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 and Vojtěch ŽÁDNÍK. Conformal theory of curves with tractors. Journal of Mathematical Analysis and Applications. San Diego, USA: Elsevier, 2019, vol. 473, No 1, p. 112-140. ISSN 0022-247X. Available from: https://dx.doi.org/10.1016/j.jmaa.2018.12.038. URL info
• HAMMERL, Matthias, Katja SAGERSCHNIG, Josef ŠILHAN, Arman TAGHAVI-CHABERT and Vojtěch ŽÁDNÍK. Conformal Patterson-Walker metrics. The Asian Journal of Mathematics. Boston: International Press, 2019, vol. 23, No 5, p. 703-734. ISSN 1093-6106. Available from: https://dx.doi.org/10.4310/AJM.2019.v23.n5.a1. URL info
• HAMMERL, Matthias, Katja SAGERSCHNIG, Josef ŠILHAN, Arman TAGHAVI-CHABERT and Vojtěch ŽÁDNÍK. Fefferman-Graham ambient metrics of Patterson-Walker metrics. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. HOBOKEN: WILEY, 2018, vol. 50, No 2, p. 316-320. ISSN 0024-6093. Available from: https://dx.doi.org/10.1112/blms.12136. URL info
• ŠILHAN, Josef and Vojtěch ŽÁDNÍK. O křivkách a křivostech (On curves and curvatures). Kvaternion. 2018, vol. 2018, 1-2, p. 25-36. ISSN 1805-1324. URL info
• MICHEL, Jean-Philippe, Petr SOMBERG and 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, vol. 47, No 2, p. 587-619. ISSN 0035-7596. Available from: https://dx.doi.org/10.1216/RMJ-2017-47-2-587. info
• ŠILHAN, Josef and Rod GOVER. Conformal Operators on Weighted Forms; Their Decomposition and Null Space on Einstein Manifolds. Annales Henri Poincaré. Switzerland, 2014, vol. 15, No 4, p. 679-705. ISSN 1424-0637. Available from: 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, vol. 33, Supplement, p. 162-176. ISSN 0926-2245. Available from: https://dx.doi.org/10.1016/j.difgeo.2013.10.016. URL info
• ŠILHAN, Josef, Jean-Philippe MICHEL and 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, vol. 10, No 16, p. "nestrankovano", 26 pp. ISSN 1815-0659. Available from: https://dx.doi.org/10.3842/SIGMA.2014.016. info
• ŠILHAN, Josef, Vladimír SOUČEK, Petr SOMBERG and Matthias HAMMERL. Invariant prolongation of overdetermined PDEs in projective, conformal, and Grassmannian geometry. Annals of Global Analysis and Geometry. Springer, 2012, vol. 42, No 1, p. 121-145. ISSN 0232-704X. Available from: https://dx.doi.org/10.1007/s10455-011-9306-9. URL info
• ŠILHAN, Josef and 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, vol. 53, No 3, p. "nestrankovano", 26 pp. ISSN 0022-2488. Available from: https://dx.doi.org/10.1063/1.3692324. URL info
• ŠILHAN, Josef, Vladimír SOUČEK, Petr SOMBERG and Matthias HAMMERL. On a new normalization for tractor covariant derivatives. Journal of the European Mathematical Society. Springer, 2012, vol. 14, No 6, p. 1859-1883. ISSN 1435-9855. Available from: https://dx.doi.org/10.4171/JEMS/349. URL info
• ŠILHAN, Josef and Andreas ČAP. Equivariant quantizations for AHS-structures. Advances in Mathematics. San Diego: Elsevier Science, 2010, vol. 224, No 4, p. 1717-1734. ISSN 0001-8708. info
• ŠILHAN, Josef and Rod GOVER. The conformal Killing equation on forms; prolongations and applications. Differential Geometry and its Applications. Amsterdam: Elsevier Science, 2008, vol. 26, No 3, p. 244-266, 22 pp. ISSN 0926-2245. URL info
• ŠILHAN, Josef and Rod GOVER. Conformal Operators on Forms and Detour Complexes on Einstein Manifolds. Communications in Mathematical Physics. Springer Berlin / Heidelberg, 2008, vol. 284, No 2, p. 291-316, 25 pp. ISSN 0010-3616. URL info
• ŠILHAN, Josef and Rod GOVER. Commuting Linear Operators and Decompositions; Applications to Einstein Manifolds. Acta Applicandae Mathematicae. Kluwer, 2008, vol. 109, No 2, p. 555-589. ISSN 0167-8019. URL info
• ŠILHAN, Josef and Rod GOVER. Commuting linear operators and algebraic decompositions. Archivum Mathematicum. Brno, 2007, vol. 43, No 5, p. 373-387, 14 pp. 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, vol. 14, No 2, p. 481--499, 18 pp. ISSN 0949-5932. info
• ŠILHAN, Josef. Algorithmic computations of Lie algebra cohomologies. Supplemento ai Rendiconti del Circolo Matematico di Palermo,Serie II. Palermo, 2003, vol. 2003, No 71, p. 191-197. ISSN 0009-725X. info

2020/06/17