Second Week


MONDAY, AUGUST 25 
09:00  10:00

Registration (Room 5345) 
10:00  11:30

E. Bierstone Resolution of singularities (from an analyst's point of view) Lecture 1: Introduction. Blowing up and strict transform; main goals; examples 
14:00  15:30

D.H. Phong Singularities in harmonic and geometric analysis Lecture 1: Singularities and critical integrability exponents 
15:30  16:00

Coffee break (Room 6245) 
16:00  17:30

R. Melrose Metrics, fibrations and singular spaces Lecture 1: Introduction: Invertibility of the Laplacian. Manifolds with corners, bmaps, bfibrations, real blowup 

TUESDAY, AUGUST 26 
09:00  10:30

E. Bierstone Resolution of singularities (from an analyst's point of view) Lecture 2: Transforming a function to normal crossings by blowingsup. Proof of a simple version of resolution of singularities 
10:30  11:00

Coffee break (Room 6245) 
11:00  12:30

D.H. Phong Singularities in harmonic and geometric analysis Lecture 2: Singularities and integral operators 
15:00  16:30

R. Melrose Metrics, fibrations and singular spaces Lecture 2: Pseudodifferential operators, composition, inverses. Example: the conic case 

WEDNESDAY, AUGUST 27 
09:00  10:30

E. Bierstone Resolution of singularities (from an analyst's point of view) Lecture 3: Desingularization of toric varieties. Combinatorial resolution of singularities 
10:30  11:00

Coffee break (Room 6245) 
11:00  12:30

D.H. Phong Singularities in harmonic and geometric analysis Lecture 3: Canonical metrics in Kähler geometry 
15:00  16:30

R. Melrose Metrics, fibrations and singular spaces Lecture 3: Resolution of the spaces and metrics. Singular (m) fibrations and blow up. A conjecture 

THURSDAY, AUGUST 28 
09:00  10:30

E. Bierstone Resolution of singularities (from an analyst's point of view) Lecture 4: Invariants and the desingularization principle. Desingularization of parametrized families 
10:30  11:00

Coffee break (Room 6245) 
11:00  12:30

D.H. Phong Singularities in harmonic and geometric analysis Lecture 4: Singularities and energy functionals 
15:00  16:30

R. Melrose Metrics, fibrations and singular spaces Lecture 4: Stratified metrics and Hodge theory 