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 information

  • 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
  • My Erdős number: 4.

    Research interests

  • Quantum algebra: Hopf algebras and quantum groups, quantum (quasi-)shuffle algebras.
  • Lie theory and algebraic combinatorics: bases in Lie algebras and quantum groups, applications to degenerations of flag varieties and total positivity.

    News

  • Starting from 2019 there is a regular A(achen)-B(ochum)-C(ologne)-D(arstellungstheorie) Seminar, holding at one of the three universities. The opening workshop of the seminar will be a 3-days long workshop, taking place at RWTH Aachen. For further informations and registration, please visit the website of the workshop:
    Opening workshop of the ABCD seminar
    ABCD Seminar Wintersemester 2019/20

    My (pre-)publications

    Preprints:

      Most of my (pre-)publications are available here.
    • [31] Exact structures and degeneration of Hall algebras (with Mikhail Gorsky), preprint.
    • [30] Lusztig polytopes and FFLV polytopes (with Gleb Koshevoy), preprint.
    • [29] Cones from quantum groups to tropical flag varieties (with Ghislain Fourier and Markus Reineke), preprint.
    • [28] Supports for linear degenerations of flag varieties (with Markus Reineke), preprint.
    • [27] A Borel-Weil-Bott type theorem of quantum shuffle algebras, revised chapter from Ph.D thesis, old preprint.
    • [26] Dedekind η-function and quantum groups, revised chapter from Ph.D thesis, old preprint.

    (pre-)Published papers:

    • [25] A Continuous family of marked poset polytopes (with Ghislain Fourier, Jan-Philipp Litza and Christoph Pegel), SIAM J. Discrete Math., 2020, 34(1), 611--639.
    • [24] Degenerate Schubert varieties in type A (with Rocco Chirivì and Ghislain Fourier), Transformation Groups (2020). https://doi.org/10.1007/s00031-020-09558-4.
    • [23] The Minkowski property and reflexivity of marked poset polytopes (with Ghislain Fourier and Christoph Pegel), Electronic Journal of Combinatorics, P1.27, Volume 27, Issue 1 (2020).
    • [22] Degenerations of flag varieties from PBW filtration, Oberwolfach report 2019.
    • [21] Linear degenerations of flag varieties: partial flags, defining equations, and group actions (with Giovanni Cerulli Irelli, Evgeny Feigin, Ghislain Fourier and Markus Reineke), Mathematische Zeitschrift, 2020, 296(1), 453--477.
    • [20] Weighted PBW degenerations and tropical flag varieties (with Evgeny Feigin, Ghislain Fourier and Igor Makhlin), Communications in Contemporary Mathematics, Vol. 21, No. 01, 1850016 (2019).
    • [19] Symmetries on plabic graphs and associated polytopes (with Ghislain Fourier), Comptes Rendus Mathématique, Volume 356, Issue 6, Pages 581-585, June 2018.
    • [18] Toric degenerations of Gr(2,n) and Gr(3,6) via plabic graphs (with Lara Bossinger, Ghislain Fourier, Milena Hering and Martina Lanini), Annals of Combinatorics, September 2018, Volume 22, Issue 3, pp 491--512.
    • [17] Simplices in Newton-Okounkov bodies and the Gromov width of coadjoint orbits (with Peter Littelmann and Milena Pabiniak), Bulletin of the London Mathematical Society, Volume 50, Issue 2, April 2018, 202--218.
    • [16] From standard monomial theory to semi-toric degenerations via Newton-Okounkov bodies (with Peter Littelmann), Trans. Moscow Math. Soc. 2017, 275--297.
    • [15] Linear degenerations of flag varieties (with Giovanni Cerulli Irelli, Evgeny Feigin, Ghislain Fourier and Markus Reineke), Mathematische Zeitschrift, (2017) 287:615--654.
    • [14] Degree cones and monomial bases of Lie algebras and quantum groups (with Teodor Backhaus and Ghislain Fourier), Glasgow Mathematical Journal, Volume 59, Issue 3 September 2017, pp. 595--621.
    • [13] On toric degenerations of flag varieties (with Ghislain Fourier and Peter Littelmann), in Representation Theory -- Current Trends and Perspectives, edited by H. Krause et al, Series of Congress Reports, EMS, 2017.
    • [12] Essential bases and toric degenerations arising from birational sequences (with Ghislain Fourier and Peter Littelmann), Adv. Math, Volume 312, 25 May 2017, Pages 107--149.
    • [11] Multi-brace cotensor Hopf algebras and quantum groups (with Marc Rosso), Mathematische Zeitschrift, June 2017, Volume 286, Issue 1, pp 657--678.
    • [10] Marked chain-order polytopes (with Ghislain Fourier), 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] Torus fixed points in Schubert varieties and normalized median Genocchi numbers (with Ghislain Fourier), 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] PBW-Type filtration on quantum groups of type A_n (with Ghislain Fourier and Markus Reineke), 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] Cofree pointed Hopf algebras on Hopf bimodule algebras (with Run-Qiang Jian), 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.

    Activities

    Seminar/Conference Talks

    • PBW theorem revisited, 07/07/2020, Oberseminar (Oberwebinar) Algebra, Universität zu Köln, Germany.
    • Exact structures and degenerations of Hall algebras, Paris algebra seminar, 06/07/2020, Webinar.
    • From PBW filtration to linear degenerate flag varieties, 03/12/2019, Oberseminar Algebra, University of Stuttgart, Stuttgart, Germany.
    • Degenerations of flag varieties, 07/10/2019, MFO Workshop "Degeneration techniques in representation theory", Oberwolfach, Germany. Slides for the first part of the talk.
    • Toric degenerations of flag varieties and applications, 13/03/2019, National Research University Higher School of Economics, Moscow, Russia.
    • Global geometry of linear degenerate flag varieties, 19/01/2019, Institute for Advanced Study in Mathematics of Harbin Institute of Technology, Harbin, China.
    • Geometry of linear degenerate flag varieties, 17/12/2018, RWTH Aachen, Aachen, Germany.
    • Degenerations of flag varieties, 29/10/2018, Università del Salento, Lecce, Italy.
    • Birational sequences and toric degenerations of flag varieties, 26/04/2018, Oberseminar zur Algebra und Algebraischen Kombinatorik, Leibniz Universität Hannover, Hannover, Germany.
    • From quantum groups to tropical flag varieties, 24/01/2018, Workshop Tensor categories, Hopf algebras and quantum groups, Philipps-Universität Marburg, Marburg, Germany.
    • Semi-toric degenerations of Grassmanians arising from Newton-Okounkov bodies, 22/08/2017, Workshop on Toric Degenerations, University of Bristol, Bristol, UK.
    • Toric degenerations of flag varieties via Newton-Okounkov bodies, 10/07/2017, ETH Zürich, Zürich, Switzerland.
    • Toric degenerations of flag varieties via Newton-Okounkov bodies, 17/03/2017, ALTA Oberseminar, Universität Bremen, Bremen, Germany.
    • 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, 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, Universität Bielefeld, Bielefeld, Germany.
    • Polytopes arising from mirror plabic graphs, 03/03/2016, MFO, 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, Paris, France.
    • Les algèbres q-Bosons , Séminaire Quant X–Paris 7, le 16/11/2010, École Polytechnique, Palaiseau, France.

    Teachings

  • 2016-, 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.

    Students

  • Bachelor students:
    • Stefanie Heidler: Markierte Poset Polytope, 2018.
    • Kiran Patel: Lattice polytopes with one or more interior lattice points, 2018.
    • Antonio Garcia Morales: Groebner basis of toric ideals, 2020.
    • Charly Schwabe: Quadratische Leitideale von exzeptionellen Wurzelsystemen, 2020.
  • Master students:
    • Zheng Huang: Ueber die Aequivalenz der Kategorien Hives und Crystals, 2018.
    • Johannes Wirths: Plabic graphs and total positivity in Grassmannians, 2018.
    • Dennis Jahn: Two-faces of order and chain polytopes, 2018.
    • Verity Mackscheidt: The positive Grassmannian - Decompositions, parametrisation and application in the KP-equation, 2019.
    • Thuy-Mi Nguyen: Bridge polytopes and positive Grassmannians, 2020.
    • Edgar Levcuk: Newton-Okounkov Polytopes and Flag Varieties, 2020.
    • Richard Obersheimer: Hodge theory of matroids, 2020.
    • Nina Samek: Saturated Newton polytopes from symmetric functions, 2020.


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