Huế  GAA seminar

Next seminar

Time: 14h30   26/10/2023 Place: Seminar Room

Speaker: Dinh Tuan Huynh, Hue University of Education, Hue University.

Title: On the Gauss maps of complete minimal surfaces in R^m.

Abstract: We prove that if the Gauss map of a  minimal surface immersed in R^m 

omits a generic hypersurface of large enough degree, then it must be constant.

Archive

29 June 2023, 15h-17h, Speaker: Prof. Dao Hai Long, Kansas University, USA

Title: Fractals, Hanoi Tower and Syzygies

Abstract: Syzygies are objects invented and utilized by David Hilbert in 1890 to study relations among polynomial equations, and have played a big role in the development of modern algebraic geometry. The quest to understand patterns of syzygies is both challenging and interesting, and sometimes reveals unexpected connections to other branches of mathematics. In this talk, I will describe recent joint work with David Eisenbud on monomials with linear syzygies.  It turns out that certain fractal structures that appear in many contexts, from game theory to number theory, play a significant role in building optimal examples. 

01 June 2023, 14h30-16h, Speaker: Tôn Thất Quốc Tấn (PhD), ĐH FPT

Title: Fiber cone under perturbations of an ideal

Abstract.

Let (R,m) be a Noetherian local ring and J be an m-primary ideal of R. Let K be an ideal such that K contains J and f_1,...,f_r, a J-filter regular sequence in R, and I = (f_1,...,f_r). In this talk, we will consider the perturbation problems of I under J-adic perturbations. More precisely, we prove that the fiber cone of R/I with respect to K is preserved under J-adic perturbations of I. Consequently, the comparisons between the Castelnuovo-Mumford of the associated graded ring and fiber cone under perturbation are given. Moreover, in the case that R is a generalized Cohen-Macaulay ring, we give a linear bound for the perturbation index of the special fiber cone of R/I.

25 May 2023, 14h30-16h, Speaker: Dr Phạm Đình Đồng, ĐHSP Huế

Title: Three-stage minimum risk point estimation with termination defined via Gini’s mean difference

Abstract: In this talk, we revisit the classic inference problem of minimum risk point estimation for an unknown normal mean when the variance also remains unknown. We propose an alternative three-stage sampling procedure with termination defined via Gini’s mean difference rather than the traditional sample standard deviation. A number of asymptotic properties are investigated both theoretically and empirically. An extensive set of simulations is conducted to demonstrate the remarkable performance of the new procedure. For practical purposes, we also include illustrations using real data sets on the number of days marigold seeds need to flower. It is a joint work with J. Hu.

Time: 18 May 2023, 14h30-16h Speaker: Dr Huỳnh Đình Tuân, ĐHSP Huế

Title: Degeneracy of holomorphic mappings into Fermat type hypersurfaces.

Abstract:  We prove that if f:C^p--->CPn is a holomorphic mapping of maximal rank whose image lies in the Fermat hypersurface of degree d>(n+1) max{n-p,1}, then the image of f is contained in a linear subspace of dimension at most [(n-1)/2]. Analog in the logarithmic case is also given. Our result strengthens a classical result of Green.

Time: 11 May 2023: 14h30-16h, Speaker: Dr. Trần Quang Hóa, ĐHSP Huế.

Title: Powers of sums and their associated primes

Abstract:  Let $A, B$ be polynomial rings over a field $k$, and $I\subseteq A, J\subseteq B$ proper homogeneous ideals. We analyze the associated primes of powers of $I+J\subseteq A\otimes_k B$ given the data on the summands. The associated primes of large enough powers of $I+J$ are determined.

We then answer positively a question due to I. Swanson and R. Walker  about the persistence property of $I+J$ in many new cases. This is a joint work with Hop D. Nguyen.

Time: 04 May 2023, 14h30-16h Speaker: Dr. Nguyễn Thành Thái, ĐHSP Huế

Title: Convex bodies associated to graded families of ideals

Abstract: Followed the seminal work of Okounkov studying the log-concavity of the degrees of algebraic varieties via volumes of some associated convex sets, the works of Kaveh-Khovanskii and Lazarsfeld-Mustata develop systematically the theory of Newton-Okounkov bodies. It has become a very active research area and provides various beautiful connections between (asymptotic) algebro-geometric information and combinatorial data from convex sets. In this talk, we shall present the notion of Newton-Okounkov bodies of graded families of ideals. We shall discuss some progress on the study of asymptotic properties and invariants of graded families of ideals via Newton-Okounkov polyhedra. Our results are in joint projects with Hop Dang Nguyen and Tài Huy Hà.

Time: 27 April 2023, 14h30-16h Speaker: Dr. Nguyễn Thành Thái, ĐHSP Huế

Title: Duality for Asymptotic Invariants

Abstract:  In this talk we shall present a duality for sequences of numbers which interchanges superadditive and subadditive sequences, and inverts their asymptotic growths. We shall discuss at least two algebro-geometric contexts where this duality shows up: how it interchanges the sequence of initial degrees of symbolic powers of an ideal of points with the sequence of regularities of a family of ideals generated by powers of linear forms; and how it underpins the reciprocity between the Seshadri constant and the asymptotic regularity of a finite set of points. This is joint work with Michael DiPasquale and Alexandra Seceleanu.

Time: 13 April 2023, 14h30-16h, Speaker: Dr. Huỳnh Đình Tuân, ĐHSP Huế

Title: Universal entire curves in projective spaces with slow growth

Abstract: We construct universal entire holomorphic curves h: C---CPn whose Nevanlinna characteristic functions grow slower than any preassigned transcendental growth rate. This answers a question asked by Dinh-Sibony in an extended version.

Time: 16 Mar 2023, 14h30-16h Speaker: Dr. Nguyễn Thị Mỹ Duyên, ĐHSP Huế

Title: Halfspace type theorem for self shrinker (Part2)

Abstract: First, we introduce some concepts related to the topic like curvature flow,  mean curvature flow, self shrinkers..... Then we present Hoffman-Meeks' halfspace theorem as well as Cavalcante-Espinar's halfspace type theorems for self shrinkers of codimension >1.

Time: 09 Mar 2023, 14h30-16h Speaker: Assoc. Dr. Đoàn Thế Hiếu, ĐHSP Huế

Title: Halfspace type theorem for self shrinker (Part1)

Abstract: First, we introduce some concepts related to the topic like curvature flow,  mean curvature flow, self shrinkers..... Then we present Hoffman-Meeks' halfspace theorem as well as Cavalcante-Espinar's halfspace type theorems for self shrinkers of codimension 1.

Time: 02 Mar 2023, 14h30-16h Speaker: Dr. Văn Đức Trung, ĐHSP Huế

Title: Regularity of the Rees algebra of edge ideals

Abstract: In this talk we present a new result of Nandi and Nanduri on the upper bounds for regularity of the Rees algebra of edge ideals.

Time: 23 Feb 2023, 14h30-16h  Speaker: Assoc. Dr. Cao Huy Linh, ĐHSP Huế

Title:  On the Rees algebra of edge ideals (continue)

Abstract:  In this talk, we present some basic notions of simple graphs, edge ideals and Rees algebra. 

We will also discuss recent results on the regularity of Rees algebra of edge ideals in terms of some combinatorial invariants.

Time: 16 Feb 2023, 14h30-16h  Speaker: Assoc. Dr. Cao Huy Linh, ĐHSP Huế

Title: Title: On the Rees algebra of edge ideals

Abstract:  In this talk, we present some basic notions of simple graphs, edge ideals and Rees algebra. 

We will also discuss recent results on the regularity of Rees algebra of edge ideals in terms of some combinatorial invariants.

02 Feb 2023, 15h-16h30 Speaker: Dr. Trần Quân Kỳ, ĐHSP Huế

Title: Exponential stability of neutral stochastic functional differential equations

Abstract: In this work, we focus on the exponential stability of neutral stochastic functional differential equations. First, we review a new treatment for studying the exponential stability of neutral stochastic functional differential equations. Then a new approach is introduced to study the stability analysis of numerical approximation methods.  This work provides new criteria for which the Euler-Maruyama approximation method and the backward Euler-Maruyama approximation method can reproduce exponential stability in mean square and almost sure exponential stability for sufficiently small step sizes. It is joint work with P.H.A. Ngoc.

Time: 29 December 2022, 15h-16h30  Speaker: Dr. Trần Thiện Tín, ĐHSP Huế

Title: The line packing problem

Abstract: Click here to see.

Time: 15 December 2022, 15h-16h30 Speaker: Dr. Lê Văn Phú Cường, University of Verona, Italy

Title: Minimizing movements for hyperbolic obstacle-type problems and applications

Abstract: In this talk, we investigate a class of hyperbolic obstacle type problems, in particular by using De Giorgi’s minimizing movements scheme we provide the existence results for the problem both obstacle-free case (there is no obstalce) and obstacle case (in presence of obstacle g), which include also fractional operators as well as higher dimensional cases. In addition, we discuss some applications to singular limits of nonlinear wave equations with a balance double well potential, which is motivated by the fact that in this case certain solutions of nonlinear wave equations giving rise to interfaces (or defects) evolving by curvature such as minimal surfaces in Minkowski space. Finally, we apply our results to study nonlinear waves in adhesive phenomena, our results embrace higher dimension and fractional operators extending the previous work, and we shall also discuss some open problems. This talk is based on joint works with Mauro Bonafini (Verona), Matteo Novaga (Pisa), and Giandomenico Orlandi (Verona)

Time: 08 December 2022, 15h-16h30 Speaker: Tôn Thất Quốc Tấn (phD, FPT University)

Title: Hilbert coefficients of ideals generated by d-sequences under perturbation of an ideal.

Abstract: Let (R, m) be a noetherian local ring, J an m-primary ideal of R and

I = (f1, ..., fr) an ideal generated by filter regular sequence f1, ..., fr of R. In this

talk, we will discuss the preserve of Hilbert coefficients of R/I with respect

to J under J-adic perturbation of I provided that J is parameters ideal generated by

d-sequence of R/(f1, ..., fi) for i = 1, ..., r.

Time: 02 December 2022 (Friday) : 15h --16h30, Speaker: Prof. Marc Chardin, Sorbonne University

Title : Multigraded Tor and local cohomology.

Abstract : In standard multigraded rings (which correspond to product of projective spaces) one can extend the notion of Castelnuovo-Mumford regularity. It is also possible to extend the notion of a*-invariant; for the extension of the notion of a*-invariant, we proved with Rafael Holanda that the correspondence with Tor vanishing and degrees in a minimal free resolution extends from the single graded case to the multigraded case. We also give new insight on vanishing degrees for local cohomology with respect to product of ideals; this should in turn help to determine multigraded regularity and provide a better understanding of its signification.

01 December 2022: 15h-16h30 Speaker: Assoc. Dr. Cao Huy Linh,  ĐHSP Huế

Title: On the Hilbert perturbation index and Castelnuovo-Mumford regularity.

Abstract: Let I be an ideal of a local ring R generated by a filter regular sequence and J an m-primary ideal.  In this talk, we discuss about the Hilbert function of R/I with respect to J under perturbation of I. From this we give a relationship between Hilbert perturbation index and Castelnuovo-Mumford regularity.

10 November 2022: 15h-16h30, Speaker: Dr. Huỳnh Đình Tuân,  ĐHSP Huế

Title: On Ahlfors currents

Abstract: We answer a basic question in Nevanlinna theory that Ahlfors currents associated to the same entire curve may be nonunique. Indeed, we will construct one exotic entire curve f : C → X which produces infinitely many cohomologically different Ahlfors currents. Moreover, concerning Siu’s decomposition, for an arbitrary k ∈ Z+ ∪ {∞}, some of the obtained Ahlfors currents have singular parts supported on k irreducible

curves. In addition, they can have nonzero diffuse parts as well.

This talk is based on the recent joint work with Song-Yan Xie.

03 November 2022: 15h-16h30 Speaker: Nguyễn Duy Phước, sv ĐHSP Huế

Title: Định lý đếm Polya

Abstract: Trong báo cáo này, chúng tôi sẽ trình bày định lý đếm Polya, còn được gọi là định lý về đa thức chỉ số tuần hoàn và được chứng minh nhờ các kỹ thuật của lý thuyết nhóm. Từ đó tìm các ứng dụng vào một số bài toán sơ cấp

27 October 2022: 15h-16h30 Speaker: Dr Văn Đức Trung, ĐHSP Huế

Title: An algorithm for computing Grobner basis

Abstract: We give a brief introduction to Grobner basis and an algorithm for computing Grobner basis by using linear algebra

20 October 2022: 15h-16h30, Dr. Huỳnh Đình Tuân, ĐHSP Huế

Title: Entire holomorphic curves into the projective plane

intersecting two lines and one conic

Abstract: We establish a defect relation in Nevanlinna theory

for non degenerate entire holomorphic curves into the complex projective

plane and the configuration of two lines and one conic. Our method

can also work for the case of n+1 hypersurfaces in CPn.

13 October 2022: 15h-16h30 Speaker: Dr. Trần Quang Hóa, ĐHSP Huế

Title: A new proof of Stanley’s theorem on the strong Lefschetz property.

Abstract: See here for more details.

06 October 2022: 15h-16h30 Speaker:  Dr. Huỳnh Đình Tuân, ĐHSP Huế

Title: Around Ax-Lindemann-Schanuel type results in some geometric settings.

Abstract: In the first part of the talk, we will summarize some basic results in transcendental number theory. 

Then we will discuss some geometrical analogues of the classical Lindemann-Weierstrass Theorem and Schanuel conjecture. Finally we will propose an approach for these problems from the point of view of value distribution theory.

29 September 2022: 15h30-17h Speaker: Prof. Dr. Lê Văn Thuyết, ĐHSP Huế 

Title: Finite Frobenius rings and their applications

(Part I)

Abstract: In this talk, we present an overview of the results on Frobenius and quasi-Frobenius finite rings and their applications. First, we present the concepts related to Frobenius and quasi-Frobenius rings on arbitrary rings. From this, the concept of Frobenius finite rings and quasi-Frobenius will be deduced by removing the chain conditions on the ring. Next, we study an overview of the class of local Frobenius commutative finite rings. In this approach, we study a special class of rings called chain rings. From this, we classify the chain rings and the local Frobenius non-chain rings of all rings of order 16. Finally, we present the results of Gray mapping on local Frobenius rings of order  16.

22 September: 15h30-17h   Speaker: Dr. Trần Quang Hóa, ĐHSP Huế

Title: Asymptotic regularity of invariant chains of edge ideals

Abstract: In this talk, I will discus recent results on asymptotic regularity of invariant chains of edge ideals. More precisely, we study chains of nonzero edge ideals that are invariant under the action of the monoid Inc of increasing functions on the positive integers. Our main result shows that the sequence of Castelnuovo-Mumford regularity of ideals in such chain is eventually constant with limit either 2 or 3.

Moreover, we determine explicitly when the constancy behaviour sets in. This provides further evidence to a conjecture on the asymptotic linearity of the regularity of Inc-invariant chains of homogeneous ideals by Le, Nagel, Nguyen, and Romer(IMRN, 2021). This is a joint work with Do Trong Hoang and Hop D. Nguyen

15 September: 15h30-17h:  Speaker: Prof.  Martin Kreuzer (Universität Passau, Fakultät für Informatik und Mathematik,  Lehrstuhl für Symbolic Computation)

Title: Algebraic Modelling

08 September 2022:  Speaker: Dr. Lê Ngọc Long (Hue University of education, Hue University)

Title: Optimal Re-embeddings of Affine Algebras

Abstract: See here for more details