebraic varieties over the field of complex numbers and commutative unital finitely generated algebras without nilpotents, Gelfand-Naimark theorem for compact Hausdorff spaces and unital commutative C*-algebras). The idea of non-commutative geometry is to expand this correspondence and to look at non-commutative algebras as at ‘spaces of functions’ of ‘non-commutative geometric objects’. Quantum tori are a good example of this approach. There are at least five known versions of such tori: algebraic, holomorphic, smooth, continuous, and essentially bounded measurable. Among them algebraic, continuous and smooth are the most well studied ones. Holomorphic (or complex analytic) quantum torus is a relatively new object, though it shares some properties with its counterparts. For example, I will show that it has the same condition of simplicity as algebraic, continuous and smooth quantum tori.