September 1 - December 19, 2014
Organizers: Alan L. Carey, Victor Gayral, Matthias Lesch, Walter van Suijlekom, Raimar Wulkenhaar
Description: Non-commutative geometry, in the sense of this program, is the exploration of geometric concepts through operator-algebraic methods, as initiated and outlined by Alain Connes. Among the topics and techniques central to non-commutative geometry are Hochschild and cyclic cohomology; bivariant K-theory and index theory; the measure-theoretic and topological analysis of operator algebras; and spectral geometry. Many of these methods arose from classical problems in global analysis, topology and representation theory. Collectively they have become powerful and effective tools that bring geometric ideas to bear on the analysis of a wide range of non-standard spaces arising in mathematics and physics.
Other topics in mathematics and mathematical physics such as non-commutative algebraic geometry, foliations, groupoids, stacks, gerbes, deformations and quantization have increasingly drawn on the perspectives of non-commutative geometry, with index theory often featuring prominently.
Non-commutative spaces also arise in number theory and arithmetic geometry; and in applications to topics in physics such as quantum field theory, renormalization, gauge theory, string theory, cosmology, gravity, mirror symmetry, condensed matter physics and statistical mechanics.
Topics: A primary objective was to focus on applications of NCG with a critical appraisal of their effectiveness. Both established and potential applications were explored and the organisers included a breadth of topics in the program. A summary of the scope is given by the following list:
- the NCG approach to the standard model,
- non-commutative variational methods,
- exactly solved models,
- spectral geometry,
- non-compact (non-unital) geometries,
- dynamical systems,
- number theory,
- KMS theory,
- twisted K-theory,
- condensed matter physics applications,
- Hopf algebras and quantum groups,
- foliations.
Associated Events: There were four workshops during the trimester:
- September 15-19, Non-commutative geometry's interactions with mathematics.
- September 22-26, Quantum physics and non-commutative geometry.
- November 24-28, Number theory and non-commutative geometry.
- December 15-18, Future directions for non-commutative geometry.
There was a summer school directed at beginning PhD students:
- September 8-12, Topics in non-commutative geometry.
There was a series of lecture courses aimed at postgraduate students and postdoctoral level researchers:
- September 29 - November 21, Special topics series.
There was also a weekly seminar series on current research topics and a working seminar within that part of the program aimed at junior researchers.
© HIM
| No. | Author(s) | Title | Preprint | Publication |
| 2014c01 | Arici, F.; Kaad, J.; Landi, G. | Pimsner algebras and Gysin sequences from principal circle actions | 1409.5335 | J. Noncommut. Geom.10(1) (2016), 29–64. https://doi.org/10.4171/JNCG/228 |
| 2014c02 | Boeijink, J.; van den Dungen, K. | On globally non-trivial almost-commutative manifolds | 1405.5368 | J. Math. Phys. 55(10) (2014), 33. https://doi.org/10.1063/1.4898769 |
| 2014c03 | D'Andrea, F.; Landi, G. | Quantum weighted projective and lens spaces | 1410.4508 | Comm. Math. Phys. 340(1) (2015), 325–353. https://doi.org/10.1007/s00220-015-2450-5 |
| 2014c04 | van Erp, E.; Julg, P. | The geometry of the osculating nilpotent group structures of the Heisenberg calculus | 1007.4759 | J. Lie Theory. 28(1) (2018), 107–138. https://www.heldermann.de/JLT/JLT28/JLT281/jlt28007.htm |
| 2014c05 | Cornelissen, G.; Reynolds, J. | The perfect power problem for elliptic curves over function fields | 1411.7787 | New York J. Math. 22 (2016), 95–114. http://nyjm.albany.edu:8000/j/2016/22_95.html |
| 2014c06 | Gayral, V.; Jondreville, D. | Deformation quantization for actions of (ℚp)d | 1409.3349 | J. Funct. Anal. 268(11) (2015), 3357–3403. https://doi.org/10.1016/j.jfa.2014.12.017 |
| 2014c07 | Bourne, C.; Carey, A. L.; Rennie, A. | The bulk-edge correspondence for the quantum Hall effect in Kasparov theory | 1411.7527 | Lett. Math. Phys. 105(9) (2015), 1253–1273. https://doi.org/10.1007/s11005-015-0781-y |
| 2014c08 | Lechtenfeld, O.; Popov, A. D.; Szabo, R. J. | Sasakian quiver gauge theories and instantons on Calabi-Yau cones | 1412.4409 | Adv. Theor. Math. Phys. 20(4) (2016), 821–882. https://doi.org/10.4310/ATMP.2016.v20.n4.a4 |
| 2014c09 | Dabrowski, L.; Landi, G.; Luef, F. | Sigma-model solitons on noncommutative spaces | 1501.02331 | Lett. Math. Phys. 105(12) (2015), 1663–1688. https://doi.org/10.1007/s11005-015-0790-x |
| 2014c10 | Pennig, U. | A non-commutative model for higher twisted K-Theory | 1502.02807 | J. Topol. 9(1) (2016), 27–50. https://doi.org/10.1112/jtopol/jtv033 |
| 2014c11 | Mesland, B.; Rennie, A. | Nonunital spectral triples and metric completeness in unbounded KK-theory | 1502.04520 | J. Funct. Anal. 271(9) (2016), 2460–2538. https://doi.org/10.1016/j.jfa.2016.08.004 |
| 2014c12 | Franco, N.; Eckstein, M. | Causality in noncommutative two-sheeted space-times | 1502.04683 | J. Geom. Phys. 96 (2015), 42–58. https://doi.org/10.1016/j.geomphys.2015.05.008 |
| 2014c13 | Meyer, R.; Pennig, U. | Crossed module actions on continuous trace C*-algebras | 1506.01311 | Comm. Math. Phys. 346(1) (2016), 115–142. https://doi.org/10.1007/s00220-016-2638-3 |
| 2014c14 | Cornelissen, G.; Kool, J. | Edge reconstruction of the Ihara zeta function | 1507.03411 | Electron. J. Combin. 25(2) (2018), 22. https://doi.org/10.37236/5909 |
| 2014c15 | Lesch, M.; Moscovici, H. | Modular curvature and Morita equivalence | 1505.00964 | Geom. Funct. Anal. 26(3) (2016), 818–873. https://doi.org/10.1007/s00039-016-0375-6 |
| 2014c16 | Fathizadeh, F.; Gabriel, O. | On the Chern-Gauss-Bonnet theorem and conformally twisted spectral triples for C*-dynamical systems | 1506.07913 | SIGMA Symmetry Integrability Geom. Methods Appl. 12(16) (2016), 21. https://doi.org/10.3842/SIGMA.2016.016 |
| 2014c17 | Barnea, I.; Joachim, M.; Mahanta, S. | Model structure on projective systems of C*-algebras and bivariant homology theories | 1508.04283 | New York J. Math. 23 (2017), 383–439. http://nyjm.albany.edu:8000/j/2017/23_383.html |
| 2014c18 | Mahanta, S. | C*-algebraic drawings of dendroidal sets | 1501.05799 | Algebr. Geom. Topol. 19(3) (2019), 1171–1206. https://doi.org/10.2140/agt.2019.19.1171 |
| 2014c19 | Mahanta, S. | Colocalizations of noncommutative spectra and bootstrap categories | 1412.8370 | Adv. Math. 285 (2015), 72–100. https://doi.org/10.1016/j.aim.2015.07.029 |
| 2014c20 | Baer, C.; Strohmaier, A. | An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary | 1506.00959 | Amer. J. Math. 141(5) (2019), 1421–1455. https://doi.org/10.1353/ajm.2019.0037 |
| 2014c21 | Kurkov, M. A.; Lizzi, F.; Sakellariadou, M.; Watcharangkool, A. | Spectral action with zeta function regularization | 1412.4669 | Phys. Rev. D. 91(6) (2015), 10. https://doi.org/10.1103/PhysRevD.91.065013 |
| 2014c22 | Devastato, A.; Lizzi, F.; Flores, C. V.; Vassilevich, D. | Unification of coupling constants, dimension 6 operators and the spectral action | 1410.6624 | Inter. J. of Modern Physics. 30(7) (2015). https://doi.org/10.1142/S0217751X15500335 |
| 2014c23 | Fathizadeh, F. | On the scalar curvature for the noncommutative four torus | 1410.8705 | J. Math. Phys. 56(6) (2015), 14. https://doi.org/10.1063/1.4922815 |
| 2014c24 | Matassa, M. | An analogue of Weyl's law for quantized irreducible generalized flag manifolds | 1410.8029 | J. Math. Phys. 56(9) (2015), 20. https://doi.org/10.1063/1.4931606 |
| 2014c25 | Baum, P. F.; Dabrowski, L.; Hajac, P. M. | Noncommutative Borsuk-Ulam-type conjectures | 1502.05756 | Banach Center Publications. 106 (2015), 9-18. https://doi.org/10.4064/bc106-0-1 |
| 2014c26 | Carey, A.; Grosse, H.; Kaad, J. | On a spectral flow formula for the homological index | 1501.05453 | Adv. Math. 289 (2016), 1106–1156. https://doi.org/10.1016/j.aim.2015.10.030 |
| 2014c27 | Fathi, A.; Khalkhali, M. | On certain spectral invariants of Dirac operators on noncommutative tori | 1504.01174 | |
| 2014c28 | Fathizadeh, F.; Ghorbanpour, A.; Khalkhali, M. | Rationality of spectral action for Robertson-Walker metrics | 1407.5972 | J. High Energy Phys. 2014(64) (2014). https://doi.org/10.1007/JHEP12(2014)064 |
| 2014c29 | Fathi, A.; Ghorbanpour, A.; Khalkhali, M. | Curvature of the determinant line bundle for the noncommutative two torus | 1410.0475 | Math. Phys. Anal. Geom. 20(2) 4 (2017), 20. https://doi.org/10.1007/s11040-016-9234-9 |
| 2014c30 | Arnlind, J.; Wilson, M. | Riemannian curvature of the noncommutative 3-sphere | 1505.07330 | J. Noncommut. Geom. 11(2) (2017), 507–536. https://doi.org/10.4171/JNCG/11-2-3 |
| 2014c31 | Takeishi, T. | Irreducible representations of Bost-Connes systems | 1412.6900 | J. Noncommut. Geom. 10(3) (2016), 889–906. https://doi.org/10.4171/JNCG/251 |
| 2014c32 | Neumann, N.; van Suijlekom, W. D. | Perturbation semigroup of matrix algebras | 1410.5961 | J. Noncommut. Geom. 10(1) (2016), 245–264. https://doi.org/10.4171/JNCG/233 |
| 2014c33 | Deeley, R. J.; Goffeng, M.; Mesland, B. | The bordism group of unbounded KK-cycles | 1503.07398 | J. Topol. Anal. 10(2) (2018), 355–400. https://doi.org/10.1142/S1793525318500012 |
| 2014c34 | van den Dungen, K.; Rennie, A. | Indefinite Kasparov modules and pseudo-Riemannian manifolds | 1503.06916 | Ann. Henri Poincaré. 17(11) (2016), 3255–3286. https://doi.org/10.1007/s00023-016-0463-z |
| 2014c35 | Forsyth, I.; Rennie, A. | Factorisation of equivariant spectral triples in unbounded KK-theory | 1505.02863 | J. Aust. Math. Soc. 107(2) (2019), 145–180. https://doi.org/10.1017/s1446788718000423 |
| 2014c36 | Bourne, C.; Carey, A. L.; Rennie, A. | A non-commutative framework for topological insulators | 1509.07210 | Rev. Math. Phys. 28(2) (2016), 51. https://doi.org/10.1142/S0129055X16500045 |
| 2014c37 | Lorscheid, O. | Scheme theoretic tropicalization | 1508.07949 | |
| 2014c38 | Samary, Dine O.; Pérez-Sánchez, C. I.; Vignes-Tourneret, F.; Wulkenhaar, R. | Correlation functions of a just renormalizable tensorial group field theory: the melonic approximation | 1411.7213 | Classical Quantum Gravity. 32(17) (2015), 18. https://doi.org/10.1088/0264-9381/32/17/175012 |
| 2014c39 | Connes, A.; Consani, C. | Absolute algebra and Segal's Gamma sets | 1502.05585 | J. of Number Theory. 162 (2016), 518-551. https://doi.org/10.1016/j.jnt.2015.12.002 |
| 2014c40 | van Erp, E.; Yuncken, R. | A groupoid approach to pseudodifferential operators | 1511.01041 | Journal für die reine und angewandte Mathematik. 2019(756) (2019), 151-182. https://doi.org/10.1515/crelle-2017-0035 |
| 2014c41 | Renault, J. N.; Williams, D. P. | Amenability of groupoids arising from partial semigroup actions and topological higher rank graphs | 1501.03027 | Trans. Amer. Math. Soc. 369(4) (2017), 2255–2283. https://doi.org/10.1090/tran/6736 |
| 2014c42 | Savin, A. Y.; Sternin, B. Y. | Elliptic G-operators on manifolds with isolated singularities | 1511.01886 | J. Math. Sci. 233(6) (2018), 930–948. https://doi.org/10.1007/s10958-018-3973-z |
| 2014c43 | Levitina, G.; Sukochev, F.; Zanin, D. | Lipschitz properties of smoothed signum for the Dirac operator | in preparation | |
| 2014c44 | Bourne, C.; Kellendonk, J.; Rennie, A. | The K-theoretic bulk-edge correspondence for topological insulators | 1604.02337 | Ann. Henri Poincaré. 18(5) (2017), 1833–1866. https://doi.org/10.1007/s00023-016-0541-2 |
| 2014c45 | Eckstein, M.; Franco, N.; Miller, T. | The noncommutative geometry of Zitterbewegung | 1610.10083 | Phys. Rev. D. 95(6) (2017). https://doi.org/10.1103/PhysRevD.95.061701 |
| 2014c46 | van Suijlekom, W. D. | Localizing gauge theories from noncommutative geometry | 1411.6482 | Adv. Math. 290 (2016), 682–708. https://doi.org/10.1016/j.aim.2015.11.047 |
| 2014c47 | Bytsenko, A. A.; Szabo, R. J.; Tureanu, A. | Stratified fiber bundles, Quinn homology and brane stability of hyperbolic orbifolds | 1502.07560 | J. Phys. A. 49(16) (2016), 25. https://doi.org/10.1088/1751-8113/49/16/165401 |
| Name | Affiliation |
| Francesca Arici | SISSA |
| Joakim Arnlind | Linköping University |
| Sara Azzali | Universität Potsdam |
| Abhishek Banerjee | Indian Institute of Science |
| Tathagata Banerjee | Georg-August-Universität Göttingen |
| Paul Frank Baum | Penn State University |
| Jord Boeijink | Radboud University Nijmegen |
| Christopher Bourne | Australian National University |
| Latham Boyle | Perimeter Institute for Theoretical Physics |
| Simon Brain | Radboud University Nijmegen |
| Branimir Cacic | Texas A&M University |
| Clarisson Rizzie Canlubo | University of Copenhagen |
| Alan Carey | Australian National University |
| Paulo Carrillo Rouse | Université Toulouse 3 |
| Pierre E. Cartier | IHES |
| Partha Sarathi Chakraborty | Chennai Institute of Technology |
| Sayan Chakraborty | University of Münster |
| Alain Connes | College de France |
| Gunther L.M. Cornelissen | Universiteit Utrecht |
| Joachim Cuntz | Westfälische Wilhelms-Universität Münster |
| Francesco D'Andrea | University of Naples Federico II |
| Ludwik Dabrowski | SISSA |
| Koen van den Dungen | Australian National University |
| Michal Eckstein | Jagiellonian University |
| Erik van Erp | Dartmouth College |
| Kevin Falk | Aix-Marseille Université |
| Shane Farnsworth | Perimeter Institute for Theoretical Physics |
| Farzad Fathi Zadeh | University of Western Ontario |
| Iain Forsyth | Australian National University |
| Nicolas Franco | Jagiellonian University |
| Nicolas Franco | Jagiellonian University |
| Olivier Gabriel | Universität Göttingen |
| Olivier Gabriel | Universität Göttingen |
| Victor Gayral | Université de Reims Champagne Ardenne |
| Victor Gayral | Université de Reims Champagne Ardenne |
| Asghar Ghorbanpour | University of Western Ontario |
| Axel de Goursac | MPI Bonn |
| Harald Grosse | University of Vienna |
| Piotr M. Hajac | Mathematical Institute of the Polish Academy of Sciences (IMPAN) |
| Pedram Hekmati | The University of Adelaide |
| Nigel Higson | Penn State University |
| Forsyth Iain | Australian National University |
| Bruno Iochum | Centre de Physique Théorique |
| Roberta Anna Iseppi | Radboud University Nijmegen |
| David Jondreville | U.F.R. Sciences Exactes et Naturelles |
| Jins de Jong | Westfälische Wilhelms-Universität Münster |
| Pierre Julg | Université d'Orléans |
| Jens Kaad | Institut de Mathématiques de Jussieu |
| Johannes Kellendonk | Université Claude Bernard Lyon 1 |
| Masoud Khalkhali | Western University, London, Ontario, Canada |
| Ehssan Khanmohammadi | Penn State University |
| Niek de Kleijn | University of Copenhagen |
| Yuri Kordyukov | Russian Academy of Sciences |
| Marcelo Laca | University of Victoria |
| Giovanni Landi | Università di Trieste |
| Edwin Langmann | KTH Royal Institute of Technology |
| Matthias Lesch | Universität Bonn |
| Galina Levitina | University of New South Wales |
| Fedele Lizzi | Università di Napoli Federico II |
| Franz Luef | NTNU Trondheim |
| Yoshiaki Maeda | Tohoku University |
| Yoshiaki Maeda | Tohoku University |
| Snigdhayan Mahanta | Universität Regensburg |
| Marco Matassa | University of Oslo |
| Bram Mesland | University of Warwick |
| Ralf Meyer | Georg-August-Universität Göttingen |
| Jouko Mickelsson | Helsinki University |
| Ryszard Nest | Copenhagen University |
| Ryszard Nest | Copenhagen University |
| Victor Nistor | Penn State University |
| Juan Orduz | Humboldt Universität zu Berlin |
| Hervé Oyono-Oyono | Institut Elie Cartan de Lorraine |
| Sylvie Paycha | Universität Potsdam |
| Ulrich Pennig | Westfälische Wilhelms-Universität Münster |
| Ulrich Pennig | Westfälische Wilhelms-Universität Münster |
| Carlos Perez-Sanchez | WWU Münster |
| Denis Perrot | Universite Claude Bernard Lyon 1 |
| Hessel Posthuma | University of Amsterdam |
| Bahram Rangipour | University of New Briunswick |
| Jean Renault | Université d'Orléans |
| Adam Rennie | University of Wollongong |
| Sajad Sadeghi | Western University |
| Aurelien Sagnier | Université Paris 7 Diderot |
| Mairi Sakellariadou | King's College London |
| Jean-Luc Sauvageot | Université Paris 7 |
| Anton Savin | Peoples' Friendship University of Russia |
| Thomas Schick | Georg-August-Universität Göttingen |
| Andrzej Sitarz | Jagiellonian University |
| Scott Smedinghoff | Dartmouth College |
| Christoph Stephan | Universität Potsdam |
| Alexander Strohmaier | Loughborough University |
| Walter Daniel van Suijlekom | Radboud University Nijmegen |
| Fedor Sukochev | University of NSW |
| Richard Szabo | Heriot-Watt University |
| Takuya Takeishi | University of Tokyo |
| Aleksi Tavkhelidze | Georg-August Universität Göttingen |
| Baris Evren Ugurcan | The University of Western Ontario |
| Dmitry Vasilevich | Universidade Federal do ABC |
| Joannes Jitse Venselaar | California Institute of Technology |
| Stefan Wagner | University of Helsinki |
| Mitsuru Wilson | University of Western Ontario |
| Anja Wittmann | Universität Freiburg |
| Jianchao Wu | Westfälische Wilhelms-Universität Münster |
| Raimar Wulkenhaar | Westfälische Wilhelms-Universität Münster |
| Zhizhang Xie | Texas A&M University |
| Bora Yalkinoglu | IRMA CNRS |
| Robert Yuncken | Universite Blaise Pascal, Clermont-Ferrand II |
This list does not include people who only participated in the workshops.
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