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 A6, Room 406
Tel: +84 24 37563474
Email: phung AT

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
1Phung Ho Hai, João Pedro dos Santos, Regular-singular connections on relative complex schemes, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2023: VOL. XXIV, ISSUE 3, (SCI-E, Scopus).
2Phung Ho Hai, João Pedro dos Santos, Finite torsors on projective schemes defined over a discrete valuation ring, Algebraic Geometry, 10, (2023), page 1-40, (SCI-E, Scopus).
3Indranil Biswas, Phung Ho Hai, João Pedro Dos Santos, On the fundamental group schemes of certain quotient varieties, Tohoku Mathematical Journal, 73(2021), 565-595, (SCI-E, Scopus).
4Phung Ho Hai, João Pedro dos Santos, On the Structure of Affine Flat Group Schemes Over Discrete Valuation Rings, II , International Mathematics Research Notices, 12 (2021), Pages 9375–9424, (SCI(-E), Scopus).
5Nguyên Luong Thái Bình, Nguyên Thi Phuong Dung, Phung Ho Hai, Jacobi-Trudi Type Formula for Character of Irreducible Representations of gl(m|1), Acta Mathematica Vietnamica, 44 (2019), pp 603–615, Scopus.
6Phung Ho Hai, João Pedro P. dos Santos, The action of the etale fundamental group scheme on the connected component of the essentially finite one, Mathematische Nachrichten, 291 (2018),1733–1742, SCI(-E); Scopus.
7Nguyen 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, SCI(-E); Scopus.
8Nguyen Dai Duong, Phung Ho Hai, Tannakian duality over Dedekind rings and applications, Mathematische Zeitschrift, 288 (2018),1103–1142, SCI(-E); Scopus.
9Nguyen 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,SCI(-E); Scopus.
10Phung Ho Hai, On an injectivity lemma in the proof of Tannakian duality, Journal of Algebra and Its Applications, 15 (2016),SCI(-E); Scopus.
11Phung Ho Hai, Gauss-Manin stratification and stratified fundamental group schemes, Annales de l'institut Fourier, 63 (2013), 2267-2285, doi: 10.5802/aif.2829, SCI(-E); Scopus.
12Nguyen Thi Phuong Dung, Phung Ho Hai, Nguyen Huy Hung, Construction of irreducible representations of the quantum super group $GL_q(3\mid 1)$, Acta Mathematica Vietnamica 36 (2011), 215 -- 229, Scopus.
13Phung Ho Hai, H. Esnault, Two small remarks on Nori fundamental group scheme, In: Advanced Studies in Pure Mathematics, 60 (2010), 237 -- 243.
14Phung Ho Hai, B. Kriegk and M. Lorenz, $N$-homogeneous superalgebras, J. Noncommut. Geom. 2 (2008), 1 - 51, preprint arXiv:0704.1888.
15H. Esnault, Phung Ho Hai, Packets in Grothendieck's section conjecture, Adv. Math. 218 (2008), 395 - 416.
16H. 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.
17Phung Ho Hai, Tannaka-Krein duality for Hopf algebroids, Israel J. Math. 167 (2008), 193 - 225, preprint arXiv:math/0206113.
18Phung Ho Hai, H. Esnault, The fundamental groupoid scheme and applications, Annales de l’Institut Fourier, 58 (2008), 2381-2412.
19Phung Ho Hai, Martin Lorenz, Koszul algebras and the quantum MacMahon master theorem, Bull. Lond. Math. Soc. 39 (2007), 667 - 676, preprint arXiv:math/0603169.
20Hélène Esnault, Phung Ho Hai, The Gauss-Manin connection and Tannaka duality, Int. Math. Res. Not. 2006, Art. ID 93978, 35 pp.
21Phung Ho Hai, On the representation categories of matrix quantum groups of type A, Vietnam J. Math. 33 (2005), 357 - 367.
22Phung Ho Hai, The homological determinant of quantum groups of type $A$. Proc. Amer. Math. Soc. 133 (2005), 1897 - 1905 (electronic), preprint arXiv:math/0305115.
23Nguyen Thi Phuong Dung, Phung Ho Hai, Irreducible representations of quantum linear groups of type A1|0, J. Algebra 282 (2004), 809 - 830.
24Phung 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.
25Phung 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.
26Phung 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
27Phung Ho Hai, Characters of quantum groups of type $A_n$, Comm. Algebra 30 (2002), 1085 - 1117, preprint arXiv:math/9807045.
28Phung Ho Hai, Realizations of quantum hom-spaces, invariant theory, and quantum determinantal ideals, J. Algebra 248 (2002), 50 - 84.
29Phung Ho Hai, The integral on quantum supergroups of type AR|S, Asian J. Math. 5 (2001), 751 - 769.
30Phung 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.
31Phung Ho Hai, On matrix quantum groups of type A_n. Internat. J. Math. 11 (2000), 1115 - 1146.
32Phung Ho Hai, Hecke symmetries. Commutative algebra, homological algebra and representation theory (Catania/Genoa/Rome, 1998). J. Pure Appl. Algebra 152 (2000), 109 - 121.
33Phung Ho Hai, On structure of the quantum supergroups GLq(m|n). J. Algebra 211 (1999), 363 - 383.
34Phung Ho Hai, Poincaré series of quantum spaces associated to Hecke operators. Acta Math. Vietnam. 24 (1999), 235 - 246.
35Phung Ho Hai, Central bialgebras in braided categories and coquasitriangular structures. J. Pure Appl. Algebra 140 (1999), 229 - 250.
36Phung Ho Hai, Koszul property and Poincaré series of matrix bialgebra of type A_n. J. Algebra 192 (1997),734 - 748.
37Phung Ho Hai, Poincaré series of quantum matrix bialgebras determined by pairs of quantum spaces. Comm. Algebra 23 (1995), 879 - 890.
1IMH20240101, Joao Pedro dos Santos, Phung Ho Hai, Nguyen Dang Hop, Fiber criteria for flatness and homomorphisms of flat affine group schemes
2IMH20230402, Trần Phan Quốc Bảo, Võ Quốc Bảo, Phung Ho Hai, Tannakian duality and Gauss-Manin connections for a family of curves
3IMH20220801, Phung Ho Hai, João Pedro dos Santos, Pham Thanh Tâm, Đào Văn Thinh, Prolongation of regular singular connections on punctured affine line over a Henselian rin, preprint arxiv.
4IMH20210702, Phung Ho Hai, João Pedro dos Santos, Pham Thanh Tam, Algebraic theory of formal regular-singular connections with parameters, preprint arXiv:2107.06474.
5IMH20210605, Indranil Biswas, Phung Ho Hai, João Pedro dos Santos, Connections on trivial vector bundles over projective schemes, preprint arXiv:2106.08547