Phung Ho Hai

Full Professor, Doctor of Science

Department of Number Theory
Research interests: Tensor categories, Tannaka duality, Quantum groups,Hopf algebras, Fundamental groupschemes

Office: Building A5, Room 204
Tel: +84 24 37563474 / 305, 204
Email: phung AT
Personal homepage:

Education and academic degrees:

  • 1987: Graduate from High School for gifted students at Hanoi University
  • 1992: Graduated from Moscow State University (Title Magister of Mathematics and Physics)
  • 1996: Ph. D. in Mathematics at Munich Unversity
  • 2005: Habilitation at the University Duisburg-Essen
  • 2006: Associate Professor
  • 2012: Full Professor




List  of publications in MathSciNet


List of recent publications
1Nguyen Dai Duong, Phung Ho Hai, João Pedro P. Dos Santos, On the structure of affine flat group schemes over discrete valuation rings, Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, XVIII (2018), 977-1032.
2Nguyen Dai Duong, Phung Ho Hai, Tannakian duality over Dedekind rings and applications, Mathematische Zeitschrift, 288 (2018),1103–1142.
3Nguyen Dai Duong, Phung Ho Hai, Nguyen Huy Hung, On the flatness and the projectivity over Hopf subalgebras of Hopf algebras over Dedekind rings, Journal of Algebra, 478 (2017), 237–260.
4Phung Ho Hai, On an injectivity lemma in the proof of Tannakian duality, Journal of Algebra and Its Applications, 15 (2016).
5Phung Ho Hai, Gauss-Manin stratification and stratified fundamental group schemes, Annales de l'institut Fourier, 63 (2013), 2267-2285, doi: 10.5802/aif.2829.
6Nguyen Thi Phuong Dung, Phung Ho Hai, Nguyen Huy Hung, Construction of irreducible representations of the quantum super group $GL_q(3\mid 1)$Acta Math. Vietnamica  36 (2011), 215 -- 229.
7Phung Ho Hai, H. Esnault, Two small remarks on Nori fundamental group scheme, In: Advanced Studies in Pure Mathematics, 60 (2010), 237 -- 243.
8Phung Ho Hai, B. Kriegk and M. Lorenz, $N$-homogeneous superalgebras, J. Noncommut. Geom. 2 (2008), 1 - 51, preprint arXiv:0704.1888.
9H. Esnault, Phung Ho Hai, Packets in Grothendieck's section conjecture, Adv. Math. 218 (2008), 395 - 416.
10H. Esnault, Phung Ho Hai, X. Sun, On Nori's fundamental group scheme. In: Geometry and dynamics of groups and spaces, 377 - 398, Progr. Math., 265, Birkhọuser, Basel, 2008.preprint arXiv:math/0605645.
11Phung Ho Hai, Tannaka-Krein duality for Hopf algebroids, Israel J. Math. 167 (2008), 193 - 225, preprint arXiv:math/0206113.
12Phung Ho Hai, H. Esnault, The fundamental groupoid scheme and applications, Annales de l’Institut Fourier, 58 (2008), 2381-2412.
13Phung Ho Hai, Martin Lorenz, Koszul algebras and the quantum MacMahon master theorem, Bull. Lond. Math. Soc. 39 (2007), 667 - 676, preprint arXiv:math/0603169.
14Hélène Esnault, Phung Ho Hai, The Gauss-Manin connection and Tannaka duality, Int. Math. Res. Not. 2006, Art. ID 93978, 35 pp.
15Phung Ho Hai, On the representation categories of matrix quantum groups of type A, Vietnam J. Math. 33 (2005), 357 - 367.
16Phung Ho Hai, The homological determinant of quantum groups of type $A$. Proc. Amer. Math. Soc. 133 (2005), 1897 - 1905 (electronic), preprint arXiv:math/0305115.
17Nguyen Thi Phuong Dung, Phung Ho Hai, Irreducible representations of quantum linear groups of type A1|0, J. Algebra 282 (2004), 809 - 830.
18Phung Ho Hai, Nguyen Phuong Dung, On the Poincare series of quadratic algebras associated to Hecke symmetries, Int. Math. Res. Not. 2003, N0 40, 2193 - 2203.
19Phung Ho Hai, On a theorem of Deligne on characterization of Tannakian categories. In: Arithmetic fundamental groups and noncommutative algebra (Berkeley, CA, 1999), 517 - 531, Proc. Sympos. Pure Math., 70, Amer. Math. Soc., Providence, RI, 2002.
20Phung Ho Hai, An embedding theorem for abelian monoidal categories, Compositio Math. 132 (2002), 27 - 48, preprint arXiv:math/0004160.  Corrigendum: ``An embedding theorem for abelian monoidal categories'' [Compositio Math. 132 (2002), N0 1, 27 - 48]. Compos. Math. 144 (2008), 1349 - 1350
21Phung Ho Hai, Characters of quantum groups of type $A_n$, Comm. Algebra 30 (2002), 1085 - 1117, preprint arXiv:math/9807045.
22Phung Ho Hai, Realizations of quantum hom-spaces, invariant theory, and quantum determinantal ideals, J. Algebra 248 (2002), 50 - 84.
23Phung Ho Hai, The integral on quantum supergroups of type AR|S, Asian J. Math. 5 (2001), 751 - 769.
24Phung Ho Hai, Splitting comodules over Hopf algebras and application to representation theory of quantum groups of type A0|0. J. Algebra 245 (2001), 20 - 41.
25Phung Ho Hai, On matrix quantum groups of type A_n. Internat. J. Math. 11 (2000), 1115 - 1146.
26Phung Ho Hai, Hecke symmetries. Commutative algebra, homological algebra and representation theory (Catania/Genoa/Rome, 1998). J. Pure Appl. Algebra 152 (2000), 109 - 121.
27Phung Ho Hai, On structure of the quantum supergroups GLq(m|n). J. Algebra 211 (1999), 363 - 383.
28Phung Ho Hai, Poincaré series of quantum spaces associated to Hecke operators. Acta Math. Vietnam. 24 (1999), 235 - 246.
29Phung Ho Hai, Central bialgebras in braided categories and coquasitriangular structures. J. Pure Appl. Algebra 140 (1999), 229 - 250.
30Phung Ho Hai, Koszul property and Poincaré series of matrix bialgebra of type A_n. J. Algebra 192 (1997),734 - 748.
31Phung Ho Hai, Poincaré series of quantum matrix bialgebras determined by pairs of quantum spaces. Comm. Algebra 23 (1995), 879 - 890.
1IMH20180502, Indranil Biswas, Phung Ho Hai, João Pedro dos Santos, On the fundamental group schemes of certain quotient varieties
2IMH20171201, Phung Ho Hai, Joao Pedro P. dos Santos, On the structure of affine flat group schemes over discrete valuation rings, II.
3IMH20161201, Phung Ho Hai, JO˜AO PEDRO P. DOS SANTOS, The action of the Étale fundametal group scheme on the connected component of the essentialy finite one