GENERALIZED GEOMETRY: NATURALITY, CONNECTIONS AND LOW DIMENSIONS

  • Rubio Nuñez, Roberto (Principal Investigator)
  • García Martínez, Luis Emilio (Collaborator)
  • Mou ka, Filip (Collaborator)
  • Ramos Cavalcanti, Gil (Collaborator)
  • Torres, Rafael (Collaborator)
  • Navarro Garmendia, José (Investigator)
  • Ariel, Tom (Collaborator)

Project Details

Description

GENERALIZED GEOMETRY CURRENTLY FACES THREE CHALLENGES: BETTER COMPREHENDING THE SETUP, EXPLOITING ITS RELATION TO LOW DIMENSIONS IN VIEW OF THE RECENT DEVELOPMENTS AND FINDING APPLICATIONS WITHIN GEOMETRY AND TOPOLOGY. GENTLE (GENERALIZED GEOMETRY: NATURALITY, CONNECTIONS AND LOW DIMENSIONS) AIMS AT ADDRESSING THESE THREE CHALLENGES BY BRINGING INTO THE PICTURE THE INTERACTION OF GENERALIZED GEOMETRY WITH FIELDS WHOSE RELEVANCE REMAINS LARGELY UNEXPLORED: UNDERSTANDING THE NATURAL STRUCTURAL OBJECTS OF GENERALIZED GEOMETRY, UNVEILING THE ROLE OF THE SKEW-SYMMETRIC BRACKET AND CONNECTIONS, CLASSIFYING THE HOLONOMY OF CONNECTIONS WITH TORSION VIA GENERALIZED GEOMETRY, DEFINING A GENERALIZED HANDLE ATTACHMENT AND TACKLING THE OPEN QUESTION OF THE EXISTENCE OF A TYPE-CHANGE STABLE GENERALIZED COMPLEX 4-MANIFOLD WITH NEGATIVE EULER CHARACTERISTIC, DETERMINING NEW INVARIANTS ON BIANCHI 3-FOLDS VIA B3-GENERALIZED GEOMETRY, AND ESTABLISHING A CORRESPONDENCE BETWEEN TRANSLATION SURFACES AND POISSON AND B2-GENERALIZED STRUCTURES. THE TEAM OF GENTLE INCLUDES A LEADING YOUNG RESEARCHER ON GENERALIZED GEOMETRY, ONE OF THE PIONEERS OF GENERALIZED GEOMETRY, AN EXPERT ON GENERALIZED SURGERY, TWO EARLY-CAREER RESEARCHERS SPECIALIZED IN AREAS WITH POTENTIAL INTERACTION WITH GENERALIZED GEOMETRY AND A PHD STUDENT. GENTLE AIMS AT PRODUCING HIGH-QUALITY DISRUPTIVE RESEARCH, SHARING IT OPENLY AND EFFECTIVELY WITH THE MATHEMATICAL COMMUNITY, AND COMMUNICATING TO SOCIETY.
StatusActive
Effective start/end date1/09/2331/08/26

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