Phung Ho Hai

Full Professor, Doctor of Science Department of Geometry and Topology Research interests: Tensor categories, Tannaka duality, Quantum groups,Hopf algebras, Fundamental groupschemes

Address
Office: Building A6, Room 406
Tel: +84 24 37563474
Email: phung AT math.ac.vn

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

Positions:

• Director of Institute of Mathematics Hanoi (IMH): 2017-2022
• Deputy-Director of Institute of Mathematics Hanoi (IMH): 2012-2017
• Since 1996: member of Institute of Mathematics, Hanoi
• 1997-2000: Postdoctoral felow at ICTP (Trieste), MPI-Mathematik (Bonn), MSRI (Berkeley)
• Since 2003: member of Research Group Esnault-Viehweg, University Duisburg-Essen
• Since 2007: member of the Transregio-Sonderforschungsbereich  Bonn-Essen-Mainz
• 2005-2008: Heisenberg-fellow of the DFG
• Since 2008: Deputy Editor-in-Chief of Acta Mathematica Vietnamica
  

 

PUBLICATIONS

List  of publications in MathSciNet

 

List of recent publications

1	Võ Quốc Bảo, Phung Ho Hai, Dao Van Thinh, Cohomology of the differential fundamental group of algebraic curves, Bulletin des Sciences Mathématiques, Volume 203, August 2025, 103646, https://doi.org/10.1016/j.bulsci.2025.103646, (SCI-E, Scopus).
2	Phung Ho Hai, Nguyen Dang Hop, João Pedro dos Santos , Fiber criteria for flatness and homomorphisms of flat affine group schemes, Journal of Pure and Applied Algebra, Volume 229, Issue 6, June 2025, 107949, (SCI-E, Scopus).
3	Phung Ho Hai, João Pedro dos Santos, Phạm Thanh Tâm, Algebraic theory of formal regular-singular connections with parameters, Rendiconti del Seminario Matematico della Università di Padova, Volume 152 (2024) pages 171–228, (SCI-E, Scopus).
4	Phung Ho Hai, João Pedro dos Santos, Phạm Thanh Tâm, Dao Van Thinh, Prolongation of regular-singular connections on punctured affine line over a Henselian ring, Communications in Algebra, Volume 52, 2024 - Issue 8, Pages 3194-3208, (SCI-E, Scopus).
5	Indranil Biswas, Phung Ho Hai, Joao Pedro dos Santos, Connections on trivial vector bundles over projective schemes Comptes Rendus. Mathématique, Volume 362 (2024), pp. 309-325, (SCI-E, Scopus).
6	Phung 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).
7	Phung 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).
8	Indranil 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). Corrected version: see link (https://arxiv.org/abs/1809.06755).
9	Phung 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).
10	Nguyên 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.
11	Phung 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.
12	Nguyen 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.
13	Nguyen Dai Duong, Phung Ho Hai, Tannakian duality over Dedekind rings and applications, Mathematische Zeitschrift, 288 (2018),1103–1142, SCI(-E); Scopus.
14	Nguyen 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.
15	Phung Ho Hai, On an injectivity lemma in the proof of Tannakian duality, Journal of Algebra and Its Applications, 15 (2016),SCI(-E); Scopus.
16	Phung 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.
17	Nguyen 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.
18	Phung Ho Hai, H. Esnault, Two small remarks on Nori fundamental group scheme, In: Advanced Studies in Pure Mathematics, 60 (2010), 237 -- 243.
19	Phung Ho Hai, B. Kriegk and M. Lorenz, $N$-homogeneous superalgebras, J. Noncommut. Geom. 2 (2008), 1 - 51, preprint arXiv:0704.1888.
20	H. Esnault, Phung Ho Hai, Packets in Grothendieck's section conjecture, Adv. Math. 218 (2008), 395 - 416.
21	H. 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.
22	Phung Ho Hai, Tannaka-Krein duality for Hopf algebroids, Israel J. Math. 167 (2008), 193 - 225, preprint arXiv:math/0206113.
23	Phung Ho Hai, H. Esnault, The fundamental groupoid scheme and applications, Annales de l’Institut Fourier, 58 (2008), 2381-2412.
24	Phung Ho Hai, Martin Lorenz, Koszul algebras and the quantum MacMahon master theorem, Bull. Lond. Math. Soc. 39 (2007), 667 - 676, preprint arXiv:math/0603169.
25	Hélène Esnault, Phung Ho Hai, The Gauss-Manin connection and Tannaka duality, Int. Math. Res. Not. 2006, Art. ID 93978, 35 pp.
26	Phung Ho Hai, On the representation categories of matrix quantum groups of type A, Vietnam J. Math. 33 (2005), 357 - 367.
27	Phung Ho Hai, The homological determinant of quantum groups of type $A$. Proc. Amer. Math. Soc. 133 (2005), 1897 - 1905 (electronic), preprint arXiv:math/0305115.
28	Nguyen Thi Phuong Dung, Phung Ho Hai, Irreducible representations of quantum linear groups of type A1|0, J. Algebra 282 (2004), 809 - 830.
29	Phung 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.
30	Phung 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.
31	Phung 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
32	Phung Ho Hai, Characters of quantum groups of type $A_n$, Comm. Algebra 30 (2002), 1085 - 1117, preprint arXiv:math/9807045.
33	Phung Ho Hai, Realizations of quantum hom-spaces, invariant theory, and quantum determinantal ideals, J. Algebra 248 (2002), 50 - 84.
34	Phung Ho Hai, The integral on quantum supergroups of type AR|S, Asian J. Math. 5 (2001), 751 - 769.
35	Phung 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.
36	Phung Ho Hai, On matrix quantum groups of type A_n. Internat. J. Math. 11 (2000), 1115 - 1146.
37	Phung Ho Hai, Hecke symmetries. Commutative algebra, homological algebra and representation theory (Catania/Genoa/Rome, 1998). J. Pure Appl. Algebra 152 (2000), 109 - 121.
38	Phung Ho Hai, On structure of the quantum supergroups GLq(m|n). J. Algebra 211 (1999), 363 - 383.
39	Phung Ho Hai, Poincaré series of quantum spaces associated to Hecke operators. Acta Math. Vietnam. 24 (1999), 235 - 246.
40	Phung Ho Hai, Central bialgebras in braided categories and coquasitriangular structures. J. Pure Appl. Algebra 140 (1999), 229 - 250.
41	Phung Ho Hai, Koszul property and Poincaré series of matrix bialgebra of type A_n. J. Algebra 192 (1997),734 - 748.
42	Phung Ho Hai, Poincaré series of quantum matrix bialgebras determined by pairs of quantum spaces. Comm. Algebra 23 (1995), 879 - 890.

Preprints

1	IMH20250701, Võ Quốc Bảo, Phung Ho Hai, Dao Van Thinh, Cohomology of the stratified fundamental group of curves
2	IMH20250402, Phung Ho Hai, João Pedro Dos Santos, Dao Van Thinh, Singular schemes and infinitesimal non-commutative witt vectors
3	IMH20230402, Trần Phan Quốc Bảo, Võ Quốc Bảo, Phung Ho Hai, Tannakian duality and Gauss-Manin connections for a family of curves