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Gabriel Catren, Mathieu Anel, (eds.)
New Spaces for Mathematics and Physics
conference (IHP Paris, Oct-Sept 2015)
and book project
on current developments regarding foundations of geometry in mathematics and physics.
Pierre Cartier on schemes.
Anders Kock on synthetic differential geometry
Jean Pradines on Lie groupoids
Patrick Iglesias-Zemmour on diffeological spaces.
André Joyal on topos theory.
Michel Vaquié on sheaves and gros toposes.
Carlos Simpson on algebraic stacks and the Artin representability theorem.
Mathieu Anel on derived geometry.
Maxim Kontsevich on derived noncommutative geometry in terms of formal duals of stable infinity-categories (enhanced triangulated categories).
Shahn Majid on noncommutative geometry
Timothy Porter on the homotopy hypothesis-theorem.
Denis-Charles Cisinski on motives.
Mike Shulman on homotopy type theory.
Damien Calaque on derived symplectic geometry.
Urs Schreiber on Higher Prequantum Geometry.
Dan Freed on extended TQFT and the cobordism hypothesis.
Cecilia Flori on Bohr toposes.
Hanno Sahlmann on spin networks.
Mikhail Kapranov on superalgebra as sphere spectrum-graded algebra.
Mikhail Kapranov, Supergeometry in mathematics and physics, in Gabriel Catren, Mathieu Anel, (eds.) New Spaces for Mathematics and Physics (arXiv:1512.07042)
Mikhail Kapranov, Super-geometry, talk at New Spaces for Mathematics & Physics, IHP Paris, Oct-Sept 2015 (video recording)
Roger Penrose on twistors.
Marcos Mariño on AdS-CFT
John Baez on experiments.
Yuri Manin on Wick rotation in cosmology.