### Algebra and related fields

 My work includes research and teaching in mathematics, both of which are a source of inspiration and interesting challenges. Currently, I am a researcher at the Hanoi Institute of Mathematics.Previously, I was a postdoc at the University of Genoa, and Otto-von-Guericke University Magdeburg. Curriculum Vitae of Nguyen. Research Interests   Commutative algebra, homological algebra and algebraic combinatorics. Whenever possible, I like to learn new topics, techniques, problems, or simply something funny. To paraphrase I.M. Gel'fand, good mathematics is tightly connected with beauty, simplicity, exactness, and not the least crazy ideas. This is of course not the only way to discuss good mathematics. It might also not be an original idea of Gel'fand; the mention of "beauty" is perhaps influenced by Hardy's classic "A mathematician's apology". The discussion of "What is good practice of mathematics?" is for me a case where finding an answer is more important than knowing the answer. Technically, I am interested in minimal free resolutions and sygyzies, combinatorial commutative algebra and effective methods. I am also interested in homological methods and invariants, in particular homological dimensions, derived category methods. The topics that I am paying attention to include ordinary and symbolic powers of ideals, free resolutions over Koszul algebras. Selected publications (more work by Hop D. Nguyen)* Linearity defect of edge ideals and Fröberg's theorem. [pdf]   (with Thanh Vu), J. Algebr. Combin. 44 (2016), 165–199.* Regularity bounds for complexes and their homology. [pdf]   Math. Proc. Cambridge Phil. Soc. 159 (2015), 355–377.* Absolutely Koszul algebras and the Backelin-Roos property. [pdf]   (with Aldo Conca, Srikanth B. Iyengar and Tim Römer),   Acta. Math. Vietnam. 40 (2015), 353–374. * Koszul determinantal rings and 2 x e matrices of linear forms. [pdf]    (with Phong Dinh Thieu and Thanh Vu), Michigan Math. J. 64 (2015), 349–381.* Regularity over homomorphisms and a Frobenius characterization of Koszul algebras. [pdf]    (with Thanh Vu), J. Algebra 429 (2015), 103–132."Từ phác thảo đến tác phẩm, con đường ấy phải quỳ mà đi." (Vladimír Holan)"Having seen the silk paintings of a fellow painter today, I think he drew it too meticulously, and his paintings are stiff and lacking of intimacy that way. I had told him one should study the subject closely, as closely as possible, and prepare the drawing materials carefully, the more carefully the better, but when it comes to drawing, one should be as innocent as a playing child. But my words were futile for he draws in order to sell his art, and his drawing method aptly assists his business." (Rough translation from the art diary "Viết dưới ánh đèn dầu" of Bùi Xuân Phái)                                                                                    Updated on 21 May 2019
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