Final Report Summary - GEMIS (Generalized Homological Mirror Symmetry and Applications)
During the 5 years period we have achieved the main goal developing the parallel Classical Homological Mirror Symmetry and Hodge theory.
We have developed
- The the theory of Gaps and Spectra
- Tropical Hodge theory
- Noncommutative Hodge theory
We have added several new directions which initially come rather unexpectedly but are they are major reasearch directions now.
1) Categories HMS and Dynamical Systems, noncommutative Mordell Lang,
2) Noncommutative Hodge theory and stability Hodge Structures.
3) Homological Mirror Symmetry via VGIT.
4) Homological Projective duality and applications to Classical geometry.
As a result the achievements of GEMIS have enhanced in a major way the role of categorical structure in Mathematics and Physics. Going far beyond or state of art opening new unexpected connections of category theory and physics with
- Dynamical Systems
- Number Theory
- Integrable sytems
- Random walks
- Logic
- Complexity
In this respects the achievements of GEMIS have enhanced in a major way the role of categorical structure in Mathematics and Physics.
GEMIS has made a major progress in consolidation of what was known in HMS and opening new research directions for the generations to come.
Via series of conferences and workshops we have gotten many young people working in this directions ensuring in such way the rigor and the fututres of these fields. We have gotten 9 postdocs involved in this research.
Three of them Ballard, Kerr and Favero have permannent positions now.
We have had 4 PhD students starting their PhDs in the framework of GEMIS.
Two of them are finishing in May 2014 with jobs already lined up for them.
In this respects the achievements of GEMIS have enhanced in a major way the role of categorical structures in Mathematics and Physics.
We have developed
- The the theory of Gaps and Spectra
- Tropical Hodge theory
- Noncommutative Hodge theory
We have added several new directions which initially come rather unexpectedly but are they are major reasearch directions now.
1) Categories HMS and Dynamical Systems, noncommutative Mordell Lang,
2) Noncommutative Hodge theory and stability Hodge Structures.
3) Homological Mirror Symmetry via VGIT.
4) Homological Projective duality and applications to Classical geometry.
As a result the achievements of GEMIS have enhanced in a major way the role of categorical structure in Mathematics and Physics. Going far beyond or state of art opening new unexpected connections of category theory and physics with
- Dynamical Systems
- Number Theory
- Integrable sytems
- Random walks
- Logic
- Complexity
In this respects the achievements of GEMIS have enhanced in a major way the role of categorical structure in Mathematics and Physics.
GEMIS has made a major progress in consolidation of what was known in HMS and opening new research directions for the generations to come.
Via series of conferences and workshops we have gotten many young people working in this directions ensuring in such way the rigor and the fututres of these fields. We have gotten 9 postdocs involved in this research.
Three of them Ballard, Kerr and Favero have permannent positions now.
We have had 4 PhD students starting their PhDs in the framework of GEMIS.
Two of them are finishing in May 2014 with jobs already lined up for them.
In this respects the achievements of GEMIS have enhanced in a major way the role of categorical structures in Mathematics and Physics.