Universität Bonn

Junior Trimester Program: "Optimal Transportation"

January 5 - April 24, 2015

Description: The Junior Hausdorff Trimester Program gave young mathematicians (postdocs, junior faculty) the opportunity to carry out collaborative research on Optimal Transportation.

The main focus was on the following research topics:

  • Global and local properties of metric measure spaces with synthetic Ricci curvature bounds
  • Optimal transport and stochastic analysis
  • Scale separation of gradient flows in continuous and discrete setting

Associated Events: 

  • Workshop: Analytic approaches to scaling limits for random system
  • Workshop: Gradient flows and entropy methods
  • Winter School & Workshop: New developments in Optimal Transport, Geometry and Analysis
  • Conference: New Trends in Optimal Transport
  • Workshop: Optimal transport and stochastics
TP_2015_01.png
© Wikimedia Commons

Publications

No. Author(s) Title Preprint Publication
2015a01 Bandara, L.; Lakzian, S.; Munn, M. Geometric singularities and a flow tangent to the Ricci flow 1505.050354 Ann. Sc. Norm. Super. Pisa Cl. Sci. XVII(2) (2017), 763-804.
https://doi.org/10.2422/2036-2145.201506_0105
2015a02 Bandara, L. Continuity of solutions to space-varying pointwise linear elliptic equations 1505.061506 Publ. Mat. 61(1) (2017), 239 – 258.
https://doi.org/10.5565/PUBLMAT_61117_097
2015a03 Erbar, M.; Fathi, M.; Laschos, V.; Schlichting, A. Gradient flow structure for McKean-Vlasov equations on discrete spaces 1601.080988 Discrete and Continuous Dynamical Systems. 36(12) (2016), 6799-6833.
https://doi.org/10.3934/dcds.20160969
2015a04 Fathi, M.; Stoltz, G. Improving dynamical properties of metropolized discretizations of overdamped Langevin dynamics 1505.0490510 Numer. Math. 136 (2017), 545–602.
https://doi.org/10.1007/s00211-016-0849-311
2015a05 Fathi, M.; Simon, M. The gradient flow approach to hydrodynamic limits for the simple exclusion process 1507.0648912 From Particle Systems to Partial Differential Equations III. 162
https://doi.org/10.1007/978-3-319-32144-8_813
2015a06 Fathi, M.; Shu, Y. Curvature and transport inequalities for Markov chains in discrete spaces 1509.0716014 Bernoulli. 24(1) (2018), 672 – 698.
https://doi.org/10.3150/16-BEJ89215
2015a07 Cavalletti, F.; Mondino, A. Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds 1502.0646516 Invent. Math. 208 (2017), 803–849.
https://doi.org/10.1007/s00222-016-0700-617
2015a08 Cavalletti, F.; Mondino, A. Sharp geometric and functional inequalities in metric measure spaces with lower Ricci curvature bounds 1505.0206118 Geom. Topol. 21(1) (2017), 603 – 645.
https://doi.org/10.2140/gt.2017.21.60319
2015a09 Ketterer, C. On the geometry of metric measure spaces with variable curvature bounds 1506.0327920 Geom Anal. 27 (2017), 1951–1994.
https://doi.org/10.1007/s12220-016-9747-221
2015a10 Duong, M. H.; Tugaut, J. Stationary solutions of the Vlasov-Fokker-Planck equation: existence, characterization and phase-transition 1505.0121222 Applied Mathematics Letters. 52 (2016), 38-45.
https://doi.org/10.1016/j.aml.2015.08.00323
2015a11 Deng, Q.; Galaz-Garcia, F.; Guijarro, L.; Munn, M. Three-dimensional Alexandrov spaces with positive or nonnegative Ricci curvature 1602.0772424 Potential Anal. 48 (2018), 223–238.
https://doi.org/10.1007/s11118-017-9633-y25
2015a12 Jylhä, H.; Rajala, T. L∞ estimates in optimal mass transportation 1508.0520526 Journal of Functional Analysis. 270(11) (2016), 4297-4321.
https://doi.org/10.1016/j.jfa.2015.12.01927
2015a13 Kitabeppu, Y.; Lakzian, S. Characterization of low dimensional RCD*(K,N) spaces 1505.0042028 Anal. Geom. Metr. Spaces. 4(1) (2016), 187–215.
https://doi.org/10.1515/agms-2016-000729
2015a14 Erbar, M.; Juillet, N. Smoothing and non-smoothing via a flow tangent to the Ricci flow 1603.0028030 Journal de Mathématiques Pures et Appliquées. 110 (2018), 123-154.
https://doi.org/10.1016/j.matpur.2017.07.00631
2015a15 Schlichting, A. Macroscopic limit of the Becker-Döring equation via gradient flows 1607.0873532 ESAIM: COCV. 25(22) (2019).
https://doi.org/10.1051/cocv/20180133
2015a16 Indrei, E. A sharp lower bound on the polygonal isoperimetric deficit 1502.0597834 Proc. Amer. Math. Soc. 144 (2016), 3115-3122.
http://dx.doi.org/10.1090/proc/1294735
2015a17 Indrei, E.; Minne, A. Nontransversal intersection of free and fixed boundaries for fully nonlinear elliptic operators in two dimensions 1505.0230336 Analysis and PDE. 9(2) (2016), 487–502.
http://dx.doi.org/10.2140/apde.2016.9.48737
2015a18 Acciaio, B.; Larsson, M. Semi-static completeness and robust pricing by informed investors 1510.0189038 Ann. Appl. Probab. 27(4) (2017), 2270 – 2304.
https://doi.org/10.1214/16-AAP125939
2015a19 Beiglböck, M.; Cox, A. M. G.; Huesmann, M. Optimal transport and Skorokhod embedding 1307.365640 Invent. Math. 208 (2017), 327–400.
https://doi.org/10.1007/s00222-016-0692-241
2015a20 Beiglböck, M.; Huesmann, M.; Stebegg, F. Root to Kellerer 1507.0769042 Séminaire de Probabilités XLVIII.
https://doi.org/10.1007/978-3-319-44465-9_143
2015a21 Friz, P. K.; Prömel, D. J. Rough path metrics on a Besov-Nikolskii type scale 1609.0313244 Trans. Amer. Math. Soc. 370(12) (2018), 8521-8550.
https://doi.org/10.1090/tran/726445
2015a22 Łochowski, R. M.; Perkowski, N.; Prömel, D. J. A superhedging approach to stochastic integration 1609.0234946 Stochastic Processes and their Applications. 128(12) (2018), 4078-4103.
https://doi.org/10.1016/j.spa.2018.01.00947
2015a23 Vovk, V. Another example of duality between game-theoretic and measure-theoretic probability 1608.0270648  
2015a24 Beiglböck, M.; Cox, A. M. G.; Huesmann, M.; Perkowski, N.; Prömel, D. J. Pathwise super-replication via Vovk's outer measure 1504.0364449  Finance Stoch. 21 (2017), 1141–1166.
https://doi.org/10.1007/s00780-017-0338-250
2015a25 Acciaio, B.; Cox, A. M.G.; Huesmann, M. Model-independent pricing with insider information: a Skorokhod embedding approach 1610.0912451  Advances in Applied Probability. 53(1) (2021), 30–56.
https://doi.org/10.1017/apr.2020.5052
2015a26 Hall, C.; Hudson, T.; van Meurs, P. Asymptotic analysis of boundary layers in a repulsive particle system 1609.0323653 Acta Appl Math. 153 (2018), 1–54.
https://doi.org/10.1007/s10440-017-0119-054
2015a27 Amenta, A. Interpolation and embeddings of weighted tent spaces 1509.0569955 J Fourier Anal Appl. 24 (2018), 108–140.
https://doi.org/10.1007/s00041-017-9521-256
2015a28 Honda, S. Elliptic PDEs on compact Ricci limit spaces and applications 1410.329657 Mem. Amer. Math. Soc. 253(1211) (2018), v+92.
https://doi.org/10.1090/memo/121158
2015a29 Erbar, M.; Fathi, M. Poincaré, modified logarithmic Sobolev and isoperimetric inequalities for Markov chains with non-negative Ricci curvature 1612.0051459 Journal of Functional Analysis. 274(11) (2018), 3056-3089.
https://doi.org/10.1016/j.jfa.2018.03.01160
2015a30 Honda, S. Spectral convergence under bounded Ricci curvature 1510.0534961 Journal of Functional Analysis. 273(5) (2017), 1577-1662.
https://doi.org/10.1016/j.jfa.2017.05.00962
2015a31 Mörters, P.; Redl, I. Skorokhod embeddings for two-sided Markov chains 1407.473463 Probab. Theory Relat. Fields. 165 (2016), 483–508.
https://doi.org/10.1007/s00440-015-0637-564
2015a32 Beiglböck, M.; Cox, A. M. G.; Huesmann, M. The geometry of multi-marginal Skorokhod embedding 1705.0950565  Probab. Theory Relat. Fields. 176 (2020), 1045–1096.
https://doi.org/10.1007/s00440-019-00935-z66

Participants

Name Affiliation
Beatrice Acciaio London School of Economics and Political Science
Alex Amenta Université Paris-Sud
Lashi Bandara Chalmers University of Technology and University of Gothenburg
Mathias Beiglböck University of Vienna
Fabio Cavalletti University of Pavia
Alexander Cox University of Bath
Qintao Deng Central China Normal University
Manh Hong Duong University of Warwick
Matthias Erbar Universität Bonn
Max Fathi Université Paris 6
Peter Friz TU Berlin
Fernando Galaz-Garcia Karlsruher Institut für Technologie (KIT)
Paul Gassiat Université Paris Dauphine
David Hartley Instituto de Ciencias Matemáticas
Asma Hassannezhad Max-Planck Institute for Mathematics
Shouhei Honda Kyushu University
Martin Huesmann Universität Bonn
Emanuel Indrei Carnegie Mellon University
Heikki Jylhä University of Jyväskylä
Martin Kell Max-Planck-Institute for Mathematics in the Sciences
Christian Ketterer Albert-Ludwigs-Universität Freiburg
Yu Kitabeppu Kyoto University
Eva Kopfer Universität Bonn
Kazumasa Kuwada Tokyo Institute of Technology
Sigrid Källblad Ecole Polytechnique Paris
Sajjad Lakzian Universität Bonn
Vaios Laschos Brown University
Stefano Lisini Università degli Studi di Pavia
Zhen Liu Fudan University
Jan Maas IST Austria
Kanstantsin Matetski University of Warwick
Andrea Mondino ETH Zürich
Michael Munn University of Missouri
Marcel Nutz Columbia University
Harald Oberhauser University of Oxford
Xuhui Peng Hunan Normal University
Nicolas Perkowski Université Paris Dauphine
David Prömel Humboldt-Universität zu Berlin
André Schlichting Universität Bonn
Upanshu Sharma Technische Universiteit Eindhoven
Pietro Siorpaes Universität Wien
Dejan Slepcev Carnegie Mellon University
Vladimir Vovk Royal Holloway, University of London

The list above does not include people who only participated in workshops.

Poster TP_2015_01.jpg
© HIM

Links

  1. https://www.mathematics.uni-bonn.de/him/programs/past/tp_2015_01#pubs
  2. https://www.mathematics.uni-bonn.de/en/programs/assets/report-tp_2015_01.pdf
  3. https://www.mathematics.uni-bonn.de/him/programs/past/tp_2015_01#part
  4. http://arxiv.org/abs/1505.05035
  5. https://doi.org/10.2422/2036-2145.201506_010
  6. http://arxiv.org/abs/1505.06150
  7. https://doi.org/10.5565/PUBLMAT_61117_09
  8. http://arxiv.org/abs/1601.08098
  9. https://doi.org/10.3934/dcds.2016096
  10. http://arxiv.org/abs/1505.04905
  11. https://doi.org/10.1007/s00211-016-0849-3
  12. http://arxiv.org/abs/1507.06489
  13. https://doi.org/10.1007/978-3-319-32144-8_8
  14. http://arxiv.org/abs/1509.07160
  15. https://doi.org/10.3150/16-BEJ892
  16. http://arxiv.org/abs/1502.06465
  17. https://doi.org/10.1007/s00222-016-0700-6
  18. http://arxiv.org/abs/1505.02061
  19. https://doi.org/10.2140/gt.2017.21.603
  20. http://arxiv.org/abs/1506.03279
  21. https://doi.org/10.1007/s12220-016-9747-2
  22. http://arxiv.org/abs/1505.01212
  23. https://doi.org/10.1016/j.aml.2015.08.003
  24. http://arxiv.org/abs/1602.07724
  25. https://doi.org/10.1007/s11118-017-9633-y
  26. http://arxiv.org/abs/1508.05205
  27. https://doi.org/10.1016/j.jfa.2015.12.019
  28. http://arxiv.org/abs/1505.00420
  29. https://doi.org/10.1515/agms-2016-0007
  30. http://arxiv.org/abs/1603.00280
  31. https://doi.org/10.1016/j.matpur.2017.07.006
  32. http://arxiv.org/abs/1607.08735
  33. https://doi.org/10.1051/cocv/201801
  34. http://arxiv.org/abs/1502.05978
  35. http://dx.doi.org/10.1090/proc/12947
  36. http://arxiv.org/abs/1505.02303
  37. http://dx.doi.org/10.2140/apde.2016.9.487
  38. http://arxiv.org/abs/1510.01890
  39. https://doi.org/10.1214/16-AAP1259
  40. http://arxiv.org/abs/1307.3656
  41. https://doi.org/10.1007/s00222-016-0692-2
  42. http://arxiv.org/abs/1507.07690
  43. https://doi.org/10.1007/978-3-319-44465-9_1
  44. http://arxiv.org/abs/1609.03132
  45. https://doi.org/10.1090/tran/7264
  46. http://arxiv.org/abs/1609.02349
  47. https://doi.org/10.1016/j.spa.2018.01.009
  48. http://arxiv.org/abs/1608.02706
  49. http://arxiv.org/abs/1504.03644
  50. https://doi.org/10.1007/s00780-017-0338-2
  51. http://arxiv.org/abs/1610.09124
  52. https://doi.org/10.1017/apr.2020.50
  53. http://arxiv.org/abs/1609.03236
  54. https://doi.org/10.1007/s10440-017-0119-0
  55. http://arxiv.org/abs/1509.05699
  56. https://doi.org/10.1007/s00041-017-9521-2
  57. http://arxiv.org/abs/1410.3296
  58. https://doi.org/10.1090/memo/1211
  59. http://arxiv.org/abs/1612.00514
  60. https://doi.org/10.1016/j.jfa.2018.03.011
  61. http://arxiv.org/abs/1510.05349
  62. https://doi.org/10.1016/j.jfa.2017.05.009
  63. http://arxiv.org/abs/1407.4734
  64. https://doi.org/10.1007/s00440-015-0637-5
  65. http://arxiv.org/abs/1705.09505
  66. https://doi.org/10.1007/s00440-019-00935-z
  67. https://www.mathematics.uni-bonn.de/him/programs/past/tp_2015_01#start