January 2 - April 30, 2012
Organizers: Franz Pedit, Ulrich Pinkall, Iskander A. Taimanov, Alexander Veselov, Katrin Wendland
Description: The past two decades have seen substantial developments in the theory of integrability, to the extent that integrable systems nowadays comprise a vital ingredient in algebraic, differential and enumerative geometry as well as in mathematical physics. Contributions range from Dubrovin's pioneering work on Frobenius manifolds over Hitchin's discovery of integrability of moduli spaces of stable vector or Higgs bundles up to results by Kontsevich and Okounkov-Pandharipande on the Witten conjecture and Gromov-Witten theory, and Krichever's proof of the Welter's trisecant conjecture. Furthermore, integrable systems play a pivotal role in the resolution of longstanding conjectures about the global structure of minimal, constant mean curvature and Willmore surfaces.
The most striking aspects of the theory of integrable systems, which however are becoming apparent only very slowly, feature integrability as a binding element between seemingly unrelated areas in mathematics. For example, the role of integrability in singularity theory is not well studied to the very day, although for quantum cohomology, the importance of both singularity theory and integrability is undisputed, such that direct links between the two must exist. On another account, the tt* geometry of topological quantum field theory also provides aspects of the Pedit-Dorfmeister-Wu construction in the context of Willmore surfaces.
This Hausdorff Trimester Program brought together some of the world leading scientists in the study of integrable systems in geometry and quantum field theory. One main aspect of the program was the aim to bridge between the research topics, to spark interactions, and to shed light on the binding role that integrability can play for all the themes involved.
Associated Events:
Workshop 1: Integrability - modern variations
Workshop 2: Geometric PDEs and integrability
Workshop 3: Navigating the Space of Surfaces
Workshop 4: Integrability in topological field theory
| No. | Author(s) | Title | Preprint | Publication |
| 2012a05 | Mironov, A. | Commuting higher rank ordinary differential operators | 1204.2092 | European Congress of Mathematics. (2013), 459–473. MR3469138 |
| 2012a06 | Mkrtchyan, R. L.; Veselov, A. P. | Universality in Chern-Simons theory | 1203.0766 | J. High Energy Phys. 2012(153) (2012). https://doi.org/10.1007/JHEP08(2012)153 |
| 2012a07 | Izosimov, A. | Stability of relative equilibria of multidimensional rigid body | 1203.3985 | Nonlinearity. 27(6) (2014), 1419–1443. https://doi.org/10.1088/0951-7715/27/6/1419 |
| 2012a08 | Bolsinov, A.; Izosimov, A. | Singularities of bi-Hamiltonian systems | 1203.3419 | Comm. Math. Phys. 331(2) (2014), 507–543. https://doi.org/10.1007/s00220-014-2048-3 |
| 2012a09 | Izosimov, A. | A note on relative equilibria of a free multidimensional rigid body | 1202.4082 | J. Phys. A. 45(32) (2012), 325203, 6. https://doi.org/10.1088/1751-8113/45/32/325203 |
| 2012a10 | Alexandrov, A.; Kazakov, V.; Leurent, S.; Tsuboi, Z.; Zabrodin, A. | Classical tau-function for quantum spin chains | 1112.3310 | J. High Energy Phys. 2013(64) (2013). https://doi.org/10.1007/JHEP09(2013)064 |
| 2012a11 | Marshakov, A. | Lie groups, cluster variables and integrable systems | 1207.1869 | J. Geom. Phys. 67 (2013), 16–36. https://doi.org/10.1016/j.geomphys.2012.12.003 |
| 2012a12 | Gordon, I. G.; Martino, M. | Monodromy of partial KZ functors for rational Cherednik algebras | Symmetries, integrable systems and representations. 40, 133–154. https://doi.org/10.1007/978-1-4471-4863-0_6 |
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| 2012a13 | Varchenko, A.; Wright, D. | Critical points of master functions and integrable hierarchies | 1207.2274 | Adv. Math. 263 (2014), 178–229. https://doi.org/10.1016/j.aim.2014.06.014 |
| 2012a14 | Taormina, A.; Wendland, K. | The overarching finite symmetry group of Kummer surfaces in the Mathieu group M24 | 1107.3834 | J. High Energy Phys. 2013(125) (2013). https://doi.org/10.1007/JHEP08(2013)125 |
| 2012a15 | Heller, S. | A spectral curve approach to Lawson symmetric CMC surfaces of genus 2 | 1209.3200 | Math. Ann. 360(3-4) (2014), 607–652. https://doi.org/10.1007/s00208-014-1044-4 |
| 2012a16 | Izosimov, A. | Stability in bihamiltonian systems and multidimensional rigid body | J. Geom. Phys. 62(12) (2012), 2414–2423. https://doi.org/10.1016/j.geomphys.2012.09.006 |
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| 2012a17 | Kato, H. | Castling transformations of projective structures | 1301.1063 | J. Lie Theory. 23(4) (2013), 1129–1160. https://www.heldermann.de/JLT/JLT23/JLT234/jlt23058.htm |
| 2012a18 | Alexandrov, A. | From Hurwitz numbers to Kontsevich-Witten tau-function: a connection by Virasoro operators | 1111.5349 | Lett. Math. Phys.104(1) (2014), 75–87. https://doi.org/10.1007/s11005-013-0655-0 |
| 2012a19 | Schöbel, K.; Veselov, A. P. | Separation coordinates, moduli spaces and Stasheff polytopes | 1307.6132 | Comm. Math. Phys. 337(3) (2015), 1255–1274. https://doi.org/10.1007/s00220-015-2332-x |
| 2012a20 | Mulase, M.; Sułkowski, P. | Spectral curves and the Schrödinger equations for the Eynard-Orantin recursion | 1210.3006 | Adv. Theor. Math. Phys. 19(5) (2015), 955–1015. https://doi.org/10.4310/ATMP.2015.v19.n5.a2 |
| 2012a21 | Bohle, C.; Taimanov, I. A. | Spectral curves for Cauchy-Riemann operators on elliptic curves with punctured points | 1212.5147 | Funct. Anal. Appl (transl.). 47(4) (2013), 319–322. https://doi.org/10.1007/s10688-013-0039-3 |
| 2012a22 | Bohle, C.; Taimanov, I. A. | Euclidean minimal tori with planar ends and elliptic solitons | 1212.5138 | Int. Math. Res. Not. IMRN. 2015(14) (2015), 5907–5932. https://doi.org/10.1093/imrn/rnu113 |
| 2012a23 | Feigin, M. V.; Hallnäs, M. A.; Veselov, A. P. | Baker-Akhiezer functions and generalised Macdonald-Mehta integrals | 1210.5270 | J. Math. Phys. 54(5) (2013). https://doi.org/10.1063/1.4804615 |
| 2012a24 | Mazzocco, M. | Confluences of the Painlevé equations, Cherednik algebras and q-Askey scheme | 1307.6140 | Nonlinearity. 29(9) (2016), 2565–2608. https://doi.org/10.1088/0951-7715/29/9/2565 |
Name |
Affiliation |
| Leonardo Aguirre | ETH Zürich |
| Alexander Alexandrov | Albert-Ludwigs-Universität Freiburg |
| Stuart J. Andrew | Loughborough University |
| Yaroslav V. Bazaykin | Sobolev Institute of Mathematics SB RAS |
| Christoph Bohle | Universität Tübingen |
| Nobutaka Boumuki | Osaka City University Advanced |
| Francis Everett Burstall | University of Bath |
| Leonid Chekhov | Steklov Mathematical Institute |
| Josef Dorfmeister | TU München |
| Boris Dubrovin | SISSA |
| Nicholas Early | Penn State University |
| Magnus Engenhorst | Universität Bonn |
| Oliver Fabert | Universität Freiburg |
| Misha Feigin | University of Glasgow |
| Giovanni Felder | ETH Zürich |
| Iain Gordon | University of Edinburgh |
| Petr Grinevich | Landau Institute for Theoretical Physics RAS |
| Martin Axel Hallnas | Loughborough University |
| Mark Haskins | Imperial College London |
| Laurent Hauswirth | Université de Marne-la-Vallée |
| Sebastian Heller | Universität Tübingen |
| Claus Hertling | Universität Mannheim |
| Rei Inoue Yamazaki | Chiba University |
| Anton Izosimov | Loughborough University |
| Toru Kajigaya | Tohoku University |
| Hironao Kato | Osaka City University |
| Kotaro Kawai | Tohoku University |
| Graham Kemp | Loughborough University |
| Christian Korff | University of Glasgow |
| Jorge Herbert S. Lira | Federal University of Cearh |
| Sergey Loktev | National Research University Higher School of Economics |
| Andrey Marshakov | Lebedev Physics Institute and ITEP |
| Marta Mazzocco | Loughborough University |
| Andrey Mironov | Sobolev Institute of Mathematics |
| Reiko Miyaoka | Tohoku University |
| Sophie Morier-Genoud | Université Pierre et Marie Curie |
| Yoshihiro Ohnita | Osaka City University & Osaka City University Advanced Mathematical Institute |
| Richard Palais | University of California, Irvine |
| Franz Pedit | Universität Tübingen |
| Ulrich Pinkall | TU Berlin |
| Vladimir A. Poberezhnyi | ITEP State Institute for Theoretical and Experimental Physics |
| Paolo Rossi | Universität Zürich |
| Leonid Rybnikov | Higher School of Economics |
| Emanuel Scheidegger | Universität Freiburg |
| Martin Schlichenmaier | University of Luxembourg |
| Martin Schmidt | Universität Mannheim |
| Nicholas Schmitt | Universität Tübingen |
| Veronika Schreiber | Loughborough University |
| Konrad Schöbel | Universität Jena |
| Alexander Sergeev | Saratov State University |
| Oleg Sheinman | Steklov Mathematical Institute |
| Sergei Tabachnikov | Pennsylvania State University |
| Chuu-Lian Terng | University of California, Irvine |
| Richard Thomas | Imperial College London |
| Satoshi Ueki | Tohoku University |
| Alexander Varchenko | The University of North Carolina at Chapel Hill |
| Alexander P. Veselov | Loughborough University |
| Katrin Wendland | Albert-Ludwigs-Universität Freiburg |
| Daniel Wright | The University of North Carolina at Chapel Hill |
| Anton Zabrodin | Institute for Theoretical and Experimental Physics |
| Wojciech J. Zakrzewski | Durham University |
