Tarih: June 18-29, 2018 (Arrival to the village: 17 June 2018, departure from the Village: 29 June 2018)
Amaç
Deadlines: 1 May 2018
Quota: 30 people
Fees: The normal daily fee is 110 TL; for those staying in tents the fee is 80 TL. This covers accomodation, four meals a day and all the facilities that the Village offer. If you need financial support please write it to application form.
Accommodation: Undergraduate and graduate students will mostly stay in tents. Experience shows that due to the greater freedom and independence it affords them, older students themselves prefer this arrangement. If you have any doubts about this subject please write to us. Though we can give no guarantees, you can be sure we will do our best to come to an arrangement which is satisfactory to you.
Lecture Notes
Urs https://ncatlab.org/schreiber/
PIZ http://math.huji.ac.il/~piz/
Patrick Iglesias-Zemmour (piz@math.huji.ac.il): Diffeology
– Category {Diffeology} Set theoretic construction and stability.
– The case of singular quotients and an example or two in infinite dimension.
– Modelling diffeologies (manifolds, orbifolds, manifolds with corners
).
– Differential calculus and De Rham cohomology (with Serap Gürer).
– Fiber bundles and homotopy.
– Moment Maps and integration of closed forms, general prequantization.
Murad Özaydin (mozaydin@math.ou.edu): Non-Commutative Geometry
– Geometry-Algebra dictionary: C*-Algebras, Gelfand-Naimark duality; vector bundles, K-theory, projective modules, Serre-Swan theorem.
– Mathematical methods and models of quantum physics. Gelfand-Naimark-Segal duality.
– Quantum tori, noncommutative quotients.
– Foliations, von Neumann algebras.
– Morita equivalence.
– Hopf algebras and quantum groups.
– Deformation and quantization.
– Noncommutative algebraic geometry: affine, projective and derived.
– Noncommutative Stone-Weierstrass theorem.
– Homological algebra, cyclic cohomology.
– Connes-Chern character: topological index = analytic index.
– Spectral triples.
Urs Schreiber (Urs.Schreiber@gmail.com): Categories and Toposes – Local field theory in a differentially cohesive infinity-topos.
– Categories and limits/colimits.
– Adjoint functors and Kan extension.
– Categories of pre-sheaves.
– Simplicial sets and simplicial pre-sheaves.
– Simplicial sheaves on the site of smooth manifolds.
– Simplicial sheaves on the site of formal manifolds.