Extra Form
강연자 Raphael Ponge
소속 서울대학교
date 2011-09-22
A general goal of noncommutative geometry (in the sense of A. Connes) is to translate the main tools of differential geometry into the Hilbert space formalism of quantum mechanics by taking advantage of the familiar duality between spaces and algebras. In this setting noncommutative spaces are only represented through noncommutative algebras that play formally the role of algebras of functions on these (ghost) noncommutative spaces.?As?a?result,?this allows us to deal with a variety of geometric problems whose noncommutative nature prevent us from using tools of classical differential geometry. In particular, the Atiyah-Singer index theorem untilmately holds in the setting of noncommutative geometry.
The talk will be an overview of the subject with a special emphasis on quantum space-time and diffeomorphism invariant geometry. In particular, if time is permitted, ?it is planned to allude to recent projects in biholomorphism invariant geometry of complex domains and contactomorphism invariant geometry of contact manifolds.
첨부 '1'
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  2. 원의 유리매개화에 관련된 수학

  3. Introduction to Non-Positively Curved Groups

  4. 07Nov
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    in 수학강연회

    Noncommutative Geometry. Quantum Space-Time and Diffeomorphism Invariant Geometry

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  7. Codimension Three Conjecture

  8. 학부생을 위한 강연: 건축과 수학

  9. Classical and Quantum Probability Theory

  10. Iwasawa main conjecture and p-adic L-functions

  11. 학부생을 위한 강연: Choi's orthogonal Latin Squares is at least 61 years earlier than Euler's

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  13. Sums of squares in quadratic number rings

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  15. 곡선의 정의란 무엇인가?

  16. The significance of dimensions in mathematics

  17. Fermat´s last theorem

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  19. On some nonlinear elliptic problems

  20. Topology and number theory

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