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\begin{document}

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\section*{New Spaces for Mathematics and Physics}

\hypertarget{context}{}\subsubsection*{{Context}}\label{context}

\hypertarget{mathematics}{}\paragraph*{{Mathematics}}\label{mathematics}

[[!include mathematicscontents]]

\hypertarget{physics}{}\paragraph*{{Physics}}\label{physics}

[[!include physicscontents]]

\hypertarget{geometry}{}\paragraph*{{Geometry}}\label{geometry}

[[!include higher geometry - contents]]

This page collects pointers related to the conference and book project:

\begin{itemize}%
\item [[Gabriel Catren]], [[Mathieu Anel]], (eds.)

\emph{New Spaces for Mathematics and Physics}

\href{http://ercpqg-espace.sciencesconf.org/program}{conference} (IHP Paris, Oct-Sept 2015)

and \href{http://ercpqg-espace.sciencesconf.org/resource/page/id/1}{book project},

Cambridge University Press 2019

(\href{http://mathieu.anel.free.fr/mat/doc/Anel-Catren-NewSpacesTOC.pdf}{toc pdf})



\end{itemize}
on current developments regarding foundations of [[geometry]] in [[mathematics]] and [[physics]].

\hypertarget{contents}{}\section*{{Contents}}\label{contents}

\noindent\hyperlink{book}{Book}\dotfill \pageref*{book} \linebreak
\noindent\hyperlink{volume_i_new_spaces_in_mathematics}{Volume I: New Spaces in Mathematics}\dotfill \pageref*{volume_i_new_spaces_in_mathematics} \linebreak
\noindent\hyperlink{volume_ii_new_spaces_in_physics}{Volume II: New Spaces in Physics}\dotfill \pageref*{volume_ii_new_spaces_in_physics} \linebreak
\noindent\hyperlink{conference}{Conference}\dotfill \pageref*{conference} \linebreak
\noindent\hyperlink{smoothness_and_singularities}{Smoothness and singularities}\dotfill \pageref*{smoothness_and_singularities} \linebreak
\noindent\hyperlink{schemes_pierre_cartier}{Schemes (Pierre Cartier)}\dotfill \pageref*{schemes_pierre_cartier} \linebreak
\noindent\hyperlink{synthetic_differential_geometry__new_methods_for_old_spaces_anders_kock}{Synthetic differential geometry - new methods for old spaces (Anders Kock)}\dotfill \pageref*{synthetic_differential_geometry__new_methods_for_old_spaces_anders_kock} \linebreak
\noindent\hyperlink{lie_or_differentiable_groupoids_jean_pradine}{Lie (or differentiable) groupoids (Jean Pradine)}\dotfill \pageref*{lie_or_differentiable_groupoids_jean_pradine} \linebreak
\noindent\hyperlink{diffeologies_patrick_iglesiaszemmour}{Diffeologies (Patrick Iglesias-Zemmour)}\dotfill \pageref*{diffeologies_patrick_iglesiaszemmour} \linebreak
\noindent\hyperlink{spaces_with_categories_of_points}{Spaces with categories of points}\dotfill \pageref*{spaces_with_categories_of_points} \linebreak
\noindent\hyperlink{geometric_aspects_of_topos_theory_in_relation_with_logical_doctrines_andr_joyal}{Geometric aspects of topos theory in relation with logical doctrines (Andr\'e{} Joyal)}\dotfill \pageref*{geometric_aspects_of_topos_theory_in_relation_with_logical_doctrines_andr_joyal} \linebreak
\noindent\hyperlink{sheaves_and_functors_of_points_michel_vaqui}{Sheaves and functors of points (Michel Vaqui\'e{})}\dotfill \pageref*{sheaves_and_functors_of_points_michel_vaqui} \linebreak
\noindent\hyperlink{stacks_and_the_artin_property_carlos_simpson}{Stacks and the Artin property (Carlos Simpson)}\dotfill \pageref*{stacks_and_the_artin_property_carlos_simpson} \linebreak
\noindent\hyperlink{the_geometry_of_ambiguity_an_introduction_to_the_ideas_of_derived_geometry_mathieu_anel}{The Geometry of Ambiguity: An introduction to the ideas of Derived Geometry (Mathieu Anel)}\dotfill \pageref*{the_geometry_of_ambiguity_an_introduction_to_the_ideas_of_derived_geometry_mathieu_anel} \linebreak
\noindent\hyperlink{noncommutative_geometry}{Non-commutative geometry}\dotfill \pageref*{noncommutative_geometry} \linebreak
\noindent\hyperlink{geometry_from_statistical_physics_and_information_theory_matilde_marcolli}{Geometry from statistical physics and information theory (Matilde Marcolli)}\dotfill \pageref*{geometry_from_statistical_physics_and_information_theory_matilde_marcolli} \linebreak
\noindent\hyperlink{geometry_in_triangulated_categories_maxim_kontsevich}{Geometry in triangulated categories (Maxim Kontsevich)}\dotfill \pageref*{geometry_in_triangulated_categories_maxim_kontsevich} \linebreak
\noindent\hyperlink{quantum_differential_geometry_shahn_majid}{Quantum differential geometry (Shahn Majid)}\dotfill \pageref*{quantum_differential_geometry_shahn_majid} \linebreak
\noindent\hyperlink{spaces_up_to_homotopy}{Spaces up to homotopy}\dotfill \pageref*{spaces_up_to_homotopy} \linebreak
\noindent\hyperlink{spaces_as_infinitygroupoids_timothy_porter}{Spaces as infinity-groupoids (Timothy Porter)}\dotfill \pageref*{spaces_as_infinitygroupoids_timothy_porter} \linebreak
\noindent\hyperlink{homological_decomposition_and_motives_denischarles_cisinski}{Homological decomposition and motives (Denis-Charles Cisinski)}\dotfill \pageref*{homological_decomposition_and_motives_denischarles_cisinski} \linebreak
\noindent\hyperlink{Shulman}{Homotopy type theory: the logic of space (Mike Shulman)}\dotfill \pageref*{Shulman} \linebreak
\noindent\hyperlink{spaces_in_classical__quantum_mechanics}{Spaces in classical \& quantum mechanics}\dotfill \pageref*{spaces_in_classical__quantum_mechanics} \linebreak
\noindent\hyperlink{derived_stacks_in_symplectic_geometry_damien_calaque}{Derived stacks in symplectic geometry (Damien Calaque)}\dotfill \pageref*{derived_stacks_in_symplectic_geometry_damien_calaque} \linebreak
\noindent\hyperlink{Schreiber}{Higher pre-quantized geometry (Urs Schreiber)}\dotfill \pageref*{Schreiber} \linebreak
\noindent\hyperlink{cobordisms_and_extended_quantum_field_theories_dan_freed}{Cobordisms and extended quantum field theories (Dan Freed)}\dotfill \pageref*{cobordisms_and_extended_quantum_field_theories_dan_freed} \linebreak
\noindent\hyperlink{notion_of_space_in_topos_quantum_theory_cecilia_flori}{Notion of space in topos quantum theory (Cecilia Flori)}\dotfill \pageref*{notion_of_space_in_topos_quantum_theory_cecilia_flori} \linebreak
\noindent\hyperlink{spaces_in_quantum_gravity}{Spaces in quantum gravity}\dotfill \pageref*{spaces_in_quantum_gravity} \linebreak
\noindent\hyperlink{spin_networks_and_spinfoams_hanno_sahlmann}{Spin networks and spinfoams (Hanno Sahlmann)}\dotfill \pageref*{spin_networks_and_spinfoams_hanno_sahlmann} \linebreak
\noindent\hyperlink{supergeometry_mikhail_kapranov}{Super-geometry (Mikhail Kapranov)}\dotfill \pageref*{supergeometry_mikhail_kapranov} \linebreak
\noindent\hyperlink{Penrose}{Twistor theory (Roger Penrose)}\dotfill \pageref*{Penrose} \linebreak
\noindent\hyperlink{stringy_geometry_and_emergent_space_marcos_mario}{Stringy geometry and emergent space (Marcos Mari\~n{}o)}\dotfill \pageref*{stringy_geometry_and_emergent_space_marcos_mario} \linebreak
\noindent\hyperlink{open_questions}{Open questions}\dotfill \pageref*{open_questions} \linebreak
\noindent\hyperlink{what_experiments_tell_us_about_space_and_time_john_baez}{What experiments tell us about space and time (John Baez)}\dotfill \pageref*{what_experiments_tell_us_about_space_and_time_john_baez} \linebreak
\noindent\hyperlink{time_between_real_and_imaginary_what_geometries_describe_the_universe_near_the_big_bang_yuri_manin}{Time between real and imaginary: what geometries describe the Universe near the Big Bang? (Yuri Manin)}\dotfill \pageref*{time_between_real_and_imaginary_what_geometries_describe_the_universe_near_the_big_bang_yuri_manin} \linebreak


\hypertarget{book}{}\subsection*{{Book}}\label{book}

\hypertarget{volume_i_new_spaces_in_mathematics}{}\subsubsection*{{Volume I: New Spaces in Mathematics}}\label{volume_i_new_spaces_in_mathematics}

I.1. Differential geometry I.1.1 Diffeologies (Patrick Iglesias-Zemmour) I.1.2 New methods for old spaces: synthetic differential geometry (Anders Kock) I.1.3 Microlocalanalysis and beyond (Pierre Schapira)

I.2. Topology and algebraic topology I.2.1 Topo-logie (Mathieu Anel \&{} Andr\'e{} Joyal) (\href{/http://mathieu.anel.free.fr/mat/doc/Anel-Joyal-Topo-logie.pdf}{pdf}) I.2.2 Spaces as infinity-groupoids (Timothy Porter) I.2.3 Homotopy type theory: the logic of space (Mike Shulman)

I.3. Algebraic geometry I.3.1 Sheaves and functors of points (Michel Vaqui\'e{}) I.3.2 Stacks (Nicole Mestrano \&{} Carlos Simpson) I.3.3 The geometry of ambiguity – An introduction to derived geometry (Mathieu Anel) I.3.4 Geometry in dg-categories (Maxim Kontsevich)

\hypertarget{volume_ii_new_spaces_in_physics}{}\subsubsection*{{Volume II: New Spaces in Physics}}\label{volume_ii_new_spaces_in_physics}

II.1. Non-commutative and super-commutative geometries II.1.1 Noncommutative Geometry, the spectral standpoint (Alain Connes) II.1.2 Topos quantum theory (Klaas Landsman) II.1.3 Super-geometry (Mikhail Kapranov)

II.2. Symplectic geometry II.2.1 Derived stacks in symplectic geometry (Damien Calaque) II.2.2 Higher pre-quantized geometry (Urs Schreiber)

II.3. Space-time II.3.1 Struggles with the Continuum (John Baez) II.3.2 Twistor theory (Roger Penrose) II.3.3 Loop quantum gravity (Muxin Han) II.3.4 Stringy geometry and emergent space (Marcos Mari\~n{}o)

\hypertarget{conference}{}\subsection*{{Conference}}\label{conference}

\hypertarget{smoothness_and_singularities}{}\subsubsection*{{Smoothness and singularities}}\label{smoothness_and_singularities}

\hypertarget{schemes_pierre_cartier}{}\paragraph*{{Schemes (Pierre Cartier)}}\label{schemes_pierre_cartier}

[[Pierre Cartier]] on [[schemes]].

(\href{https://www.youtube.com/watch?v=etdvnswIhMw}{video recording})

\hypertarget{synthetic_differential_geometry__new_methods_for_old_spaces_anders_kock}{}\paragraph*{{Synthetic differential geometry - new methods for old spaces (Anders Kock)}}\label{synthetic_differential_geometry__new_methods_for_old_spaces_anders_kock}

[[Anders Kock]] on [[synthetic differential geometry]]

(\href{https://www.youtube.com/watch?v=AXz7xu3WrPE}{video recording})

\hypertarget{lie_or_differentiable_groupoids_jean_pradine}{}\paragraph*{{Lie (or differentiable) groupoids (Jean Pradine)}}\label{lie_or_differentiable_groupoids_jean_pradine}

[[Jean Pradines]] on [[Lie groupoids]]

(\href{https://www.youtube.com/watch?v=Sg_dStsGcIw}{video recording})

\hypertarget{diffeologies_patrick_iglesiaszemmour}{}\paragraph*{{Diffeologies (Patrick Iglesias-Zemmour)}}\label{diffeologies_patrick_iglesiaszemmour}

[[Patrick Iglesias-Zemmour]] on [[diffeological spaces]].

(\href{https://www.youtube.com/watch?v=4sZDmiVOhaA}{video recording})

(lecture notes \href{http://math.huji.ac.il/~piz/documents/AITD.pdf}{pdf})

\hypertarget{spaces_with_categories_of_points}{}\subsubsection*{{Spaces with categories of points}}\label{spaces_with_categories_of_points}

\hypertarget{geometric_aspects_of_topos_theory_in_relation_with_logical_doctrines_andr_joyal}{}\paragraph*{{Geometric aspects of topos theory in relation with logical doctrines (Andr\'e{} Joyal)}}\label{geometric_aspects_of_topos_theory_in_relation_with_logical_doctrines_andr_joyal}

[[André Joyal]] on [[topos theory]].

(\href{https://www.youtube.com/watch?v=kaZpOEOAUzE}{video recording})

\hypertarget{sheaves_and_functors_of_points_michel_vaqui}{}\paragraph*{{Sheaves and functors of points (Michel Vaqui\'e{})}}\label{sheaves_and_functors_of_points_michel_vaqui}

[[Michel Vaquié]] on [[sheaves]] and [[gros toposes]].

\hypertarget{stacks_and_the_artin_property_carlos_simpson}{}\paragraph*{{Stacks and the Artin property (Carlos Simpson)}}\label{stacks_and_the_artin_property_carlos_simpson}

[[Carlos Simpson]] on [[algebraic stacks]] and the [[Artin representability theorem]].

(\href{https://www.youtube.com/watch?v=vI-09KIkBbY}{video recording})

\hypertarget{the_geometry_of_ambiguity_an_introduction_to_the_ideas_of_derived_geometry_mathieu_anel}{}\paragraph*{{The Geometry of Ambiguity: An introduction to the ideas of Derived Geometry (Mathieu Anel)}}\label{the_geometry_of_ambiguity_an_introduction_to_the_ideas_of_derived_geometry_mathieu_anel}

[[Mathieu Anel]] on [[derived geometry]] (\href{http://mathieu.anel.free.fr/mat/doc/Anel-DerivedGeometry.pdf}{pdf})

(\href{https://www.youtube.com/watch?v=198ssqlW9BI}{video recording})

\hypertarget{noncommutative_geometry}{}\subsubsection*{{Non-commutative geometry}}\label{noncommutative_geometry}

\hypertarget{geometry_from_statistical_physics_and_information_theory_matilde_marcolli}{}\paragraph*{{Geometry from statistical physics and information theory (Matilde Marcolli)}}\label{geometry_from_statistical_physics_and_information_theory_matilde_marcolli}

\hypertarget{geometry_in_triangulated_categories_maxim_kontsevich}{}\paragraph*{{Geometry in triangulated categories (Maxim Kontsevich)}}\label{geometry_in_triangulated_categories_maxim_kontsevich}

[[Maxim Kontsevich]] on [[derived noncommutative geometry]] in terms of [[formal duals]] of [[stable infinity-categories]] ([[enhanced triangulated categories]]).

\begin{itemize}%
\item [[Maxim Kontsevich]], \emph{Geometry in triangulated categories}, talk at \emph{[[New Spaces for Mathematics and Physics]]}, IHP Paris, Oct-Sept 2015 (\href{https://www.youtube.com/watch?v=XnmO9RAbl50}{video recording})

\end{itemize}
\hypertarget{quantum_differential_geometry_shahn_majid}{}\paragraph*{{Quantum differential geometry (Shahn Majid)}}\label{quantum_differential_geometry_shahn_majid}

[[Shahn Majid]] on [[noncommutative geometry]]

\hypertarget{spaces_up_to_homotopy}{}\subsubsection*{{Spaces up to homotopy}}\label{spaces_up_to_homotopy}

\hypertarget{spaces_as_infinitygroupoids_timothy_porter}{}\paragraph*{{Spaces as infinity-groupoids (Timothy Porter)}}\label{spaces_as_infinitygroupoids_timothy_porter}

[[Timothy Porter]] on thinking of spaces as infinity groupoids and the relation with the [[homotopy hypothesis]].

(\href{https://www.youtube.com/watch?v=BH_NwgM8QjI}{video recording}) ([[Spaces as infinity-groupoids.pdf|draft of article:file]])

\hypertarget{homological_decomposition_and_motives_denischarles_cisinski}{}\paragraph*{{Homological decomposition and motives (Denis-Charles Cisinski)}}\label{homological_decomposition_and_motives_denischarles_cisinski}

[[Denis-Charles Cisinski]] on [[motives]].

(\href{https://www.youtube.com/watch?v=GhcxtwUJ0TY}{video recording})

\hypertarget{Shulman}{}\paragraph*{{Homotopy type theory: the logic of space (Mike Shulman)}}\label{Shulman}

[[Mike Shulman]] \emph{Homotopy type theory: the logic of space} (\href{https://arxiv.org/abs/1703.03007}{arXiv:1703.03007})

(on [[homotopy type theory]])

\hypertarget{spaces_in_classical__quantum_mechanics}{}\subsubsection*{{Spaces in classical \& quantum mechanics}}\label{spaces_in_classical__quantum_mechanics}

\hypertarget{derived_stacks_in_symplectic_geometry_damien_calaque}{}\paragraph*{{Derived stacks in symplectic geometry (Damien Calaque)}}\label{derived_stacks_in_symplectic_geometry_damien_calaque}

[[Damien Calaque]] on [[derived geometry|derived]] [[symplectic geometry]] (\href{https://arxiv.org/abs/1802.09643}{arXiv:1802.09643})

\hypertarget{Schreiber}{}\paragraph*{{Higher pre-quantized geometry (Urs Schreiber)}}\label{Schreiber}

[[Urs Schreiber]] on [[schreiber:Higher Prequantum Geometry]].

(\href{http://arxiv.org/abs/1601.05956}{arXiv:1601.05956}, \href{https://www.youtube.com/watch?v=EaYMuyr9KII}{video recording})

\hypertarget{cobordisms_and_extended_quantum_field_theories_dan_freed}{}\paragraph*{{Cobordisms and extended quantum field theories (Dan Freed)}}\label{cobordisms_and_extended_quantum_field_theories_dan_freed}

[[Dan Freed]] on [[extended TQFT]] and the [[cobordism hypothesis]].

\hypertarget{notion_of_space_in_topos_quantum_theory_cecilia_flori}{}\paragraph*{{Notion of space in topos quantum theory (Cecilia Flori)}}\label{notion_of_space_in_topos_quantum_theory_cecilia_flori}

[[Cecilia Flori]] on [[Bohr toposes]].

\hypertarget{spaces_in_quantum_gravity}{}\subsubsection*{{Spaces in quantum gravity}}\label{spaces_in_quantum_gravity}

\hypertarget{spin_networks_and_spinfoams_hanno_sahlmann}{}\paragraph*{{Spin networks and spinfoams (Hanno Sahlmann)}}\label{spin_networks_and_spinfoams_hanno_sahlmann}

Hanno Sahlmann on spin networks.

(\href{https://www.youtube.com/watch?v=QDU46lK1FDU}{video recording})

\hypertarget{supergeometry_mikhail_kapranov}{}\paragraph*{{Super-geometry (Mikhail Kapranov)}}\label{supergeometry_mikhail_kapranov}

[[Mikhail Kapranov]] on [[superalgebra]] as [[sphere spectrum]]-graded algebra.

\begin{itemize}%
\item [[Mikhail Kapranov]], \emph{Supergeometry in mathematics and physics}, in [[Gabriel Catren]], [[Mathieu Anel]], (eds.) \emph{[[New Spaces for Mathematics and Physics]]} (\href{http://arxiv.org/abs/1512.07042}{arXiv:1512.07042})


\item [[Mikhail Kapranov]], \emph{Super-geometry}, talk at \emph{\href{http://ercpqg-espace.sciencesconf.org/program}{New Spaces for Mathematics \& Physics}}, IHP Paris, Oct-Sept 2015 (\href{https://www.youtube.com/watch?v=bjsNwKYT8JE}{video recording})



\end{itemize}
\hypertarget{Penrose}{}\paragraph*{{Twistor theory (Roger Penrose)}}\label{Penrose}

[[Roger Penrose]] on [[twistors]].

(\href{https://www.youtube.com/watch?v=kmYfYOW0vSg}{video recording})

\hypertarget{stringy_geometry_and_emergent_space_marcos_mario}{}\paragraph*{{Stringy geometry and emergent space (Marcos Mari\~n{}o)}}\label{stringy_geometry_and_emergent_space_marcos_mario}

[[Marcos Mariño]] on [[AdS-CFT]]

(\href{https://www.youtube.com/watch?v=MD_jj3O6IRE}{video recording})

\hypertarget{open_questions}{}\subsubsection*{{Open questions}}\label{open_questions}

\hypertarget{what_experiments_tell_us_about_space_and_time_john_baez}{}\paragraph*{{What experiments tell us about space and time (John Baez)}}\label{what_experiments_tell_us_about_space_and_time_john_baez}

[[John Baez]] on [[experiments]].

\hypertarget{time_between_real_and_imaginary_what_geometries_describe_the_universe_near_the_big_bang_yuri_manin}{}\paragraph*{{Time between real and imaginary: what geometries describe the Universe near the Big Bang? (Yuri Manin)}}\label{time_between_real_and_imaginary_what_geometries_describe_the_universe_near_the_big_bang_yuri_manin}

[[Yuri Manin]] on [[Wick rotation]] in [[cosmology]].

category: reference



\end{document}