Centre de recherches mathématiques
Université de Montréal
PROGRAMME
français
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Second Week
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Short programme on analysis and resolution of singularities
August 18 - September 5, 2003
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MONDAY, AUGUST 25 |
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09:00 - 10:00
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Registration (Room 5345) |
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10:00 - 11:30
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E. Bierstone Resolution of singularities (from an analyst's point of view) Lecture 1: Introduction. Blowing up and strict transform; main goals; examples |
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14:00 - 15:30
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D.H. Phong Singularities in harmonic and geometric analysis Lecture 1: Singularities and critical integrability exponents |
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15:30 - 16:00
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Coffee break (Room 6245) |
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16:00 - 17:30
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R. Melrose Metrics, fibrations and singular spaces Lecture 1: Introduction: Invertibility of the Laplacian. Manifolds with corners, b-maps, b-fibrations, real blow-up |
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TUESDAY, AUGUST 26 |
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09:00 - 10:30
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E. Bierstone Resolution of singularities (from an analyst's point of view) Lecture 2: Transforming a function to normal crossings by blowings-up. Proof of a simple version of resolution of singularities |
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10:30 - 11:00
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Coffee break (Room 6245) |
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11:00 - 12:30
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D.H. Phong Singularities in harmonic and geometric analysis Lecture 2: Singularities and integral operators |
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15:00 - 16:30
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R. Melrose Metrics, fibrations and singular spaces Lecture 2: Pseudodifferential operators, composition, inverses. Example: the conic case |
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WEDNESDAY, AUGUST 27 |
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09:00 - 10:30
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E. Bierstone Resolution of singularities (from an analyst's point of view) Lecture 3: Desingularization of toric varieties. Combinatorial resolution of singularities |
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10:30 - 11:00
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Coffee break (Room 6245) |
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11:00 - 12:30
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D.H. Phong Singularities in harmonic and geometric analysis Lecture 3: Canonical metrics in Kähler geometry |
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15:00 - 16:30
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R. Melrose Metrics, fibrations and singular spaces Lecture 3: Resolution of the spaces and metrics. Singular (m-) fibrations and blow up. A conjecture |
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THURSDAY, AUGUST 28 |
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09:00 - 10:30
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E. Bierstone Resolution of singularities (from an analyst's point of view) Lecture 4: Invariants and the desingularization principle. Desingularization of parametrized families |
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10:30 - 11:00
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Coffee break (Room 6245) |
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11:00 - 12:30
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D.H. Phong Singularities in harmonic and geometric analysis Lecture 4: Singularities and energy functionals |
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15:00 - 16:30
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R. Melrose Metrics, fibrations and singular spaces Lecture 4: Stratified metrics and Hodge theory |