On the semantics of noncommutative geometry and exotic summation formulas.
Model Theory in Geometry and Arithmetic May 12, 2014  May 16, 2014
Location: SLMath: Eisenbud Auditorium
v1348
On the semantics of noncommutative geometry and exotic summation formulas.
Abtract. The wellknown duality of classical algebraic geometry between affine varieties and their coordinate rings has a perfect analogue in the theory of
commutative C^*algebras, which can be seen by the Gel'fandNaimark theorem as the algebras of continuous complexvalued functions on a compact Hausdorff space.
We interpret this as the SyntaxSemantics duality.
In modern geometry and physics one deals with much more advanced generalisations of coordinate algebras, such as schemes, stacks and noncommutative
C^*algebras, where a geometric counterpart is no longer readily available and in many cases is believed impossible.
I will discuss some results of a modeltheoretic project which challenges this point of view. This will be illustrated by an application calculating classically nonconvergent infinite sum.
v1348
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