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EIN2019-103354

Financiado

THE INTERFACE BETWEEN KAHLER AND NON-KAHLER COMPLEX GEOMETRY

THE PRESENT PROPOSAL IS ORIENTED TOWARDS AN ERC CONSOLIDATOR GRANT APPLICATION TO THE EUROPEAN RESEARCH COUNCIL IN THE INCOMING TWO YEARS, THE FUNDING FROM EUROPA INVESTIGACION 2019 WOULD ALLOW ME TO FACE POTENTIAL WEAKNESS AS WEL... ver más

01/01/2019

UAM

10K€

Presupuesto del proyecto: 10K€

Líder del proyecto

UNIVERSIDAD AUTÓNOMA DE MADRID No se ha especificado una descripción o un objeto social para esta compañía.

Total investigadores 3182

Financiación concedida El organismo AGENCIA ESTATAL DE INVESTIGACIÓN notifico la concesión del proyecto el día 2019-01-01

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UAM

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Líder del proyecto

UNIVERSIDAD AUTÓNOMA DE MADRID

Total investigadores 3182

Presupuesto del proyecto 10K€

Descripción del proyecto THE PRESENT PROPOSAL IS ORIENTED TOWARDS AN ERC CONSOLIDATOR GRANT APPLICATION TO THE EUROPEAN RESEARCH COUNCIL IN THE INCOMING TWO YEARS, THE FUNDING FROM EUROPA INVESTIGACION 2019 WOULD ALLOW ME TO FACE POTENTIAL WEAKNESS AS WELL AS STRENGTHEN MY CURRENT SCIENTIFIC PROPOSAL CYINTERFACE, THE GENERAL OBJECTIVES ARE:OBJECTIVE 1, STRENGTHEN MY NETWORK OF CONTACTS WITH SOME OF THE LEADERS IN THE AREAS OF CYINTERFACE (DIFFERENTIAL GEOMETRY, ALGEBRAIC GEOMETRY, MIRROR SYMMETRY) AND ESTABLISH NEW COLLABORATIONS,OBJETIVE 2, FOSTER TRAINING ACTIVITIES ORIENTED TOWARDS : A) THE PREPARATION OF A SUCCESFUL ERC COG APPLICATION AND B) STRENGTHEN THE EXPERTISE OF THE RESEARCH TEAM,SUMMARY OF CYINTERFACE:A HIGH-PROFILE OPEN QUESTION WHICH LIES AT THE INTERFACE BETWEEN KAHLER AND NON-KAHLER COMPLEX GEOMETRY IS THE CLASSIFICATION OF ALGEBRAIC CALABI-YAU THREEFOLDS VIA TRANSITIONS AND FLOPS: SUITABLE SURGERY OPERATIONS ALONG 2-SPHERES WHICH MAY OFTEN END UP IN A NON-KAHLER MANIFOLD, STRIKINGLY, THESE DRASTIC CHANGES IN THE TOPOLOGY CAN BE REGARDED AS A PERFECTLY SMOOTH PROCESS IN STRING THEORY, THIS PROCESS RELATES VIA THE HULL-STROMINGER SYSTEM (HS) OF PARTIAL DIFFERENTIAL EQUATIONS TO A PHYSICAL PREDICTION, WITH A POTENTIALLY LARGE IMPACT ON DIFFERENT FIELDS OF MATHEMATICS: A MUCH EXPECTED GENERALIZATION OF MIRROR SYMMETRY--KNOWN AS (0,2) MIRROR SYMMETRY,THE MAIN GOAL OF THIS PROJECT WILL BE TO GO SIGNIFICANTLY BEYOND THE STATE OF THE ART IN THE STUDY OF NON-KAHLER CALABI-YAU MANIFOLDS, WITH A SPECIAL EMPHASIS IN COMPLEX DIMENSION THREE, THE FIRST GENERAL OBJECTIVE WILL BE O1) TO DEVELOP A THEORY OF CANONICAL METRICS ON COMPLEX NON-KAHLER MANIFOLDS, TOWARDS THE EXISTENCE AND UNIQUENESS FOR HS, WITH THESE NEW TOOLS AT HAND, O2) ADDRESSES THE GEOMETRIZATION OF TRANSITIONS AND FLOPS BETWEEN KAHLER AND NON-KAHLER THREEFOLDS, AND YAU'S CONJECTURE FOR HS, IN O3) I WILL ESTABLISH FIRM HANDHOLDS FOR A MATHEMATICAL THEORY OF (0,2) MIRROR SYMMETRY ON NON-KAHLER CALABI-YAU MANIFOLDS USING VERTEX ALGEBRAS, FINALLY, O4) CONSTRUCTS GENERATING FUNCTIONS FOR CONJECTURAL ENUMERATIVE INVARIANTS,SOME OF THE NEW TECHNIQUES I AIM TO APPLY HAVE BEEN DEVELOPED BY THE PI IN HIS LONG TERM STUDY OF HS --- SOME OTHERS WILL BE DEVELOPED IN THIS PROJECT, I ALSO INTEND TO DELVE INTO AND EXTEND THE NEW APPROACH TO HS THAT I HAVE RECENTLY PROPOSED TO GO SIGNIFICANTLY BEYOND THE STATE OF THE ART IN THE STUDY OF THESE EQUATIONS, THE PRESENT PROPOSAL BUILDS MY PREVIOUSLY SUPPORTED BY PROJECT 655162--STROMINGER--H2020-MSCA-IF-2014, WITH AMBITIONS THAT GO FAR BEYOND, CALABI-YAU\NON-KAHLER GEOMETRY\MIRROR SYMMETRY

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