of Mathematics of Czech Academy of Sciences
11567 Praha 1
Email: hvle AT
Tel : +420-222090779
Fax : +420-222090701
My publication list at MatSciNet at arXiv arXiv
Lecture course (20aNMAG469p1, Fall term 2020-2021)
Mathematical foundations of machine learning
on ZOOM, each Tuesday 10.40-12.10.
- 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.
- I am member of the OMS editorial team
- Book (with Nihat Ay, Juergen Jost and Lorenz Schwachhoefer)
INFORMATION GEOMETRY Springer 2017, Ergebnisse der Mathematik und ihrer Grenzgebiete
- (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, to appear as chapter in
``Geometric Structures of Statistical Physics, Information Geometry and Learning“, Springer Proceedings in Mathematics & Statistics 2021.
- (with Tô Tat Dat, Protin Frédric, 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
- (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, (accepted for Journal of Sympletic Geometry),
- (with Jiri Vanzura) Classification of -forms on 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, arXiv:1905.11448, accepted for EPJ PLUS.
- (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) Fr\"olicher-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, (accepted for Asian J. of Math.) arXiv:1804.05732.
- (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)
- Geometric structures associated with a simple Cartan 3-form http://arxiv.org/pdf/1103.1201.pdf
Journal Geom. Phys. 70(2013), 205-223.
My current and past collaborators
- Nihat Ay, Jean-Francois Barraud, 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,