doc. Mgr. Josef Šilhan, Ph.D.

Associate professor, Department of Mathematics and Statistics

Office: pav. 08/02020
Kotlářská 267/2
611 37 Brno

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Phone: +420 549 49 5474
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Curriculum vitae

Person Identification
  • doc. Josef Šilhan, PhD.
    born November 29, 1976, Mostiště
  • Masaryk University
    Department of Mathematics and Statistics
    Building 08
    Kotlarska 2
    611 37 Brno
    Czech Republic
Employment Position
  • Associate professor
Education and Academic Qualifications
  • 2016: habilitation in Mathematics - Geometry; MU Brno; thesis: "Invariant quantization and differential symmetries on AHS structures"
  • 2006: PhD. in Mathematics, The University of Auckland; thesis: "Invariant differential operators in conformal geometry" (supervisor: A. R. Gover)
  • 2004: PhD. in Mathematics, MU Brno; thesis: "Cohomology of Lie algebras" (supervisor: J. Slovák)
  • 2001: Mgr. in Informatics, MU Brno; thesis: "Algorithmic Computation of the Cohomology of Complex Semisimple Lie Algebras" (supervisor: J. Slovák)
  • 2000: Mgr. in Mathematics, MU Brno; thesis: "Set Covering Problem" (supervisor: J. Kaďourek)
Employment Summary
  • 2016 - : Associate Professor at Masaryk University
  • 2010 - 2016: Assistant Professor at Masaryk University
  • 2009 - 2010: Visiting Research Fellow, Max-Planck-Institute for Mathematics, Bonn, 1 year
  • 2008 - 2009: Junior Research Fellow, The Erwin Schr\"{o}dinger International Institute for Mathematical Physics (ESI), Vienna (Austria), 6 months
  • 2008: CEI research fellow, International School for Advanced Studies (SISSA), Trieste (Italy), 5 months
  • 2006 - 2008: Research Fellow, Eduard \v{C}ech Center for Algebra and Geometry (Czech Republic)
  • 2001 - 2003: research worker, Masaryk University in Brno
Pedagogical Activities
  • Linear models, Linear algebra, Differential geometry of curves and surfaces, Differential geometry (Masaryk University)
  • Hyperbolic geometry (University of Auckland)
Scientific and Research Activities
  • Conformal geometry and related structures, invariant differential operators, representation theory, tractor calculus
Academical Stays
  • Humboldt University, 3 weeks (2007)
  • The University of Auckland, 2-4 weeks several times (2007, 2008, 2009, 2011, 2015)
  • University of Luxembourgh, 2 weeks (2011)
  • University of Liege, Lutych, 2 weeks (2013)
  • Catholic University of Louvain, 2 weeks (2014, 2015)
  • University of Greifswald, 1 week (2014, 2015)
  • Politecnico di Torino, 2 weeks (2018)
Research projects
  • Principal investigator: Geometrické struktury, diferenciální operátory a symetrie (GAČR standardní grant, GA19-06357S), 2019-2021
  • Team member:
    Homotopické a homologické metody a nástroje úzce související s matematickou fyzikou (GAČR EXPRO-projekt, GX19-28628X), 2019-2023
    Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku (GAČR centrum excelence, GBP201/12/G028), 2012-1028
    Algebraické metody v geometrii s potenciálem k aplikacím (MŠMT projekt, CZ.1.07/2.3.00/20.0003), 2011-2014
Appreciation of Science Community
  • Invited lectures at universities in Auckland and Berlin
  • Awarded New Zealand Institute for Mathematics & its Applications (NZIMA) Postgraduate Scholarship, February 2003
  • Invited and supported participant at the workshop "Conformal structure in Geometry, Analysis and Physics", Palo Alto, California, August 2003
  • ŠILHAN, Josef a Vojtěch ŽÁDNÍK. Conformal theory of curves with tractors. Journal of Mathematical Analysis and Applications. San Diego, USA: Elsevier, roč. 473, č. 1, s. 112-140. ISSN 0022-247X. doi:10.1016/j.jmaa.2018.12.038. 2019. URL info
  • HAMMERL, Matthias, Katja SAGERSCHNIG, Josef ŠILHAN, Arman TAGHAVI-CHABERT a Vojtěch ŽÁDNÍK. Conformal Patterson-Walker metrics. The Asian Journal of Mathematics. Boston: International Press, roč. 23, č. 5, s. 703-734. ISSN 1093-6106. doi:10.4310/AJM.2019.v23.n5.a1. 2019. URL info
  • HAMMERL, Matthias, Katja SAGERSCHNIG, Josef ŠILHAN, Arman TAGHAVI-CHABERT a Vojtěch ŽÁDNÍK. Fefferman-Graham ambient metrics of Patterson-Walker metrics. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. HOBOKEN: WILEY, roč. 50, č. 2, s. 316-320. ISSN 0024-6093. doi:10.1112/blms.12136. 2018. URL info
  • ŠILHAN, Josef a Vojtěch ŽÁDNÍK. O křivkách a křivostech. Kvaternion. roč. 2018, 1-2, s. 25-36. ISSN 1805-1324. 2018. URL info
  • MICHEL, Jean-Philippe, Petr SOMBERG a Josef ŠILHAN. PROLONGATION OF SYMMETRIC KILLING TENSORS AND COMMUTING SYMMETRIES OF THE LAPLACE OPERATOR. Rocky Mountain Journal of Mathematics. TEMPE: ROCKY MT MATH CONSORTIUM, roč. 47, č. 2, s. 587-619. ISSN 0035-7596. doi:10.1216/RMJ-2017-47-2-587. 2017. info
  • ŠILHAN, Josef a Rod GOVER. Conformal Operators on Weighted Forms; Their Decomposition and Null Space on Einstein Manifolds. Annales Henri Poincaré. Switzerland, roč. 15, č. 4, s. 679-705. ISSN 1424-0637. doi:10.1007/s00023-013-0258-4. 2014. URL info
  • ŠILHAN, Josef. Conformally invariant quantization – towards the complete classification. Differential Geometry and its Applications. Amsterdam: Elsevier Science, roč. 33, Supplement, s. 162-176. ISSN 0926-2245. doi:10.1016/j.difgeo.2013.10.016. 2014. URL info
  • ŠILHAN, Josef, Jean-Philippe MICHEL a Fabian RADOUX. Second Order Symmetries of the Conformal Laplacian. Symmetry, Integrability and Geometry: Methods and Applications. Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine, roč. 10, č. 16, s. "nestrankovano", 26 s. ISSN 1815-0659. doi:10.3842/SIGMA.2014.016. 2014. info
  • ŠILHAN, Josef, Vladimír SOUČEK, Petr SOMBERG a Matthias HAMMERL. Invariant prolongation of overdetermined PDEs in projective, conformal, and Grassmannian geometry. Annals of Global Analysis and Geometry. Springer, roč. 42, č. 1, s. 121-145. ISSN 0232-704X. doi:10.1007/s10455-011-9306-9. 2012. URL info
  • ŠILHAN, Josef a Rod GOVER. Higher symmetries of the conformal powers of the Laplacian on conformally flat manifolds. Journal of Mathematical Physics. USA: American Institute of Physics (AIP), roč. 53, č. 3, s. "nestrankovano", 26 s. ISSN 0022-2488. doi:10.1063/1.3692324. 2012. URL info
  • ŠILHAN, Josef, Vladimír SOUČEK, Petr SOMBERG a Matthias HAMMERL. On a new normalization for tractor covariant derivatives. Journal of the European Mathematical Society. Springer, roč. 14, č. 6, s. 1859-1883. ISSN 1435-9855. doi:10.4171/JEMS/349. 2012. URL info
  • ŠILHAN, Josef a Andreas ČAP. Equivariant quantizations for AHS-structures. Advances in Mathematics. San Diego: Elsevier Science, roč. 224, č. 4, s. 1717-1734. ISSN 0001-8708. 2010. info
  • ŠILHAN, Josef a Rod GOVER. The conformal Killing equation on forms; prolongations and applications. Differential Geometry and its Applications. Amsterdam: Elsevier Science, roč. 26, č. 3, s. 244-266, 22 s. ISSN 0926-2245. 2008. URL info
  • ŠILHAN, Josef a Rod GOVER. Conformal Operators on Forms and Detour Complexes on Einstein Manifolds. Communications in Mathematical Physics. Springer Berlin / Heidelberg, roč. 284, č. 2, s. 291-316, 25 s. ISSN 0010-3616. 2008. URL info
  • ŠILHAN, Josef a Rod GOVER. Commuting Linear Operators and Decompositions; Applications to Einstein Manifolds. Acta Applicandae Mathematicae. Kluwer, roč. 109, č. 2, s. 555-589. ISSN 0167-8019. 2008. URL info
  • ŠILHAN, Josef a Rod GOVER. Commuting linear operators and algebraic decompositions. Archivum Mathematicum. Brno, roč. 43, č. 5, s. 373-387, 14 s. ISSN 1212-5059. 2007. URL info
  • ŠILHAN, Josef. A real analog of Kostant's version of the Bott-Borel-Weil theorem. Journal of Lie Theory. Lemgo (Germany): Heldermann Verlag, roč. 14, č. 2, s. 481--499, 18 s. ISSN 0949-5932. 2004. info
  • ŠILHAN, Josef. Algorithmic computations of Lie algebra cohomologies. Supplemento ai Rendiconti del Circolo Matematico di Palermo,Serie II. Palermo, roč. 2003, č. 71, s. 191-197. ISSN 0009-725X. 2003. info


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