Dr.Sc.
Hông
Vân
Lê
Dr.Sc.
Hông
Vân
LêAddress: Zitna 25, 11567 Praha
Email: hvle AT math.cas.cz
Tel.: +420-222090779
My CV
My publication list at MatSciNet at arXiv arXiv
Lecture course (NMAG469, Fall term 2024-2025) Tuesday (10:40 - 12:10) K358
Mathematical foundations of machine learning
Seminars
- Prague-Hradec Kralove seminar Cohomology in algebra, geometry, physics and statistics, usually on
Wednesday 11.30-12.30 at the blue lecture room at the ground floor of the rear building of IM CAS, Zitna 25, Praha 1 or on ZOOM.
On our presence in Researchseminar.org you can find links to youtube videos and/or slides of most of the lectures hold on our seminar.
You can subscribe/unsubscribe the mailing list here.
- Book (with Nihat Ay, Juergen Jost and Lorenz Schwachhoefer)
INFORMATION GEOMETRY Springer 2017, Ergebnisse der Mathematik und ihrer Grenzgebiete
Recent (pre)prints
- (with Domenico Fiorenza) Unital C_∞-algebras and the real homotopy type of (r-1)-connected compact manifolds of dimension ≤ l (r-1)+2 arXiv:2310.19506
- Supervised learning with probabilistic morphisms and kernel mean embeddings, arXiv:2305.06348
- (with Willem A. de Graaf) Semisimple elements and the little Weyl group of real semisimple Zm-graded Lie algebras, Linear Algebra and its Applications, 703 (2024), 423-445 arXiv:2212.03775
- Natural differentiable structures on statistical models and the Fisher metric, Information Geometry (2022) arXiv:2208.06539
- (with Domenico Fiorenza) CR-twistor spaces over manifolds with G2 -and Spin(7)-structures, Annali di Matematica (2023) arXiv:2203.04233
- (with Michail Borovoi , Willem A. de Graaf) Classification of real trivectors in dimension nine, Journal of Algebra, 603 (2022) 118-163, arXiv:2108.00790.
- (with F. Protin, M. Jules, D.T. Nguyen, H. T.T. Nguyen, C. Piffault, W. Rodriguez, T.D. To, W. Tuschmann, T. Yeo, N. T. Zung), Unified modelling
of epidemics by coupled dynamics via Monte-Carlo Markov Chain algorithms, arXiv:2106.13463
- (with Michail Borovoi , Willem A. de Graaf) Real graded Lie algebras, Galois cohomology, and classification of trivectors in R^9, arXiv:2106.00246
- (with Kaoru Ono) Floer-Novikov cohomology and Symplectic Fixed Points, Revisited,
Proceedings of the International Geometry Center Vol. 13, no. 4 (2020), pp. 89 -115, https://doi.org/10.15673/tmgc.v13i4.1809
- (with Alexey Tuzhilin) Nonparametric Estimations and the Diffeological Fisher Metric, arXiv:2011.13418, Chapter in ``Geometric Structures of Statistical Physics,
Information Geometry and Learning“ 120-138, Springer Proceedings in Mathematics & Statistics vol. 361, 2021
- (with Tô Tat Dat, Protin Fréderic, Nguyen T.T. Hang, Martel Jules, Nguyen Duc Thang, Charles Piffault, Rodriguez Willy, Figueroa Susely,
Wilderich Tuschmann, Nguyen Tien Zung)
Epidemic Dynamics via Wavelet Theory and Machine Learning with Applications to Covid-19,
Biology 2020, 9(12), 47 Special_issues Theories and Models on COVID-19_Epidemics arXiv:2010.12004
- (with Jürgen Jost and Tat Dat Tran) Differentiation of measures on complete Riemannian manifolds, arXiv:2008.13252
- (with Domenico Fiorenza) Formally integrable complex structures on higher dimensional knot spaces, Journal of Symplectic Geometry, 19 (2021), Nr 3, 507-529,
- (with Jiri Vanzura) Classification of k-forms on R^n and the existence of associated geometry on manifolds,
Chebyshevskii Sbornik, v. 21 (2020), 352-372, arXiv:1912.03338
- Diffeological statistical models, the Fisher metric and probabilistic mappings, arXiv:1912.02090, Mathematics 2020, 8(2), 167
Special Issue Geometry and Topology in Statistics.
- (with Jürgen Jost and Tat Dat Tran) Probabilistic morphisms and Bayesian nonparametrics,
Eur. Phys. J. Plus (2021) 136:441, arXiv:1905.11448.
- (with Domenico Fiorenza, Kotaro Kawai and Lorenz Schwachhöfer) Almost formality of manifolds of low dimension,
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)Vol. XXII (2021), 79-107, arXiv:1902.08406.
- (with Kotaro Kawai and Lorenz Schwachhöfer) Frölicher-Nijenhuis backet on manifolds with special holonomy,
arXiv:1810.12714, "Lectures and Surveys on G2 manifolds and related topics", Fields Institute Communications, p. 201-215, 2020.
- (with Domenico Fiorenza, Lorenz Schwachhöfer, and Luca Vitagliano) Strongly homotopy Lie algebras
and deformations of calibrated submanifolds, Asian J. of Math. 25(2021), 341 – 368.
- (with Jean-Francois Barraud, Agnès Gadbled and Roman Golovko) A Novikov fundamental group,
IMRN Volume 2020, Issue 24, December 2020, Pages 10447–10494, https://doi.org/10.1093/imrn/rnz032, arXiv:1710.10353
- (with Lorenz Schwachhöfer, Nihat Ay and Jürgen Jost) Congruent families of tensors, arXiv:1705.11014,
DOI: 10.1007/978-3-319-97798-0_6, in book: Information Geometry and Its Applications, Springer Proceedings in Mathematics and Statistics, v. 252, 2018.
- (with Jürgen Jost and Lorenz Scwachhöfer) Cram\'er-Rao inequality on singular statistical models I, arXiv:1703.09403 .
- (with Kotaro Kawai and Lorenz Schwachhöfer) Fr\"olicher-Nijenhuis cohomology on $G_2$ and Spin(7)-manifolds,
arXiv:1703.05133, International Journal of Mathematics, vol. 29. N12 (2018), 1850075 (36 pages).
- (with Kotaro Kawai and Lorenz Schwachhöfer) Frölicher-Nijenhuis bracket and geometry of G2-and Spin(7)-manifolds,
arxiv.org/abs/1605.01508, AMPA 197(2018), 411-432.
- (with Jiri Vanzura) McLean's second variation formula revisited arXiv:1605.01267, Journal of Geometry and Physics vol. 113, 2017, 188-196.Xiifferential Geometry (math.DG); Mathematical Physics (math-p1, arXiv:1605.0
- (with Alfonso Tortorella and Luca Vitagliano) Jacobi bundles and the BFV-complex, arXiv:1601.04540
Journal of Geometry and Physics vol. 121, 2017, 347-377.iifferential Geometry (math.DG); Ma
- The Calabi invariant and the least number of periodic solutions of locally Hamiltonian equations arXiv:1511.00638
- (with Nihat Ay, Jürgen Jost, Lorenz Schwachhöfer) Parametrized measure models, arXiv:1510.07305
J. Bernoulli 24(2018), 1692-1725.
- Corrigendum to “Compact symplectic manifolds of low cohomogeneity” J. Geometry and Physics 25(1998), 205-206,
Journal of Geometry and PhysicsVolume 96, October 2015, 212–215, arxiv.1504.05142.pdf .
- (with Yong-Geun Oh, Alfonso Tortorella and Luca Vitagliano) Deformations of coisotropic submanifolds in abstract Jacobi manifolds,
Journal of Symplectic Geometry, Volume 16, Number 4, 1051–1116, 2018, arXiv:1410.8446.pdf.
- (with Lorenz Schwachhöfer) Lagrangian submanifolds in strictly nearly Kaehler 6-manifolds,
Osaka J. Math.Volume 56, Number 3 (2019), 601-629, arXiv:1408.6433v3.pdf,
- Application of integral geometry to minimal surfaces (corrected version) http://arxiv.org/pdf/1401.5227v1.pdf
- The uniqueness of the Fisher metric as information metric http://arxiv.org/pdf/1306.1465.pdf
Annals of the Institute of Statistical Mathematics, 69(2017), 879-896.
- Lower bounds for the circuit size of partially homogeneous polynomials
http://arxiv.org/pdf/1302.3360.pdf, ECCC-TR14-139 (2014), Fundamental and Applied Mathematics, 20(2015), 153-179
(English translation in Journal of Mathematical Sciences, Vol. 225, No. 4, September, 2017, p. 639-657.)
- (with Yong-Geun Oh) Deformations of coisotropic submanifolds in locally conformal symplectic manifolds
http://arxiv.org/pdf/1208.3590.pdf, Asian Journal of Math., Vol. 20(2016), No. 3, pp. 555–598.
- (with Nihat Ay, Jürgen Jost, Lorenz Schwachhöfer) Information geometry and sufficient statistics, Probability Theory Relat. Fields,
162(2015), 327-364 , http://arxiv.org/pdf/1207.6736.pdf
- (with Jiri Vanzura) Cohomology theories on locally conformal symplectic manifolds, http://arxiv.org/pdf/1111.3841.pdf
(Asian J. of Math, Volume 19 (2015),Number 1, p. 45 -82)
My current and past co-authors
- Nihat Ay, Jean-Francois Barraud, Michail Borovoi, Willem A. de Graaf, Domenico Fiorenza,
Anatoly Fomenko, Agnes Gadbled, Roman Golovko, Alexander Ivanov, Jürgen Jost, Kotaro Kawai,
Mobeen Munir, Yong-Geun Oh, Kaoru Ono, Martin Panak, Lorenz Schwachhöfer,
Petr Somberg, Tat Dat Tran, Alfonso Tortorella, Alexey Tuzhilin, Jiri Vanzura, Luca Vitagliano,