Download Visions in Mathematics: GAFA 2000 Special Volume, Part I pp. by Noga Alon, Jean Bourgain, Alain Connes, Misha Gromov, Vitali PDF

By Noga Alon, Jean Bourgain, Alain Connes, Misha Gromov, Vitali D. Milman

"Visions in arithmetic - in the direction of 2000" used to be some of the most outstanding mathematical conferences lately. It was once held in Tel Aviv from August twenty fifth to September third, 1999, and united a number of the top mathematicians world wide. The targets of the convention have been to debate the significance, the tools, the earlier and the way forward for arithmetic as we input the twenty first century and to think about the relationship among arithmetic and similar parts. The goals of the convention are mirrored within the current set of survey articles, documenting the kingdom of artwork and destiny clients in lots of branches of arithmetic of present curiosity. this is often the 1st a part of a two-volume set that may serve any examine mathematician or complex scholar as an outline and guide in the course of the multifaceted physique of mathematical examine within the current and close to destiny.

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Additional info for Visions in Mathematics: GAFA 2000 Special Volume, Part I pp. 1-453

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3 IUT aU tUJUJP_     6ISIONS IN -ATH 02/",%-3 ). )!. ). SSUMING THE EQUATION DEFOCUSING t   LET US SUMMARIZE SOME POS ITIVE RESULTS AND MORE SPECIlC PROBLEMS 7E WILL CALL THE PROBLEM (  SUBCRITICAL RESP CRITICAL SUPERCRITICAL IF S   RESP S   S    4HUS IN DIMENSION D    THE PROBLEM IS ALWAYS SUBCRITICAL 4HE NEXT STATEMENT IS A CONSEQUENCE OF 4HEOREM  AND THE ENERGY CONCENTRATIONS #OROLLARY  )N THE DEFOCUSING (  SUBCRITICAL CASE THE )60 IS GLOB ALLY WELLPOSED FOR DATA IN (  < ( S S t  )N PARTICULAR CLASSICAL SOLUTIONS EXIST FOR ALL TIME )N THE CRITICAL CASE THERE IS THE FOLLOWING PARTIAL RESULT SEE ;"O= ;'R=   4HEOREM  ,ET D t  AND P   D_ DEFOCUSING CASE  4HEN THERE IS GLOBAL WELLPOSEDNESS OF THE )60 FOR RADIAL }  (  < ( S S t  6ISIONS IN -ATH 02/",%-3 ).

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