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Prof. Dr. Peter Fiebig

Peter Fiebig
  • Organisation: Department Mathematik
  • Abteilung: Professur für Mathematik (Prof. Dr. Fiebig)
  • Telefonnummer: +49 9131 85-67018
  • Faxnummer: +49 9131 85-67020
  • E-Mail: fiebig@mi.uni-erlangen.de
  • Adresse:
    Cauerstraße 11
    91058 Erlangen
    Raum 01.319

  • Modulare Darstellungstheorie algebraischer Gruppen
  • Darstellungstheorie affiner Kac-Moody Algebren im kritischen Level
  • Dualitäten in Darstellungstheorie und Geometrie

  • Ksenija Kitanov (Doktorandin seit 4/2015, nicht mehr Teil der Arbeitsgruppe)

11th Seminar on Conformal Field Theory, Erlangen, Oct. 19, 2018

10th Seminar on Conformal Field Theory, RIMS, Kyoto, Japan, Apr 23 – Apr 27, 2018

Geometry and Representation Theory of Algebraic Groups , Physikzentrum Bad Honnef, March 5. – March 9, 2018

Darmstadt-Erlangen-Freiburg seminar on Conformal Field Theory, Erlangen, July 7, 2017

Lecture series on Moment graphs in representation theory, Universität Padua, Italy, Feb. 20 – March 16, 2017

Sheaves and modular representations of reductive groups, AIM-Workshop, San Jose, California, USA, March 28-April 1, 2016

Geometric and Categorical Representation Theory Konferenz, Mooloolaba, Queensland, Australien, December 14-18, 2015

Shanghai Conference on Representation Theory, Shanghai, China, December 7-11, 2015

Lie Theory Workshop, Baton Rouge, USA, November 7/8, 2015

DMV-Konferenz 2015, Hamburg, September 21-25, 2015

Representations of Lie Algebras, Sommerschule, Marienheide, September 7-11, 2015

LMS-CMI Research School and workshop on Algebraic Lie theory and representation theory, Glasgow and Edinburgh, August 25-September 5, 2014

MSRI program Geometric Representation Theory, Berkeley, USA, August-December 2014

RIMS Project 2014 Geometric Representation Theory, Kyoto, Japan, July 2014-March 2015

Conference and Summer School on Representation Theory, Cargese, Corsica, June 16-27, 2014

Lectures on modular representations of algebraic groups, Chennai, India, October 7-18, 2013

Summer School on Category O, Freiburg, August 6-9, 2013

Perverse sheaves in Representation Theory, Besse, France, June 24-27, 2013

Gradings and Decomposition Numbers, Stuttgart, Germany, September 24-28, 2012

Lie Algebras and Applications, Uppsala, Sweden, September 5-9, 2012

Schubert Calculus, Osaka, Japan, July 23-27, 2012

Summer School and Workshop on Lie Theory and Representation Theory III, Shanghai, China, June 9-29, 2012

DFG-Schwerpunkt 1388 „Darstellungstheorie“

  • Lineare Algebra I: Wintersemester 2011/12: pdf
  • Lineare Algebra II: Sommersemester 2012: pdf
  • Algebra II: Ringe und Moduln im Wintersemester 2009/10: pdf
  • Moment graphs in representation theory and topology, Vortragsreihe in Köln, September/Oktober 2009: pdf (englisch)
  • Vorlesung zu Bruhatgraphen im Wintersemester 2008/09: pdf (englisch)
  • Darstellungstheorie von Lie-Algebren im Wintersemester 2012/13: pdf
  • Algebra im Wintersemester 2010: Gruppen, Ringe, Körper, Galois-Theorie und Transzendenz von Pi: pdf

Shanghai Lectures on Characters of representations and the topology of flag varieties
  • Lecture 1, Representations of algebraic groups: pdf
  • Lecture 2, Representations of modular Lie algebras: pdf
  • Lecture 3, Steinberg’s tensor product theorem and Lusztig’s conjecture: pdf
  • Lecture 4, Kazhdan-Lusztig theory: pdf
  • Lecture 5, The modular multiplicity conjecture and periodic polynomials: pdf
  • Lecture 6, Moment graphs: pdf
  • Lecture 7, Perverse sheaves and parity sheaves: pdf
  • Lecture 8, Proofs of multiplicity conjectures: pdf

Hauptseminar (HS)

Übung (UE)

  • Übungen zur Mathematik für Physikstudierende 2

    • Fr 12:00-14:00, Raum SR 01.178
    • Einzeltermin am 24.05.2019 12:00-14:00, Raum SR Biologie
    • Do 16:00-18:00, Raum HB
    • Fr 12:00-14:00, Raum HC
    • Einzeltermin am 29.05.2019 16:00-18:00, Raum HB
    • Einzeltermin am 19.06.2019 16:00-18:00, Raum HB
    • Fr 12:00-14:00, Raum 00.581 (außer 24.05.2019)

Vorlesung (VORL)

  • Character, Multiplicity and Decomposition Problems in the Representation Theory of complex Lie Algebras, in „Lie Groups, Differential Equations, and Geometry. Advances and Surveys.“ Springer UNIPA Series, G. Falcone, ed., 2017, 41-70.
  • (mit Martina Lanini) The combinatorial category of Andersen, Jantzen and Soergel and filtered moment graph sheaves, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 86(2) (2016), 203-212.
  • Subquotient categories of the affine category O at the critical level, preprint 2015, arXiv:1510.09131, in „Representation Theory – Current Trends and Perspectives“, EMS Series of Congress Reports (2017), 233-254.
  • (mit Martina Lanini) Filtered moment graph sheaves, preprint 2015, arXiv:1508.05579.
  • (mit Martina Lanini) Filtered modules on moment graphs and Lusztig’s periodic patterns, preprint 2015, arXiv:1504.01699.
  • Moment graphs in representation theory and geometry, preprint 2013arXiv:1308.2873, in „Schubert calculus (Osaka 2012)“, Advanced Studies in Pure Mathematics 71 (2016), 75-96.
  • On the subgeneric restricted blocks of affine category O at the critical level, preprint 2012, arXiv:1206.0683, in „Symmetries, Integrable Systems and Representations“, Springer Proceedings in Mathematics and Statistics 40 (2013), 65-84.
  • On the restricted projective objects in the affine category O at the critical level, preprint 2011, arXiv:1103.1540, in „Algebraic Groups and Quantum Groups“ (Nagoya, Japan, 2010),  Contemp. Math. 565 (2012), 55-70.
  • (mit Geordie Williamson) Parity sheaves, moment graphs and the p-smooth locus of Schubert varieties, preprint 2010, arXiv:1008.0719Ann. Inst. Fourier 64(2) (2014), 489-536.
  • (mit Tomoyuki Arakawa) The linkage principle for restricted critical level representations of affine Kac-Moody algebras, preprint 2009, arXiv:0909.4214, Compos. Math. 148 (2012), 1787-1810.
  • (mit Tomoyuki Arakawa) On the restricted Verma modules at the critical level, preprint 2008, arXiv:0812.3334, Trans. Amer. Math. Soc. 364 (2012), 4683-4712.
  • An upper bound on the exceptional characteristics for Lusztig’s character formula, preprint 2008, arXiv:0811.1674, J. Reine Angew. Math. 673 (2012), 1-31.
  • Lusztig’s conjecture as a moment graph problem, preprint 2007, arXiv:0712.3909, Bull. London Math. Soc. 42(6) (2010), 957-972.
  • Sheaves on affine Schubert varieties, modular representations and Lusztig’s conjecture, preprint 2007, arXiv:0711.0871, J. Amer. Math. Soc. 24 (2011), 133-181.
  • The multiplicity one case of Lusztig’s conjecture, preprint 2006, math.RT/0607501, Duke Math. J. 153 (2010), 551-571.
  • Kazhdan-Lusztig theory via sheaves on Bruhat graphs, preprint 2005, math.RT/0512311 , in „Algebraic and Geometric Combinatorics“ (Anogia, Crete, 2005), 195-204, Contemp. Math. 423 (2007).
  • The combinatorics of Coxeter categories, preprint 2005, math.RT/0512176 , Trans. Amer. Math. Soc. 360, no. 8, (2008), 4211-4233.
  • Sheaves on moment graphs and a localization of Verma flags, preprint 2005, math.RT/0505108, Adv. Math. 217 (2008), 683-712.
  • The combinatorics of category O for symmetrizable Kac-Moody algebras preprint 2003, math.RT/0305378, Transform. Groups 11 (2006), No. 1, 29-49.
  • Centers and translation functors for category O over symmetrizable Kac-Moody algebras, Math. Z. 243 (2003), No. 4, 689-717.
  • Zentren deformierter Darstellungskategorien und Verschiebungsfunktoren, Dissertation, Universität Freiburg (2001), pdf