May - August 2008
Organizers: Alain Connes, Matthias Lesch, Matilde Marcolli
Description: The interactions between mathematics and quantum physics played an important role in recent developments in mathematics. Areas of mathematics which have been inspired very much from physics are Conformal Field Theory, Mirror Symmetry, and Noncommutative Geometry.
The aim of this Hausdorff Trimester Program was to bring together leading experts from these areas. The program was divided into two main parts. The first, May and June, concentrated on quantum field theories, whereas the second, June and August, focussed around non-commutative geometry. The modern geometric quantum field theory involves mathematical areas like topology, diffferential geometry and functional analysis, whereas non-commutative geometry has its idea in the fact that a (nice) space is completely characterized by the C*-algebra of continuous functions, which allows a generalization, mainly propagated by and based on work of A. Connes, by considering non-commutative C*-algebras. Whereas in the first topic one of the big problems is to construct topological or geometric quantum field theories and to study their properties, a guiding principle for the second topic is to generalize theorems known for manifolds like index theorems to the non-commutative world. In both cases the interaction with theoretical physics is a central theme.
Associated Events:
Workshop 1: Mirror Symmetry
Workshop 2: Noncommutative Geometry
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| No. | Author(s) | Title | Preprint | Publication |
| 2008b01 | Abbaspour, H.; Chataur, D. | On the homology of the space of singular knots | 0901.0263 | Homology Homotopy Appl. 15(1) (2013), 101–126. https://doi.org/10.4310/HHA.2013.v15.n1.a6 |
| 2008b02 | Abbaspour, H.; Tradler, T.; Zeinalian, M. | Algebraic string bracket as a Poisson bracket | 0807.2351 | J. Noncommut. Geom. 4(3) (2010), 331–347. https://doi.org/10.4171/JNCG/58 |
| 2008b03 | Carey, A.; Potapov, D.; Sukochev, F. | Spectral flow is the integral of one forms on the Banach manifold of self adjoint Fredholm operators | 0807.2129 | Adv. Math. 222(5) (2009), 1809–1849. https://doi.org/10.1016/j.aim.2009.06.020 |
| 2008b04 | Carey, A. L.; Wang, B-L. | Riemann-Roch and index formulae in twisted K-theory | 0909.4848 | Superstrings, geometry, topology, and C*-algebras, 95–131. https://doi.org/10.1090/pspum/081/2681760 |
| 2008b05 | Cohn, H.; Elkies, N. D.; Kumar, A.; Schürmann, A. | Point configurations that are asymmetric yet balanced | 0812.2579 | Proc. Amer. Math. Soc. 138(8) (2010), 2863–2872. https://doi.org/10.1090/S0002-9939-10-10284-6 |
| 2008b06 | Fathi Zadeh, F.; Khalkhali, M. | The algebra of formal twisted pseudodifferential symbols and a noncommutative residue | 0810.0484 | Lett. Math. Phys. 94(1) (2010), 41–61. https://doi.org/10.1007/s11005-010-0419-z |
| 2008b07 | Feigin, E. | The PBW filtration, Demazure modules and toroidal current algebras | 0806.4851 | SIGMA Symmetry Integrability Geom. Methods Appl. 4(70) (2008). https://doi.org/10.3842/SIGMA.2008.070 |
| 2008b08 | Gálvez, I.; Gorbounov, V.; Tonks, A. | Homotopy Gerstenhaber structures and vertex algebras | math/0611231 | Appl. Categ. Structures. 18(1) (2010), 1–15. https://doi.org/10.1007/s10485-008-9170-3 |
| 2008b09 | Gorbounov, V.; Schechtman, V. | Homological algebra and divergent series | 0712.3670 | SIGMA Symmetry Integrability Geom. Methods Appl. 5(34) (2009). https://doi.org/10.3842/SIGMA.2009.034 |
| 2008b10 | Jarvis, T. J.; Kimura, T. | A representation-valued relative Riemann-Hurwitz theorem and the Hurwitz-Hodge bundle | 0810.2488 | |
| 2008b11 | Khalkhali, M.; Pourkia, A. | Hopf cyclic cohomology in braided monoidal categories | 0807.3890 | Homology Homotopy Appl. 12(1) (2010), 111–155. https://dx.doi.org/10.4310/HHA.2010.v12.n1.a9 |
| 2008b12 | Khalkhali, M.; Landi, G.; van Suijlekom, W. D. | Holomorphic structures on the quantum projective line | 0907.0154 | Int. Math. Res. Not. IMRN. 2011(4) (2011), 851–884. https://doi.org/10.1093/imrn/rnq097 |
| 2008b13 | Kong, L.; Runkel, I. | Cardy algebras and sewing constraints. I | 0807.3356 | Comm. Math. Phys. 292(3) (2009), 871–912. https://doi.org/10.1007/s00220-009-0901-6 |
| 2008b14 | Krishna, A.; Park, J. | Moving lemma for additive Chow groups | 0909.3155 | Algebra Number Theory. 6(2) (2012), 293–326. https://doi.org/10.2140/ant.2012.6.293 |
| 2008b15 | Lesch, M.; Moscovici, H.; Pflaum, M. J. | Connes-Chern character for manifolds with boundary and eta cochains | 0912.0194 | Mem. Amer. Math. Soc. 220(1036) (2012). https://doi.org/10.1090/S0065-9266-2012-00656-3 |
| 2008b16 | Sachse, C.; Wockel, C. | The diffeomorphism supergroup of a finite-dimensional supermanifold | 0904.2726 | Adv. Theor. Math. Phys. 15(2) (2011), 285–323. https://dx.doi.org/10.4310/ATMP.2011.v15.n2.a2 |
| 2008b17 | Sati, H. | OP2 bundles in M-theory | 0807.4899 | Commun. Number Theory Phys. 3(3) (2009), 495–530. https://doi.org/10.4310/CNTP.2009.v3.n3.a3 |
| 2008b18 | Sati, H. | Anomalies of E8 gauge theory on string manifolds | 0807.4940 | Internat. J. Modern Phys. A. 26(13) (2011), 2177–2197. https://doi.org/10.1142/S0217751X1105333X |
| 2008b19 | van Suijlekom, W. D. | The structure of renormalization Hopf algebras for gauge theories I: Representing Feynman graphs on BV-algebras | 0807.0999 | Comm. Math. Phys. 290(1) (2009), 291–319. https://doi.org/10.1007/s00220-009-0829-x |
| 2008b20 | Wockel, C. | Principal 2-bundles and their gauge 2-groups | 0803.3692 | Forum Math. 23(3) (2011), 565–610. https://doi.org/10.1515/FORM.2011.020 |
| 2008b21 | Vignes-Tourneret, F. | The multivariate signed Bollobás-Riordan polynomial | 0811.1584 | Discrete Math. 309(20) (2009), 5968–5981. https://doi.org/10.1016/j.disc.2009.04.026 |
| 2008b22 | Paycha, S. | Divergent multiple sums and integrals with constraints: a comparative study | - | Noncommutative geometry and physics: renormalisation, motives, index theory, 103–174. https://doi.org/10.4171/008-1/4 |
| 2008b23 | Khalkhali, M.; Pourkia, A. | A super version of the Connes-Moscovici Hopf algebra | 1011.2550 | Noncommutative geometry and global analysis, 181–198. https://doi.org/10.1090/conm/546/10789 |
| 2008b24 | Freed, D. S.; Hopkins, M. J.; Lurie, J.; Teleman, C. | Topological quantum field theories from compact Lie groups | 0905.0731 | A celebration of the mathematical legacy of Raoul Bott, 367–403. https://doi.org/10.1090/crmp/050/26 |
| 2008b25 | Spera, M.; Wurzbacher, T. | Good coverings for section spaces of fibre bundles | - | Topology Appl. 157(6) (2010), 1081–1085. https://doi.org/10.1016/j.topol.2010.01.008 |
| 2008b26 | Lesch, Matthias | Pseudodifferential operators and regularized traces | 0901.1689 | Motives, quantum field theory, and pseudodifferential operators, 37–72. LINK |
| 2008b27 | Heydarpour, M. | The Green's functions of the boundaries at infinity of the hyperbolic 3-manifolds | 0912.1731 | J. Geom. Phys. 62(4) (2012), 851–866. https://doi.org/10.1016/j.geomphys.2011.11.008 |
| 2008b28 | Benameur, M-T.; Carey, A. L. | Higher spectral flow and an entire bivariant JLO cocycle | 1108.4528 | J. K-Theory. 11(1) (2013), 183–232. https://doi.org/10.1017/is012008031jkt193 |
Name |
Affiliation |
| Hossein Abbaspour | Université de Nantes |
| Abishek Banerjee | Johns Hopkins University |
| Hanno von Bodecker | Ruhr-Universität Bochum |
| David Edward Bruschi | University of Bologna |
| Alejandro Cabrera | IMPA |
| John Arlo Caine | Max-Planck-Institute for Mathematics |
| Alan Carey | Australian National University |
| Qingtao Chen | University of California at Berkeley |
| Caterina Consani | John Hopkins University |
| Orit Davidovich | University of Texas at Austin |
| Evgeny Feigin | University - Higher School of Economics HSE |
| Dan Freed | University of Texas at Austin |
| Vassily Gorbounov | University of Aberdeen |
| Alexander Gorokhovsky | University of Colorado |
| Fei Han | National University of Singapore |
| Mohammed Hassanzadeh | University of Western Ontario |
| Eli Hawkins | University of York |
| Majid Heydarpour | Institute for Advanced Studies in Basic Sciences |
| Michael Hopkins | Harvard University |
| Masoud Khalkhali | University of Western Ontario |
| Takashi Kimura | Boston University |
| Liang Kong | Institute for Advanced Study in Tsinghua University |
| Matthias Lesch | Universität Bonn |
| Dan Li | Florida State University |
| Matilde Marcolli | Max-Planck-Institute for Mathematics |
| Henri Moscovici | Ohio State University |
| Martin Olbermann | University of California at Berkeley |
| Marie Francoise Ouedraogo | Université de Ouagadougou |
| Chiara Pagani | University of Copenhagen |
| Deepak Parashar | University of Warwick |
| Jinhyun Park | Purdue University |
| Sylvie Paycha | Université Blaise Pascal |
| Fabio Perroni | Universität Zürich |
| Markus Josef Pflaum | University of Colorado |
| Arash Pourkia | University of Western Ontario |
| Arturo Prat-Waldron | Max Planck Institute for Mathematics |
| Rishni Ratnam | Australian National University |
| Ingo Runkel | Kings College London |
| Christoph Sachse | MPI für Mathematik in den Naturwissenschaften |
| Hisham Sati | Yale University |
| Chris Schommer-Pries | University of California at Berkeley |
| Urs Schreiber | Universität Hamburg |
| Ali Shojaei-Fard | |
| Andrzeij Woiciech Sitarz | Jagiellonian University |
| Stephan A. Stolz | University of Notre Dame |
| Walter Daniel van Suijlekom | Radboud Universiteit Nijmegen |
| Peter Teichner | Max-Planck-Institut für Mathematik |
| Constantin Teleman | University of Berkeley |
| Fabien Vignes-Tourneret | University of Vienna |
| Konrad Waldorf | Universität Regensburg |
| Bai-Ling Wang | Australian National University |
| Christoph Wockel | Universität Hamburg |
| Tilmann Wurzbacher | C.N.R.S. et Université Paul Verlaine - Metz |
| Yi-Jun Yao | Vanderbilt University |
| Farzad Fathi Zadeh | University of Western Ontario |
This list does not include people who only participated in the workshops.
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