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Extra Form
Lecturer Raphael Ponge
Dept. 서울대학교
date Sep 22, 2011
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.
Atachment
Attachment '1'
List of Articles
Category Subject Dept. Lecturer
Math Colloquia Spectral Analysis for the Anomalous Localized Resonance by Plasmonic Structures file 인하대학교 강현배
Math Colloquia Conformal field theory and noncommutative geometry file 동경대학교 Kawahigashi
Math Colloquia 극소곡면의 등주부등식 file KIAS 최재경
Math Colloquia Topology of configuration spaces on graphs file KAIST 고기형
Math Colloquia 학부생을 위한 강연회: What is the algebraic number theory? file KAIST 구자경
Math Colloquia 정년퇴임 기념강연회: 숙제 file 서울대학교 지동표
Math Colloquia Integer partitions, q-series, and Modular forms file 서울과학기술 대학 김병찬
Math Colloquia Root multiplicities of hyperbolic Kac-Moody algebras and Fourier coefficients of modular forms file Univ. of Connecticut 이규환
Math Colloquia 학부생을 위한 강연: 브라질과 프랑스는 왜 축구를 잘 할까? - 경제와 수학과 축구와 법률 file 서울대학교 법과대학 김화진
Math Colloquia A new view of Fokker-Planck equations in finite and Infinite dimensional spaces file Bielefeld Univ./Purdue Univ. Michael Roeckner
Math Colloquia 원의 유리매개화에 관련된 수학 file 건국대학교 최인송
Math Colloquia Introduction to Non-Positively Curved Groups file KAIST 김상현
Math Colloquia Noncommutative Geometry. Quantum Space-Time and Diffeomorphism Invariant Geometry file 서울대학교 Raphael Ponge
Math Colloquia 행렬함수 Permanent의 극소값 결정과 미해결 문제들 file 제주대학교/서울대학교 송석준
Math Colloquia The Mathematics of the Bose Gas and its Condensation file KAIST 이지운
Math Colloquia Codimension Three Conjecture file 교토대학교/서울대학교 Masaki Kashiwara
Math Colloquia 학부생을 위한 강연: 건축과 수학 file UI 건축사무소 위진복
Math Colloquia Classical and Quantum Probability Theory file 충북대학교 지운식
Math Colloquia Iwasawa main conjecture and p-adic L-functions file 포항공과대학교 박지훈
Math Colloquia 학부생을 위한 강연: Choi's orthogonal Latin Squares is at least 61 years earlier than Euler's file 연세대학교 송홍엽
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