doc. Mgr. Josef Šilhan, Ph.D.

Curriculum vitae

Person Identification

• doc. Josef Šilhan, PhD.
  born November 29, 1976, Mostiště
  single

Workplace

• 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

Publications

• ŠILHAN, Josef a Vojtěch ŽÁDNÍK. Conformal theory of curves with tractors. Journal of Mathematical Analysis and Applications. San Diego, USA: Elsevier, 2019, roč. 473, č. 1, s. 112-140. ISSN 0022-247X. Dostupné z: https://dx.doi.org/10.1016/j.jmaa.2018.12.038. 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, 2019, roč. 23, č. 5, s. 703-734. ISSN 1093-6106. Dostupné z: https://dx.doi.org/10.4310/AJM.2019.v23.n5.a1. 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, 2018, roč. 50, č. 2, s. 316-320. ISSN 0024-6093. Dostupné z: https://dx.doi.org/10.1112/blms.12136. URL info
• ŠILHAN, Josef a Vojtěch ŽÁDNÍK. O křivkách a křivostech. Kvaternion. 2018, roč. 2018, 1-2, s. 25-36. ISSN 1805-1324. 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, 2017, roč. 47, č. 2, s. 587-619. ISSN 0035-7596. Dostupné z: https://dx.doi.org/10.1216/RMJ-2017-47-2-587. info
• ŠILHAN, Josef a Rod GOVER. Conformal Operators on Weighted Forms; Their Decomposition and Null Space on Einstein Manifolds. Annales Henri Poincaré. Switzerland, 2014, roč. 15, č. 4, s. 679-705. ISSN 1424-0637. Dostupné z: https://dx.doi.org/10.1007/s00023-013-0258-4. URL info
• ŠILHAN, Josef. Conformally invariant quantization – towards the complete classification. Differential Geometry and its Applications. Amsterdam: Elsevier Science, 2014, roč. 33, Supplement, s. 162-176. ISSN 0926-2245. Dostupné z: https://dx.doi.org/10.1016/j.difgeo.2013.10.016. 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, 2014, roč. 10, č. 16, s. "nestrankovano", 26 s. ISSN 1815-0659. Dostupné z: https://dx.doi.org/10.3842/SIGMA.2014.016. 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, 2012, roč. 42, č. 1, s. 121-145. ISSN 0232-704X. Dostupné z: https://dx.doi.org/10.1007/s10455-011-9306-9. 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), 2012, roč. 53, č. 3, s. "nestrankovano", 26 s. ISSN 0022-2488. Dostupné z: https://dx.doi.org/10.1063/1.3692324. 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, 2012, roč. 14, č. 6, s. 1859-1883. ISSN 1435-9855. Dostupné z: https://dx.doi.org/10.4171/JEMS/349. URL info
• ŠILHAN, Josef a Andreas ČAP. Equivariant quantizations for AHS-structures. Advances in Mathematics. San Diego: Elsevier Science, 2010, roč. 224, č. 4, s. 1717-1734. ISSN 0001-8708. info
• ŠILHAN, Josef a Rod GOVER. The conformal Killing equation on forms; prolongations and applications. Differential Geometry and its Applications. Amsterdam: Elsevier Science, 2008, roč. 26, č. 3, s. 244-266, 22 s. ISSN 0926-2245. URL info
• ŠILHAN, Josef a Rod GOVER. Conformal Operators on Forms and Detour Complexes on Einstein Manifolds. Communications in Mathematical Physics. Springer Berlin / Heidelberg, 2008, roč. 284, č. 2, s. 291-316, 25 s. ISSN 0010-3616. URL info
• ŠILHAN, Josef a Rod GOVER. Commuting Linear Operators and Decompositions; Applications to Einstein Manifolds. Acta Applicandae Mathematicae. Kluwer, 2008, roč. 109, č. 2, s. 555-589. ISSN 0167-8019. URL info
• ŠILHAN, Josef a Rod GOVER. Commuting linear operators and algebraic decompositions. Archivum Mathematicum. Brno, 2007, roč. 43, č. 5, s. 373-387, 14 s. ISSN 1212-5059. 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, 2004, roč. 14, č. 2, s. 481--499, 18 s. ISSN 0949-5932. info
• ŠILHAN, Josef. Algorithmic computations of Lie algebra cohomologies. Supplemento ai Rendiconti del Circolo Matematico di Palermo,Serie II. Palermo, 2003, roč. 2003, č. 71, s. 191-197. ISSN 0009-725X. info

2020/06/17