Theses
- Habilitation thesis - Symplectic Spinors and Hodge Theory, Faculty of Mathematics and Physics, Charles University, 2016
(the first page is in Czech, the rest is in English)
[3]
- Dissertation thesis - Invariant differential operators for projective contact geometries,
Mathematical Institute, Charles University in Prague, partly Vienna University, 2004 [2]
- Diploma thesis - Twistor resolution for zero-mass fields with spin 3/2,
Chair of Theoretical Physics, Charles University in Prague, 2001 (in Czech) [1]
Textbook
- Čihák, P. a kol., Matematická analýza pro fyziky V., Matfyzpress, Praha, 2003, 2014, 2016, 320 p., in Czech, 1 out of 6 authors
[inf]
Journal publications - mostly preprint versions
- Images of elliptic operators on Hilbert bundles over compact manifolds, submitted, preprint, [24]
- Separation and symmetry on two dimensional manifolds with S. Hudecek, submitted [23]
- Twistor operators in symplectic geometry, Adv. Appl. Clifford Algebr. 32 (2022), no. 1, Paper No. 14, [22]
- Induced C*-complexes in metaplectic geometry, Communications in Mathematical Physics,
Volume 365, Issue 1 (2019), 61–91 [21]
- Elliptic complexes over C*-algebras of compact
operators, Journal of Geometry and Physics, Vol. 101 (2016), 27-37 [20]
- Hodge theory for complexes over C*-algebras with an application to A-ellipticity, Annals Global Analysis and Geometry, Vol. 47 (2015) 4, 359-372
[19]
- Analysis over C*-Algebras and the Oscillatory representation, Journal of Geometry and Symmetry in Physics, Vol. 33
(2014), 1-25 [18]
- Cohomology of the de Rham complex twisted by
the oscillatory representation, Differential Geometry and Application, Vol. 33 (2014), 290-297 [17]
- Hodge theory for elliptic complexes over unital C*-algebras, Annals Global Analysis and Geometry, Vol. 45 (2014) 3, 197-210 [16]
- Howe duality for the metaplectic group acting on symplectic spinor valued forms,
Journal of Lie theory, Vol. 22 (2012) 4, 1049-1063
[15]. For a version from 2008, see arXiv
- Symplectic Killing spinors, Comment. Math. Univ. Carolin., Vol. 53 (2012) 1, 19-35
[14]
- Ellipticity of symplectic twistor complexes, Archivum Math., Vol. 44 (2011), 4, 309-327 [13]
- Complex of twistor operators in spin symplectic geometry,
Monatshefte für Mathematik, Vol. 161 (2010) 4, 381-398 [12]
- Structure of the curvature tensor on symplectic spinors,
Journal Geometry and Physics, Vol. 60 (2010) 9, 1251-1261 [11]
- Symplectic Dirac operator and Its higher spin analogues,
Num. Anal. and Appl. Math., Vol. 1048 (2008) 674-677 [10]
- Classification of 1st order symplectic spinor operators
in contact projective geometries, Differential Geometry and Application, Vol. 26 (2008) 3, 553-565 [9]
- Symplectic Dirac operator and its generalization, Adv. Appl. Clifford Algebra, Vol. 18 (2008) 3-4, 853-863 [8]
- Decomposition of a tensor product of a higher symplectic
spinor module and the defining representation of 𝔰𝔭(2n,ℂ), Journal of Lie Theory, Vol. 17 (2007) 1, 63-72 [7]
- Relation of the spectra of symplectic Dirac
and Rarita--Schwinger operator on flat symplectic manifolds, Archivum Math., Vol. 43 (2007) Suppl. 5, 467-484
[6], [6']
- Classification of 𝔭-homomorphisms between higher symplectic spinors,
Rend. Circ. Mat. di Palermo Ser. II, Vol. 79 (2006), 117-127
[5], [5']
- Symplectic spinor valued forms and operators acting between them,
Archivum Math., Vol. 42 (2006) Suppl. 5, 279-290
[4], [4']
- A description of 𝔭-homomorphisms between harmonic modules in projective contact geometry,
Proceedings of Int. Conf. Differential Geometry and Application, MatfyzPress (2005), 333-340
[3']
- On a distinguished class of infinite dimensional representations of 𝔰𝔭(2n, ℂ),
Rend. Circ. Mat. di Palermo Ser. II, Vol. 75 (2005), 269-277
[2], [2']
- Bernstein--Gelfand--Gelfand diagrams for contact graded odd dimensional orthogonal
geometries, Acta Univ. Carol. Math. et Phys., Vol. 45 (2004) 1, 67-77 [1]
Reviews for Journals
- "Index Theory With Applications to Mathematics and Physics, by D. D. Bleecker
and B. Booß-Bavnbeck, International Press, 2013, 769 pp.", J. Geom. Symm. Physics, Vol. 34, 2014, pp. 97-100.
- "A Spinorial Approach to Riemannian and Conformal Geometry,
by J.-P. Bourguignon, O. Hijazi, J.-L. Milhorat, A. Moroianu and S. Moroianu, Europ. Math. Soc., 2015, 462 pp.",
J. Geom. Symm. Physics, Vol. 42, 2016, pp. 99-103.
Study materials
- Schurova dualita a Youngovy diagramy, upravené poznámky z přednášky Reprezentace Lieových grup I (zapsali P. Franc, P. Franek, P. Luft, Z. Kasarová, moje maličkost, L. Křížka, M. Sikora a L. Šišma) [SY]
- Lineární algebra I, mírně upravené poznámky přednášky Lineární algebra 1 (zapsali P. Pšeno a M. Formánek) [LA1]
Slides from excerpted talks on seminars/workshops/conferences
- - Workshop and Conference "Geometry Structures", Complexes of symplectic twistor operators , University of Bari, Aug 29-Sept 2, 2022, [] /dd>
- - Program (conference & workshop & courses) "Geometry for Higher Spin Gravity: Conformal Structures, PDEs, and Q-manifolds", Differential operators invariant
with respect to compact operators, Erwin Schroedinger Institute for Matehmatics and Physics, Vienna (Vienna), Aug. 23 - Sept. 17, 2021.
- - Meeting of the ´´Expro Centre´´ "Homotopical and homological methods and tools related to mathematical physics",
Elliptic operators on homogeneous bundles over compact spaces, Masaryk University, Charles University,
Telc (Vysocina region), October 2019 [].
- - Conference "Dirac operators in differential geometry and global analysis, In memory of Thomas Friedrich (1949-2018)",
Elliptic operators on homogeneous bundles over compact spaces,
Mathematical Institute of Polish Academy of Sciences, University Marburg, University of Warmia and Mazury, conference centre in Bedlewo by Poznan (Greater Poland),
Ocotber 2019, [].
- - International conference "Differential Geometry and its Applications",
Elliptic operators and Homogeneous spaces,
University Hradec Kralove, Dept. Mathematics and Statistics of Masaryk University, Hradec Kraove (Hradec Kralove region)
September 2019, [].
- - "International Conference on Topology and Its Applications,"
Complexes of Hilbert C*-modules,
Faculty of Mathematics and Mechanics - Lomonosov Moscow State University, Dept. of Mathematics - University of Patras, Dept. of Computer and Informatics Engineering of
Technological and Educational Institute of Western Greece,
Nafpatkos (Corinthian Gulf - Western Greece, Greece), July 2018
[22].
- - Meeting of the "Eduard Cech center for algebra and geometry,"
Hodge theory for Unitary representations,
Telc (Vysocina region, Czech Republic), October 2017, [21].
- - "Annual Congress of German and Austrian Mathematical Societies,"
Hodge theory for Symplectic spinors,
German mathematical union, Austrian mathematical society,
Salzburg (Land Salzburg, Austria), September 2017
[20].
- - Meeting of "Scientific Board of Faculty of Mathematics and Physics,"
Symplektické spinory a symplektické Diracovy operátory - Habilitation Lecture,
Faculty of Matehamtics and Physics, Charles University,
Praha, May 2017
[19], in Czech.
- - School and conference "Winter School of Geometry and Physics,"
Symplectic Dirac operator for KK-Theory,
Masaryk University, Charles University, Union of Czech Mathematicians and Physicists,
Srni (Pilsen region, Czech Republic), January 2017
[18]
- - Workshop "Classical and Quantum Symmetries in Physics and Mathematics,"
Symplectic Spinors and Hodge Theory,
Friedrich Schiller University Jena,
Jena (Thuringia, Germany), July 2016
[17]
- - Seminar "Philosophical problems of computer science,"
Kvantova logika podle von Neumanna - problem nekonecne dimenze (in Czech),
Departement of Theoretical Informatics and Mathematical Logic, Charles University in Prague (Czech Republic),
November 2015
[16]
- - "Workshop on almost hermitian a contact geometry,"
Dirac operators in symplectic and contact geometry - a problem of infinite dimension,
Banach Center for Mathematics, Warsaw center of Mathematics and Computer science, Phillips University Marburg, University Warmia and Mazury,
Bedlewo near Poznan (Poland, Greater Poland), October 2015
[15]
- - School and conference "Winter School Geometry and Physics,"
Segal-Shale-Weil complex,
IESIMP (Erwin Schrodinger Institute) in Vienna, Masaryk University Brno, Charles University in Prague,
Srni (Czech republic, Pilsen region), January 2015
[14]
- - Research seminar "Mathematical Physics,"
Elliptic complexes over C*-algebras of compact operators,
Phillips University Marburg,
Mrburg (Thuringia, Germany), November 2014
[13]
- - Seminar of the Relativity group,
De Rham complex twisted by the oscillator bundle,
Institute of Theoretical Physics, Charles University in Prague,
Prague, November 2014 [12]
- - Meeting of "Eduard Cech Institute,"
Hodge theory for parametrix possessing
complexes and a class of elliptic complexes,
Trest (Czech republic, Vysocina), October 2014
[11]
- - Workshop "Differential Geometry and Gravitation,"
Hodge theory for C*-Hilbert bundles,
Banach center for Mathematics,
Warsaw (Poland), October 2013
[10]
- - "International Conference on Geometry, Integrability and Quantization,"
Hodge theory for bundles over C*-algebras,
Bulgarian Academy of Sciences, Embry-Riddle University, Tokio University of Sciences,
Sv. Konstantin and Sv. Helena (Bulgaria, Varna region), June 2013
[9]
- - Workshop "Cartan connections, Geometry of homogeneous spaces and Dynamics,"
Classification of first order operators in projective contact geometry,
International Erwin Schroedinger Institute of Mathematical Physics in Vienna,
Vienna (Austria), July 2011
[8]
- - Workshop "Lie theory and Complex geometry 2010,"
Ellipticity of the symplectic twistor complex,
Phillips University Marburg,
Marburg (Germany, Hesse), November 2010
[7]
- - "Conference on Differential Geometry and Application,"
Complex of symplectic twistor operators,
Masaryk University, Association of Czech Mathematicians and Physicists,
Brno (Czech Republic, South Moravian region), August 2010
[]
- - "International Conference on Numerical Analysis and Applied Mathematics" - Section Dirac operators and Representation theory,
Symplectic Dirac operator and Its higher spin analogues,
Psalidi (Greece, Kos Island), September 2008
[6]
- - "Workshop on Complex and CR Geometry, Partial Differential Equations and Invariant Theory - in Honour of Jospeh J. Kohn,"
Symplectic Spinors and Symplectic Dirac Operators,
Prague (Czech Republic), June-July 2008
[6]
- - Workshop and Conference "Special geometries in Mathematical Physics,"
Symplectic Killing spinors,
I. Agricola, S. Chiossi, R. Cleyton, Th. Friedrich, P.-A. Nagy (all Humboldt University in Berlin), Volkswagen-Stiftung, Haus am Meer,
Kuehlungsborn (Germany, Mecklenburg Cispomerania), March 2008
[5]
- - "Conference on Differential Geometry and Application,"
Symplectic Dirac operator on compactified comlexified
Minkowski space,
Olomouc (Czech Republic, Olomouc region), August 2007 []
- - Research seminar "Differential Geometry and Global Analysis,"
Symplectic spinors,
Humboldt University,
Berlin (Germany), December 2007 [4]
- - Honour seminar "Differential Geometry,"
Higher symplectic spin Dirac operators and Howe duality,
Leibniz University Hannover (Germany, Lower Saxony),
November 2006 [3]
- - Research seminar "Differential Geometry and Global Analysis,"
Humboldt University in Berlin,
Berlin (Germany), October 2006
[2]
- - "International conference on Clifford Alegbra and Analysis,"
Symplectic Dirac and symplectic Twistor operators,
Toulouse (France, Midi-Pyrenees), May 2005 [1]
- - Searle's Approach to the Philosophy of Mind, talk draft in Czech, 2002 [0]
Interesting Schools and Workshops (usually occuring in series)
- Almost Hermitian and Contact Geometry, 2015, Bedlewo by Poznan (Geiges, Fernadnez Marisa, Biswas ...)
- Higher Invariants, Regensburg (D), 2014
(Faltings, Bost, Bismut, Bunke, Viehmann ...)
- Mathematische Arbeitstagung 2011, Bonn (Gromow, Faltings, Gross, Beilinson, Atiyah ...)
- Geometry Summer School, Libson (P), 2008 ()
- Poisson 2008, Lausanne (CH) Proceedings (Kostant, Kosmann-Schwarzbach, Marle, Cattaneo,
Felder, Tsygan, Alekseev ...)
- Oporto meating on geometry, topology and Physics - Categorification on Knots, Faro (P), 2009 (Stroppel, Lauda ...)
- Pragmatic 2007, Catania (I)
- International Fall Workshop on Geometry and Physics, Lisbon 2007 (Barbero, da Silva, Lewandowski, Alekseevsky ...)
- Poisson geometry and Sigma models, E. Schroedinger Institute, Vienna (AT), 2007 (Baez, Alekseev ...), co-occassion (E. Frankel, d'Amour ... )
- Symmetries of Differential Equations, Minneapolis (MA, USA), 2006
(Yamaguchi, Ferapontov, Miller, Eastwood, Olver, Kalnins, Hirachi, ...)
- Arithmetics and Geometry around Quantization (AGAQ), Istanbul (TR), 2006 (Marcolli, Getzler, Bar-Natan, Gaitsgory) 2006