Seminar on Spectral Triples (MRI Masterclass)
Practical Matters
This seminar is part of the MRI Masterclass on Arithmetic Geometry and Noncommutative Geometry. There is a maximal number of (active) participants to the seminar of 11.
Location Utrecht, Maths Building room 611AB
Time Thursdays 11-13; starts week 6 (8 Feb); ends week 20 (20 May) - interrupted for "Masterclass in the Masterclass"
Evaluation You are expected to give at least one seminar talk. You will study the material beforehand, hold a blackboard presentation about it, and maybe distribute lecture notes for your talk. Your grade will be based on how you deliver your talk, and on your participation in the talks of others. Please note: giving a good seminar talk is extremely difficult; you should prepare your talks very well. For one thing, future talks might depend on it. You should make sure that the material fits into the time slot, is presented in a clear way. You should make sure that you understand what you are talking about. If you can read some German, look at Manfred Lehn's advice here.
Since most talks will be about research papers, we mainly expect you to be able to present the main results from the paper in a concise and comprehensible way. We want you to answer questions like: "What is the paper about? Which objects, which results? What is the history?" Try to give some non-trivial examples of the concepts and theorems. We don't want you to explain the details of proofs, but you are encouraged to present some idea of proof if possible and fit.
Details
| week | date | topic | Speaker |
| 6 | 11 Feb | J. Cuntz, W. Krieger, A class of C*-algebras and topological Markov chains. Invent. Math. 56 (1980), no. 3, 251--268. | Daniel |
| 7 | 18 Feb | No seminar | |
| 8 | 25 Feb | A. Connes, C*-algebras and differential geometry. arXiv:hep-th/0101093v1 In: SUPERSYMMETRY 2000 - Encyclopaedic Dictionary. (French Original: C.R. Acad. Sci. Paris, Ser. A-B, 290, 1980.) | Ori |
| 9 | 4 Mar | No seminar (MC in MC Robertson) | |
| 10 | 11 Mar | J. Plazas, Examples of noncommutative manifolds: complex tori and spherical manifolds. An invitation to noncommutative geometry, 419--445, World Sci. Publ., Hackensack, NJ, 2008. | David |
| 11 | 18 Mar | No seminar (MC in MC Consani) | |
| 12 | 25 Mar |
N. Higson, Meromorphic continuation of zeta functions associated to elliptic operators. Operator algebras, quantization, and noncommutative geometry, 129--142, Contemp. Math., 365, Amer. Math. Soc., Providence, RI, 2004. | Jason |
| 13 | 1 Apr | A. Connes, Gravity coupled with matter and the foundation of non-commutative geometry. Comm. Math. Phys. 182 (1996), no. 1, 155--176. | Mike |
| 14 | 8 Apr | G. Cornelissen, M. Marcolli, Zeta functions that hear the shape of a Riemann surface. J. Geom. Phys. 58 (2008), no. 5, 619--632. | Javier |
| 15 | 15 Apr | M. Marcolli, M.Varghese, Twisted index theory on good orbifolds. II. Fractional quantum numbers. Comm. Math. Phys. 217 (2001), no. 1, 55--87. | Maciek |
| 16 | 22 Apr | No seminar (exam week) | |
| 17 | 29 Apr | No seminar (MC in MC van Suijlekom) | |
| 18 | 6 May | J.-B. Bost, A. Connes, Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory. Selecta Math. (N.S.) 1 (1995), no. 3, 411--457. | Daniel |
| 19 | 13 May | No seminar (official day off) | |
| 20 | 20 May | A. Connes, M. Marcolli, From physics to number theory via noncommutative geometry. Part I Quantum Statistical Mechanics of Q-Lattices. Frontiers in number theory, physics, and geometry. I, 269--347, Springer, Berlin, 2006 | Alex |
| 21 | 27 May | A. Connes, G. Landi, Noncommutative manifolds, the instanton algebra and isospectral deformations. Comm. Math. Phys. 221 (2001), no. 1, 141--159. | Boris |