Id Photo
Xin FANG

Mathematisches Institut
Universität zu Köln
Weyertal 86-90
D-50931 Köln

E-mail: xfang (a..t) math.uni-koeln.de

Personal informations

  • 2016.10- Wissenschaftlicher Mitarbeiter in the Workgroup of Prof. Peter Littelmann, Universität zu Köln
  • 2014.9-2016.9 Alexander von Humboldt fellowship, Universität zu Köln (from 01.11.2014 in the Workgroup of Prof. Peter Littelmann)
  • 2014.1-2014.8 ATER (Teaching and research assistant), Université Paris Sud XI
  • 2013.9-2013.12 visitor in IHES
  • 2012.9-2013.8 ATER (Teaching and research assistant), Université Paris Diderot Paris VII
  • Ph.D Thesis (advisor: Prof. Marc Rosso) defended on 25,Oct,2012 with mention Très Honorable
  • 2009.9-2012.8 Ph.D student in Université Paris Diderot Paris VII
  • 2009.6 Master 2 degree, Université Paris Diderot Paris VII (Mention: Très Bien)
  • 2007.6 Bachelor's degree, University Sun Yat-Sen, Guangzhou, China

    Research interests

  • Quantum algebra: quantum groups, quantum (quasi-)shuffle algebras.
  • Lie theory and algebraic combinatorics: PBW filtration, degenerations of flag varieties, total positivity.

    My (pre-)publications

    Preprints in preparation:

    • [21] (with Ghislain Fourier) Symmetries on plabic graphs and associated polytopes.
    • [20] (with Ghislain Fourier, Jan-Philipp Litza and Christoph Pegel) Universal family of marked poset polytopes.

    Preprints:

      Most of my (pre-)publications are available here.
    • [19] (with Lara Bossinger, Ghislain Fourier, Milena Hering and Martina Lanini) Toric degenerations of Gr(2,n) and Gr(3,6) via plabic graphs.
    • [18] (with Peter Littelmann and Milena Pabiniak) Simplices in Newton-Okounkov bodies and the Gromov width of coadjoint orbits.
    • [17] A Borel-Weil-Bott type theorem of quantum shuffle algebras.
    • [16] Dedekind η-function and quantum groups.

    (pre-)Published papers:

    • [15] (with Giovanni Cerulli Irelli, Evgeny Feigin, Ghislain Fourier and Markus Reineke) Linear degenerations of flag varieties, Mathematische Zeitschrift, DOI 10.1007/s00209-016-1839-y.
    • [14] (with Teodor Backhaus and Ghislain Fourier) Degree cones and monomial bases of Lie algebras and quantum groups, to appear in Glasgow Mathematical Journal.
    • [13] (with Ghislain Fourier and Peter Littelmann) On toric degenerations of flag varieties, in Representation Theory -- Current Trends and Perspectives, edited by H. Krause et al, Series of Congress Reports, EMS, 2017.
    • [12] (with Ghislain Fourier and Peter Littelmann) Essential bases and toric degenerations arising from birational sequences, to appear in Adv. Math.
    • [11] (with Marc Rosso) Multi-brace cotensor Hopf algebras and quantum groups, Mathematische Zeitschrift, DOI: 10.1007/s00209-016-1777-8.
    • [10] (with Ghislain Fourier) Marked chain-order polytopes, European Journal of Combinatorics, Volume 58, November 2016, Pages 267--282.
    • [9] Polytopes arising from mirror plabic graphs, Oberwolfach Report, Volume 13, Issue 1, 626-628, 2016.
    • [8] (with Ghislain Fourier) Torus fixed points in Schubert varieties and normalized median Genocchi numbers, Séminaire Lotharingien de Combinatoire 75 (2016), Article B75f.
    • [7] Generalized Matsumoto-Tits sections and quantum quasi-shuffle algebras, Journal of Algebraic Combinatorics, Volume 43, Issue 3 (2016), pp 693-714.
    • [6] (with Ghislain Fourier and Markus Reineke) PBW-Type filtration on quantum groups of type A_n, Journal of Algebra 449 (2016) 321-345.
    • [5] Generalized virtual braid groups, quasi-shuffle product and quantum groups, Int. Math. Res. Notices. (2015) 2015 (6): 1717-1731.
    • [4] (with Run-Qiang Jian) Cofree pointed Hopf algebras on Hopf bimodule algebras, Journal of Pure and Applied Algebra 219 (2015), pp. 3913-3930.
    • [3] Non-symmetrizable quantum groups: defining ideals and specialization, Publ. RIMS Kyoto Univ, Volume 50, Issue 4 (2014) 663-694.
    • [2] On defining ideals and differential algebras of Nichols algebras. Journal of Algebra 346 (2011) 299–331.
    • [1] Quantum groups, q-Boson algebras and quantized Weyl algebras. International Journal of Mathematics Vol. 22, No. 5 (2011) 675–694.
    • [0] Autour des algèbres de battages quantiques : idéaux de définition, spécialisation et cohomologie, Ph.D Thesis. Soutenance: 25/10/2012.

    Seminar/Conference Talks

    • Newton-Okounkov bodies in Lie theory, 07/02/2017, Newton-Okounkov Bodies, Test Configurations, and Diophantine Geometry, BIRS, Banff, Canada.
    • Toric degenerations of flag varieties and applications, 19/12/2016, Oberseminar Lie-Theorie, Ruhr-Universität Bochum, Germany.
    • Feigin-Fourier-Littelmann-Vinberg polytopes and string polytopes, Algebraic combinatorics in Representation Theory, 01/09/2016, CIRM, Luminy, France.
    • Degenerations of flag varieties, 17/06/2016, BIREP Seminar, Bielefeld, Germany.
    • Polytopes arising from mirror plabic graphs, 03/03/2016, Oberwolfach, Germany.
    • New filtrations and monomial bases of quantum groups, 17/11/2015, University of Newcastle, UK.
    • Quantum quasi-shuffle algebras and quantum groups, 11/11/2015, Algebra seminar, University of Glasgow, UK.
    • Linear degenerations of flag varieties, 10/11/2015, MAXIMALS, University of Edinburgh, UK.
    • New filtrations and monomial bases of quantum groups, 07/11/2015, ARTIN Meeting 46, University of Glasgow, UK.
    • Toric degeneration of Graßmannian Gr(2,n) and PBW filtration, 26/05/2015, Universität zu Köln, Germany.
    • Quantum quasi-shuffle algebras and quantum groups, 20/05/2015, Oberseminar Kombinatorik und Algebra, Philipps-Universität Marburg, Germany.
    • Autour des quasi-battages quantiques, Journée "Algèbres de Hopf", 15/12/2014, Clermont-Ferrand, à l'occasion de l'attribution du titre de Docteur Honoris Causa de l'Université Blaise Pascal à Nicolás Andruskiewitsch.
    • Quantum shuffle algebras and their deformations, 25/11/2014, Oberseminar Algebra, Universität zu Köln, Germany.
    • Dedekind η function and quantum groups, 10/12/2013, IHES, France.
    • Cohomologies of quantum shuffle algebras, Oberseminar Algebra, 16/04/2013, Universität zu Köln, Germany.
    • Quantum shuffle algebras: cohomologies, deformations and applications, 25/03/2013, Centre for Quantum Geometry and Moduli spaces, University of Århus, Denmark.
    • Fonction η de Dedekind et groupes quantiques , Algebra seminar, 31/01/2013, Institut Camille Jordan, Université Claude Bernard Lyon 1, Lyon, France.
    • Cohomologies des algèbres de battages quantiques, Colloque Tournant du GDR TLAG, 24/01/2013, Université de Cergy-Pontoise, France.
    • Cohomologies des algèbres de battages quantiques, Seminar "Algèbre et Géométrie", 13/11/2012, LMNO, Université de Caen, France.
    • Autour des algèbres de battages quantiques , Ph.D Defense, 25/10/2012.
    • Cohomologies des algèbres de battages quantiques, Journée des doctorants, 22/03/2012, IMJ, Paris, France.
    • Les algèbres q-Bosons , Séminaire d'algèbre, le 17/01/2011, Institut Henri Poincaré, France.
    • Les algèbres q-Bosons , Séminaire Quant X–Paris 7, le 16/11/2010, École Polytechnique, France.

    Teachings

  • 2016-2017, Universität zu Köln,
  • 2014, Université Paris Sud XI,
    • Travaux dirigés du module MATH256 (Mathématiques générales 4 + Equations différentielles et systèmes dynamiques), groupe PeiPC deuxième année, Polytech Paris-Sud, 54 heures.
    • Problème de Maths pour les Concours ENSI, groupe PMCP, Université Paris-Sud, 36 heures.
    • Cours et Travaux dirigés du module MATH254 (Géométrie et Analyse de Fourier), groupe L2 chimie, Université Paris-Sud, 38 heures.
  • 2009-2013, Université Paris VII Paris Diderot,
    • Travaux dirigés du module MM4 (Algèbre et analyse fondamentales II) pour un groupe L2 mathématique, 96 heures.
    • Travaux dirigés du module MP2 (Analyse et algèbre élémentaires II) pour un groupe L1 physique, 64 heures.
    • Travaux dirigés du module MM1 (Analyse et algèbre élémentaires I) pour un groupe L1 chimie, 64 heures.
    • Module PP2-PP4 Pré-professionelle), dirigé 9 groupes des élèves L1 et L2 pour finir ses mémoires annuels, 64 heures.


  • Arbeitsgruppe Algebra und Zahlentheorie, Mathematisches Institut, Universität zu Köln