### Ngo Viet Trung

 Full Professor, Doctor of Science Department of Algebra Research interests: Commutative Algebra and Interactions to Algebraic Geometry and Combinatorics

Office: Building A6, Room 416
Tel: +84 (024 38361121 / 416
Email: nvtrung AT math.ac.vn

Honors

• Hochiminh Prize in Science and Technology 2016 (shared with Professors  Nguyen Tu Cuong and Le Tuan Hoa)
• Vietnam Talent in the Field of Natural Science (Area: Mathematics) 2009

PUBLICATIONS

#### List of publications in MathSciNet

List of recent publications
 1 Ha Minh Lam, Ngo Viet Trung, Associated primes of powers of edge ideals and ear decompositions of graphs, Transactions of the American Mathematical Society 372 (2019), 3211-3236 SCI(-E), Scopus. 2 Giulio Cavigli, Ha Huy Tai, Jürgen Herzog, Manoj Kummini, Naoki Terai, Ngo Viet Trung, Depth and regularity modulo a principal ideal. Journal of Algebraic Combinatorics 49 (2019), no. 1, 1–20, SCI(-E), Scopus. 3 Ha Huy Tai, Ngo Viet Trung, Membership Criteria and Containments of Powers of Monomial Ideals, Acta Mathematica Vietnamica, 44 (2019), pp 117–139, Scopus. 4 Maria Evelina Rossi, Dinh Thanh Trung, Ngo Viet Trung, Castelnuovo-Mumford regularity and Ratliff-Rush closure. Journal of Algebra 504 (2018), 568-586, SCI(-E); Scopus. 5 Gregor Kemper, Ngo Viet Trung, Nguyen Thi Van Anh, Toward a theory of monomial preorders, Mathematics of Computation 87 (2018), no. 313, 2513-2537, SCI(-E); Scopus. 6 Ha Huy Tài, Ngo Viet Trung, Tran Nam Trung, Depth and regularity of powers of sums of ideals. Mathematische Zeitschrift 282 (2016), 819–838, SCI(-E); Scopus. 7 Ha Thi Thu Hien, Ha Minh Lam, Ngo Viet Trung, Saturation and associated primes of powers of edge ideals, Journal of Algebra, 439 (2015), 225–244, SCI(-E); Scopus. 8 Hong Ngoc Binh, Ngo Viet Trung, The Bhattacharya function of complete monomial ideals in two variables, Communications in Algebra, 43 (2015), 2875-2886, SCI(-E), Scopus. 9 Naoki Terai, Ngo Viet Trung, On the associated primes and the depth of the second power of squarefree monomial ideals, Journal of Pure and Applied Algebra, 218 (2014), 1117–1129, SCI(-E); Scopus. 10 Gregor Kemper, Ngo Viet Trung, Krull dimension and monomial orders,Â Journal of Algebra, 399(2014), 782–800, SCI(-E); Scopus. 11 Ngo Viet Trung, Introduction to Commutative Algebra and Algebraic Geometry (in Vietnamese), Publishing House of Vietnam Academy of Science and Technology, Hanoi, 2012. 12 Ngo Viet Trung, Naoki Terai, Cohen–Macaulayness of large powers of Stanley–Reisner ideals, Advances in Mathematics, 229 (2012), 711 -- 730, SCI(-E); Scopus. 13 Ngo Viet Trung, T. M. Tuan, Equality of ordinary and symbolic powers of Stanley-Reisner ideals, Journal of Algebra,  328 (2011), 77 - 93, preprint arXiv:1009.0828, SCI(-E); Scopus. 14 Ngo Viet Trung, N. C. Minh, Cohen-Macaulayness of monomial ideals and symbolic powers of Stanley-Reisner ideals. Advances in Mathematics 226 (2011), 1285 - 1306, SCI(-E); Scopus. 15 Ngo Viet Trung, J. K. Verma, Hilbert functions of multigraded algebras, mixed multiplicities of ideals and their applications, Journal of Commutative Algebra, 2 (2010), 515 -- 565, SCI(-E); Scopus. 16 Nguyen Cong Minh, Ngo Viet Trung, Cohen-Macaulayness of powers of two-dimensional squarefree monomial ideals, J. Algebra, 322 (2009), 4219-4227. 17 J. Herzog, T. Hibi, Ngo Viet Trung, Vertex cover algebras of unimodular hypergraphs, Proc. Amer. Math. Soc., 137 (2009), 409-414, preprint arXiv:math/0703577. 18 Juergen Herzog, Takayuki Hibi, Satoshi Murai, Xinxian Zheng, Ngo Viet Trung, Kruskal-Katona type theorems for clique complexes arising from chordal and strongly chordal graphs, Combinatorica 28 (2008), 315 - 323, preprint arXiv:math/0606477. 19 Jürgen Herzog, Takayuki Hibi, Ngo Viet Trung, Xinxian Zheng, Standard graded vertex cover algebras, cycles and leaves, Trans. Amer. Math. Soc. 360 (2008), 6231 - 6249, preprint arXiv:math/0606357. 20 Marc Chardin, Nguyen Cong Minh, Ngo Viet Trung, On the regularity of products and intersections of complete intersections, Proc. Amer. Math. Soc. 135 (2007),  1597 - 1606, preprint arXiv:math/0503157. 21 Jürgen Herzoga, Takayuki Hibib, Ngo Viet Trung, Symbolic powers of monomial ideals and vertex cover algebras, Adv. Math. 210 (2007), 304 - 322. 22 Ngo Viet Trung, Jugal Verma , Mixed multiplicities of ideals versus mixed volumes of polytopes, Trans. Amer. Math. Soc. 359 (2007), 4711 - 4727, preprint arXiv:math/0504178. 23 Ngo Viet Trung, Castelnuovo-Mumford regularity and related invariants. In: Commutative algebra and combinatorics, 157 - 180, Ramanujan Math. Soc. Lect. Notes Ser. 4, Ramanujan Math. Soc., Mysore, 2007. 24 Maria Evelina Rossi, Ngo Viet Trung, Giuseppe Val, Castelnuovo-Mumford regularity and finiteness of Hilbert functions, Commutative algebra, 193 - 209, 2006, preprint arXiv:math/0407398. 25 Cao Huy Linh, Ngo Viet Trung, Uniform bounds in generalized Cohen-Macaulay rings, J. Algebra 304 (2006), 1147 - 1159, preprint arXiv:math/0606639. 26 Ngo Viet Trung, Integral closures of monomial ideals and Fulkersonian hypergraphs, Vietnam J. Math. 34 (2006), 489 - 494. 27 Ngo Viet Trung, Hsin-Ju Wang, On the asymptotic linearity of Castelnuovo-Mumford regularity, J. Pure Appl. Algebra 201 (2005), 42 - 48. 28 Ngo Viet Trung, Galois Theory (in Vietnamese), National University Press, Hanoi, 2005. 29 Craig Huneke, Ngo Viet Trung, On the core of ideals. Compos. Math. 141 (2005), 1 - 18. 30 Ha Huy Tai, Ngo Viet Trung, Asymptotic behaviour of arithmetically Cohen-Macaulay blow-ups. Trans. Amer. Math. Soc. 357 (2005), 3655 - 3672. 31 Nguyên Duc Hoang, Ngo Viet Trung, Hilbert polynomials of non-standard bigraded algebras, Math. Z. 245 (2003), 309 - 334. 4. 32 Ngo Viet Trung, Constructive characterization of the reduction numbers, Compositio Math. 137 (2003), 99 - 113. 33 Maria Evelina Rossi, Ngo Viet Trung, Giuseppe Valla, Castelnuovo-Mumford regularity and extended degree,  Trans. Amer. Math. Soc. 355 (2003), 1773 - 1786. 34 Le Tuan Hoa, Ngo Viet Trung, Borel-fixed ideals and reduction number, J. Algebra 270 (2003), N0 1, 335 - 346. 35 J. Herzog, D. Popescu, Ngo Viet Trung, Regularity of Rees algebras. J. London Math. Soc. (2) 65 (2002), 320 - 338. 36 Ngo Viet Trung, Evaluations of initial ideals and Castelnuovo-Mumford regularity. Proc. Amer. Math. Soc. 130 (2002), 1265 - 1274 (electronic). 37 Ngo Viet Trung, W. Bruns and J. Gubeladze, Problems and algorithms for affine semigroups. Semigroup Forum 64 (2002), 180 - 212. 38 Jürgen Herzog, Le Tuan Hoa, Ngo Viet Trung, Asymptotic linear bounds for the Castelnuovo-Mumford regularity, Trans. Amer. Math. Soc. 354 (2002),  1793 - 1809 (electronic). 39 Ngo Viet Trung, Lectures on linear algebra (in Vietnamese) - Giáo trình đại số tuyến tính. NXB ĐHQG Hà Nội, 2001, 272 trang. 40 Aldo Conca, Ngo Viet Trung, Giuseppe Valla, Koszul property for points in projective spaces, Math. Scand. 89 (2001), 201 - 216. 41 Ngo Viet Trung, Positivity of mixed multiplicities, Math. Ann. 319 (2001), 33 - 63. 42 Ngo Viet Trung, Groebner bases, local cohomology and reduction number. Proc. Amer. Math. Soc. 129 (2001), 9 - 18. 43 Dam Van Nhi, Ngo Viet Trung, Specialization of modules over a local ring. Commutative algebra, homological algebra and representation theory (Catania/Genoa/Rome, 1998). J. Pure Appl. Algebra 152 (2000), N0 1-3, 275 - 288. 44 Ngo Viet Trung, Castelnuovo-Mumford regularity and analytic deviation of ideals. J. London Math. Soc. (2) 62 (2000), 41 - 55. 45 Ngo Viet Trung, The largest non-vanishing degree of graded local cohomology modules. J. Algebra 215 (1999), 481 - 499. 46 S. Dale Cutkosky, Jürgen Herzog, Ngo Viet Trung, Asymptotic behaviour of Castelnuovo-Mumford regularity. Compositio Math. 118 (1999), 243 - 261. 47 Dam Van Nhi, Ngo Viet Trung, Specialization of modules. Comm. Algebra 27 (1999), 2959 - 2978. 48 Ngo Viet Trung, The Castelnuovo regularity of the Rees algebra and the associated graded ring. Trans. Amer. Math. Soc. 350 (1998), 2813 - 2832. 49 A. Simis, Ngo Viet Trung, G. Valla, The diagonal subalgebras of a blow-up ring. J. Pure Appl. Algebra 125 (1998), 305 - 328. 50 Le Tuan Hoa, Ngo Viet Trung, On the Castelnuovo-Mumford regularity and the arithmetic degree of monomial ideals. Math. Z. 229 (1998), 519 - 537. 51 Aldo Conca, Giuseppe Valla, Jurgen Herzog, Ngo Viet Trung, Diagonal subalgebras and embbedings of blow-ups of projective spaces. Amer. J. Math. 119 (1997), 859 - 901. 52 W. Bruns, J. Gubeladze, Ngo Viet Trung, Normal polytopes, triangulations and Koszul algebras. J. Reine Angew. Math. 485 (1997), 123 - 160. 53 Ngo Viet Trung, On the lifting of determinantal ideals. Manuscripta Math. 91 (1996), 467 - 481. 54 J. Aberbach, C. Huneke, Ngo Viet Trung, Reduction numbers, Briancon-Skoda theorem and the depth of Rees rings. Compositio Math. 97 (1995), 403 - 434. 55 Ngo Viet Trung, G. Valla, Upper bounds for the regularity index of fat points with uniform position property. J. Algebra 176 (1995), 182 - 209. 56 Bernd Sturmfels, Ngo Viet Trung, Wolfgang Vogel, Bounds on degrees of projective schemes. Math. Ann. 302 (1995), 417 - 432. 57 Ngo Viet Trung, Giuseppe Valla, On zero-dimensional subschemes of complete intersections. Math. Z. 219 (1995), 187 - 201. 58 Ngo Viet Trung, Manfred Herrmann, Eero Hyry, Jürgen Ribbe, On multi-Rees algebras. Math. Ann. 301 (1995), 249 - 279. 59 Ngo Viet Trung, D.Q. Viet, S. Zarzuela, When is the Rees algebra Gorenstein?. J. Algebra 175 (1995), 137 - 156. 60 Aron Simis, Ngo Viet Trung, Giuseppe Valla, Commutative algebra (ICTP, Trieste 1992). Eds.: A. Simis, N. V. Trung and G. Valla, World Scientific, 1994. 61 Ngo Viet Trung, Reduction number, a-invariant, and Rees algebras of ideals having small analytic deviation, In: Commutative Algebra (ICTP, Trieste 1992), World Scientific, 1994, 245 - 262. 62 Ngo Viet Trung, An algebraic approach to the regularity index of fat points in ${\bf P}^n$. Kodai Math. J. 17 (1994), 382 - 389. 63 Jürgen Herzog, Giuseppe Valla, Ngo Viet Trung, On hyperplane sections of reduced irreducible varieties of low codimension. J. Math. Kyoto Univ. 34 (1994), 47 - 72. 64 M. V. Catalisano, Ngo Viet Trung, G. Valla, A sharp bound for the regularity index of fat points in general position. Proc. Amer. Math. Soc. (1993), 717 - 724. 65 Ngo Viet Trung, Filter-regular sequences and multiplicity of blow-up rings of ideals of the principal class. J. Math. Kyoto Univ. 33 (1993), 665 - 683. 66 Manfred Herrmann, Ngo Viet Trung, Examples of Buchsbaum quasi-Gorenstein rings. Proc. Amer. Math. Soc. 117 (1993), 619 - 625. 67 Ngo Viet Trung, Duong Quôc Viêt, On the Cohen-Macaulay and Gorenstein property of Rees algebras of non-singular equimultiple prime ideals. Manus. Math. 76 (1992), 147 - 167. 68 Jürgen Herzog, Ngo Viet Trung, Bernd Ulrich, On the multiplicity of Rees algebras and associated graded rings of d-sequences. J. Pure Appl. Algebra 80 (1992), 273 - 297. 69 Jürgen Herzog, Ngo Viet Trung, Grobner bases and multiplicity of determinantal and Pfaffian ideals. Advances in Math. 96 (1992), 1 - 37. 70 M. Herrmann, J. Ribbe, Ngo Viet Trung, Rees algebras of non-singular equimultiple prime ideals. Nagoya Math. J. 124 (1991), 1 - 12. 71 Winfried Bruns, Aron Simis, Ngo Viet Trung, Blow-ups of straightening closed ideals in ordinal Hodge algebras. Trans. Amer. Math. Soc. 326 (1991), 509 - 518. 72 M. Herrmann, J. Ribbe, Ngo Viet Trung, S. Zarzuela, Bounds for the multiplicity of almost complete intersections. Manus. Math. 72 (1991), 275 - 296. 73 Ngo Viet Trung, On the presentation of Hodge algebras and the existence of Hodge algebra structures. Comm. Algebra 19 (1991), 1183 - 1195. 74 M. Morales, Ngo Viet Trung, O. Villamayor, Sur la fonction de Hilbert-Samuel des clôtures intégrales des puissances d'idéaux engendrés par un système de paramètres. J. Algebra 129 (1990), 96 - 102. 75 Ngo Viet Trung, Giuseppe Valla, The Cohen-Macaulay type of points in generic position. J. Algebra 125 (1989), 110 - 119. 76 Ngo Viet Trung, Shin Ikeda, When is the Rees algebra Cohen-Macaulay? Comm. Algebra 17 (12) (1989), 2893 - 2922. 77 Ngo Viet Trung, Giuseppe Valla, Degree bounds for the defining equations of arithmetically Cohen-Macaulay varieties. Math. Ann. 281 (1988), 479 - 491. 78 A. Simis, Ngo Viet Trung, The divisor class group of ordinary and symbolic blow-ups. Math. Zeits. 198 (1988), 479 - 491. 79 Ngo Viet Trung, G. Valla, On degree bounds for the defining equations of arithmetically Cohen-Macaulay and Buchsbaum varieties. Acta Math. Vietnam. 12 (1987), 113 - 122. 80 Ngo Viet Trung, Reduction exponent and degree bounds for the defining equations of graded rings. Proc. Amer. Math. Soc. 101 (1987), 229 - 236. 81 Ngo Viet Trung, Towards a theory of generalized Cohen-Macaulay modules. Nagoya Math. J. 102 (1986), 1 - 49. 82 Ngo Viet Trung, Le Tuan Hoa, Affine semigroups and Cohen-Macaulay rings generated by monomials. Trans. Amer. Math. Soc. 298 (1986), 145 - 167. 83 Ngo Viet Trung, Maximum number of independent elements and dimension of prime divisors in completions of local rings. J. Algebra 93 (1985), 418 - 438. 84 Ngo Viet Trung, Projections of one-dimensional Veronese varieties. Math. Nachr. 118 (1984), 47 - 67. 85 Ngo Viet Trung, Degree bounds for the defining equations of projective monomial curves. Acta Math. Vietnam. 9 (1984), 157 - 163. 86 Ngo Viet Trung, From associated graded modules to blowing-ups of generalized Cohen-Macaulay modules. J. Math. Kyoto Univ. 24 (1984), 611 - 622. 87 Ngo Viet Trung, Bounds for the minimum number of generators of generalized Cohen-Macaulay ideals, J. Algebra 90 (1984), 1 - 9. 88 Ngo Viet Trung, On tensor products of extensions of a field. Quart. J. Math. 35 (1984), 337 - 339. 89 Ngo Viet Trung, Absolutely superficial sequence. Math. Proc. Cambridge Phil. Soc. 93 (1983), 35 - 47. 90 Ngo Viet Trung, On certain transitivity of the graded ring associated with an ideal. Proc. Amer. Math. Soc. 85 (1982), 489 - 495. 91 Ngo Viet Trung, Standard systems of parameters of generalized Cohen-Macaulay modules, In: Proceedings of the 4th Symposium on Commutative Algebra in Japan, Karuizawa, 1982, 164 - 180. 92 Ngo Viet Trung, On the associated graded ring of a Buchsbaum ring, Math. Nachr. 107 (1982), 209 - 220. 93 Ngo Viet Trung, Classification of the double projections of Veronese varieties. J. Math. Kyoto Univ. 22 (1982), 567 - 581. 94 Ngo Viet Trung, Principal systems of ideals. Acta Math. Vietnam. 6 (1981), 57 - 63. 95 Ngo Viet Trung, A characterization of two dimensional unmixed local domains. Math. Proc. Camb. Phil. Soc. 89 (1981), 237 - 239. 96 Ngo Viet Trung, A class of imperfect prime ideals having the equality of ordinary and symbolic powers. J. Math. Kyoto Univ. 21 (1981), 239 - 250. 97 Ngo Viet Trung, Der graduierte Ring bezuglich des Primideals von Macaulay. Beitr. Algebra Geometrie 11 (1981), 35 - 40. 98 Nguyen Tu Cuong, Ngo Viet Trung, Uber schwache Sequenzen. Period. Math. Hungar. 11 (1981), 77 - 80. 99 Ngo Viet Trung, Some criteria for Buchsbaum modules. Monatsh. Math. 90 (1980), 331 - 337. 100 Ngo Viet Trung, Spezialisierungen allgemeiner Hyperflọchenschnitte und Anwendungen, In: Seminar D. Eisenbud - B. Singh - W. Vogel, Vol. I, Teubner-Verlag, Leipzig, 1980, 4 - 43. 101 Ngo Viet Trung, Über allgemeine Hyperflächenschnitte einer algebraischen Varietät. Monatsh. Math. 89 (1980), 323 - 340. 102 Ngo Viet Trung, On the symbolic powers of determinantal ideals, J. Algebra 58 (1979), 361 - 369. 103 Ngo Viet Trung, Uber die ubertragung der Ringeigenschaften zwischen R und R[u]/(F). Math. Nachr. 92 (1979), 215 - 229. 104 Peter Schenzel, Ngo Viet Trung, Nguyen Tu Cuong, Uber verallgemeinerte Cohen- Macaulay Moduln. Math. Nachr. 85 (1978),  57 - 73.

### Highlights

 06/11/19, Conference:Nhóm đại số, đối đồng điều Galois và một số vấn đề liên quan 09/11/19, Conference:Hội thảo Ứng dụng các phương pháp Thống kê trong một số nghiên cứu khoa học thực nghiệm 13/11/19, Conference:The IMH School Introduction to Algebraic Schemes and Cohomology 22/11/19, Colloquium Lecture:Berkovich spaces over Z and convergent arithmetic power series 02/12/19, Conference:School “INVERSE PROBLEMS” 04/12/19, Conference:Hội nghị Đại số-Lý thuyết số-Hình học và Tô pô 2019 13/12/19, Colloquium Lecture:How to escape the curse of dimensionality in combinatorics 20/12/19, Colloquium Lecture:Algebraic surfaces with minimal Betti numbers 17/02/20, Conference:SEAMS school “Arithmetic, Geometry and Model Theory” 04/03/20, Conference:MIS-IMH research school on Mathematics of Data