Conference on Combinatorics, Commutative Algebra, Algebraic Geometry, and Their Applications
Hanoi, 3–5/11/2025
Welcome to the Conference on Combinatorics, Commutative Algebra, Algebraic Geometry, and Their Applications.
This conference aims to provide a comprehensive overview of recent advances across these vibrant areas and to highlight their diverse applications. It is also a forum for exchange and collaboration, bringing together leading researchers and young scholars from Vietnam and around the world.
Through invited talks, contributed presentations and discussions, the conference seeks to foster new ideas, strengthen international cooperation and highlight the growing role of these fundamental areas of mathematics in science, engineering and technology.
Time and Venue
Time: 3–5 November 2025
Venue: Room 212‑E3, University of Engineering and Technology, Vietnam National University, Hanoi
Registration
There is no participation fee.
If you plan to attend, please fill out the Online registration form.
Contact email: hltruong@vnu.edu.vn
Deadline for financial support: 3 October 2025
Deadline for registration: 30 October 2025
Organizers
University of Engineering and Technology, Vietnam National University, Hanoi.
- Prof. Dr. Chu Duc Trinh, University of Engineering and Technology, Vietnam National University, Hanoi
- Prof. Dr. Hoang Le Truong, University of Engineering and Technology, Vietnam National University, Hanoi
- Nguyen Khanh Ly, University of Engineering and Technology, Vietnam National University, Hanoi
- Dr. Tran Quoc Long, University of Engineering and Technology, Vietnam National University, Hanoi
Registration
There is no participation fee.
If you plan to attend, please fill out the Online registration form. Feel free to contact us at hltruong@vnu.edu.vn for any questions.
Deadline for financial support: 3 October 2025
Deadline for registration: 30 October 2025
Invited Speakers
- Ivan Arzhantsev, HSE University
- Nguyen Quang Dieu, Hanoi National University of Education
- Le Van Dinh, FPT University, Vietnam
- Le Xuan Dung, Hong Duc University
- Sergey Gaifullin, HSE University
- Le Mau Hai, Hanoi National University of Education
- Nguyen Thi Anh Hang, Thai Nguyen University of Education
- Pham Hoang Hiep, University of Engineering and Technology, VNU, Hanoi
- Tran Quang Hoa, Hue University
- Le Tuan Hoa, Institute of Mathematics, VAST
- Do Trong Hoang, Hanoi University of Science and Technology
- Do Van Kien, Hanoi Pedagogical University 2
- Toshinori Kobayashi, Meiji University
- Le Thi Thanh Nhan, Institute of Mathematics, VAST
- Kazuho Ozeki, Nihon University
- Sudeshna Roy, Indian Institute of Technology Gandhinagar
- Tran Nam Trung, Institute of Mathematics, VAST
- Ngo Viet Trung, Institute of Mathematics, VAST
- Vu Duc Viet, University of Cologne
Abstracts
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Title: On flexibility of affine factorial varieties
Abstract: We give a criterion of factoriality of a suspension. This allows us to construct many examples of flexible affine factorial varieties. In particular, we find a homogeneous affine factorial 3‑fold that is not a homogeneous space of an algebraic group. The talk is based on a joint work with Kirill Shakhmatov. The work was prepared within the framework of the project “International Academic Cooperation” of HSE University.
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Title: Invariant chains in algebra, combinatorics, and discrete geometry
Abstract: Chains of objects that remain invariant under the action of certain groups or monoids arise naturally across algebra, combinatorics, and discrete geometry. In this talk, I will discuss some results on their finiteness properties and asymptotic behavior.
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Title: Monge-Ampère operator on complex varieties in bounded domains in ℂn
Abstract: Let V be a complex variety in a bounded hyperconvex D in ℂn. We concern with the domain of definition for the Monge-Ampère operator of plurisubharmonic functions on V. We are also concerned with the existence and uniqueness of the Monge-Ampère equation on certain class of plurisubharmonic functions. A new ingredient of our work is to single out certain class of complex varieties where the singular set is not too wild.
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Title: Betti numbers of the edge ideals of cochordal zero divisor graphs
(This is a joint work with V. Q. Thanh.)
Abstract: We associate a sequence of positive integers, termed the type sequence, with a cochordal graph. Using this type sequence, we compute all graded Betti numbers of its edge ideal. We then classify all positive integers n such that the zero divisor graph of ℤ/nℤ is cochordal and determine all the graded Betti numbers of its edge ideal.
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Title: Generically flexible affine varieties with invariant divisors
Abstract: A flexible affine algebraic variety is a variety such that each regular point is flexible, that is, its tangent space is generated by tangent vectors of Ga-orbits. A variety is called generically flexible if it contains an open set of flexible points. This set is one orbit of the group of special automorphisms SAut(X).
There are some examples of generically flexible varieties that are not flexible. But all known examples are surfaces. Moreover, the complement of the open set of flexible points has codimension two.
We construct examples of normal affine varieties X of dimension greater than or equal to 4 such that SAut(X) acts on X with an open orbit O and the complement to O in X has codimension one. Orbits for actions of SAut(X) and the automorphism group Aut(X) on X are described. It is shown that there are four Aut(X)-orbits on X: two of them consist of regular points and two consist of singular points.
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Title: Weak solutions of Hessian type equations on compact Hermitian manifolds with boundary"
(This is a joint work with Nguyen Van Phu and Trinh Tung.)
Abstract: The aim of this note is to establish the existence of weak solutions of Hessian type equations in the class of (α, m)-ω-subharmonic functions on a compact Hermitian manifold (̅X, ω) with boundary ∂X.
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Title: Powers of Ideals and Integer Programming
Abstract: In this talk I will review some new results on powers of monomial ideals, which were obtained by using Integer Programming techniques. Its aim is to show a deep connection between Commutative Algebra and Combinatorics.
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Title: Regularity of normal Rees algebras of edge ideals of graphs
(This is joint work with Cao Huy Linh and Thanh Vu.)
Abstract: This talk presents a classification of graphs whose edge ideals admit normal Rees algebras with Castelnuovo–Mumford regularity equal to their matching numbers. The classification is obtained by applying the Gallai–Edmonds Structure Theorem to characterize Tutte–Berge graphs, together with the description of the edge polytope of a graph due to Ohsugi and Hibi. These results provide a complete description of the relationship between graph structure and the homological properties of their associated Rees algebras.
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Title: Unmixed and sequentially Cohen-Macaulay skew tableau ideals
(This is joint work with Thanh Vu (IM-VAST).)
Abstract: We associate to each filling of a skew Ferrers diagram with positive integers a skew tableau ideal. In this talk, we present a classification of all unmixed and sequentially Cohen–Macaulay skew tableau ideals. As a consequence, we also obtain classifications of all Cohen–Macaulay, Buchsbaum, and generalized Cohen–Macaulay skew tableau ideals. We conclude with a discussion of several open problems.
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Title: Singularity Invariants of Complex Spaces
Abstract: In this talk, I will introduce several notions of singularity invariants for complex spaces, which have the potential to aid in their classification. We also propose some conjectures concerning the classification of complex spaces.
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Title: On g-stretched local rings and a Herzog–Iyengar’s question
(This is joint work with Hop D. Nguyen.)
Abstract: The linearity defect is a measure of the non-linearity of minimal free resolutions of modules over Noetherian local rings. In the graded k-algebra setting, it has been known that if ldR(k) < ∞ then ldR(k) = 0, i.e., R is Koszul. Herzog and Iyengar asked whether a Noetherian local ring (R, m) must be Koszul if its residue field R/m has finite linearity defect.
In this talk, we introduce the notion of g-stretched local rings as a generalization of the stretched Artinian local rings studied by Sally. We investigate the Koszul property and the finiteness of linearity defect over g-stretched rings. As a consequence, we provide a positive answer to a long-standing question of Herzog and Iyengar in the case where R is a Cohen–Macaulay local ring of almost minimal multiplicity with residue field of characteristic zero.
In addition to partial progress on Herzog–Iyengar’s problem, our work also yields a numerical characterization of all g-stretched Koszul rings, strengthening previous work of Avramov, Iyengar, and Şega.
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Title: On the Cohen-Macaulayness of the associated graded rings of certain almost complete intersections
Abstract: The purpose of this talk is to introduce a characterization of the Cohen-Macaulay property of the associated graded ring of 𝔪-primary ideals that form an almost complete intersection under certain conditions in a Cohen-Macaulay local ring (A, 𝔪). Furthermore, as an application of this characterization, we will also present results on the classification of integrally closed ideals with small first Hilbert coefficients.
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Title: A numerical characterization of the S2-ification of a Rees algebra of graded ideals through β-density function
(This is joint work with S. Das and H. L. Truong.)
Abstract:The multiplicity-based integral dependence criterion, originating in the work of D. Rees (1961), remains central to commutative algebra and singularity theory. Although Rees' theorem applies only to ideals primary to the maximal ideal, later research has aimed to generalize it to arbitrary ideals. In collaboration with S. Das and V. Trivedi, we recently obtained localization-free criteria for integral dependence using classical invariants. These results emerged as applications of density functions we constructed, inspired by Trivedi’s Hilbert-Kunz density function. For normal domains, they provide numerical characterizations of the graded pieces of the integral closure of the Rees algebra.
An S2-ification criterion for Rees algebras was first given by C. Ciupercă for ideals primary to the maximal ideal, using the first two Hilbert coefficients. He later introduced a j-multiplicity-type invariant providing a localization-based criterion applicable to arbitrary ideals.
In this talk, we present a new characterization of the S2-ification of the Rees algebra of a homogeneous ideal in a standard graded normal domain R over a field. This is achieved via the β-density function associated with the adic filtration, offering a localization-free and computationally accessible approach.
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Title: Extensions of Regular Sequence Concept and Structure of Finitely Generated Modules
Abstract: In this talk, we present our recent results in [LN], [LLN].
Let (R, 𝔪) be a Noetherian local ring, M a finitely generated R-module, and I an ideal of R. The concept of a regular sequence (first introduced by Serre under the name of R-sequence [Serr]) has been applied in many areas of mathematics. Note that M is Cohen–Macaulay if and only if every system of parameters (s.o.p.) of M is an M-sequence.
Cuong–Schenzel–Trung [CST] introduced the class of generalized Cohen–Macaulay modules and defined the notion of filtered regular sequence (or f-sequence) as a natural extension of regular sequence, showing that if R is a quotient of a Cohen–Macaulay local ring, then M is generalized Cohen–Macaulay if and only if each s.o.p. of M is an f-sequence. The class of generalized Cohen–Macaulay modules and the notion of f-sequence have become fundamental in Commutative Algebra.
The generalized regular sequence (g-sequence) was introduced in [Nh] as a further extension used to study the finiteness of associated primes of local cohomology modules. It was shown in [NM] that if R is a quotient of a Cohen–Macaulay local ring, thendimR Hi_𝔪(M) ≤ 1for all i < dimR(M) if and only if each s.o.p. of M is a g-sequence.
If M/IM ≠ 0 (resp. dimR(M/IM) > 0, dimR(M/IM) > 1) then each M-sequence (resp. f-sequence, g-sequence) in I can be extended to a maximal one, and all maximal sequences of each type have the same length. This length is denoted respectively by depth(I, M), f-depth(I, M), and g-depth(I, M), where:depth(I, M) = inf{i ∈ ℕ | Hⁱ_I(M) ≠ 0} f-depth(I, M) = inf{i ∈ ℕ | Hⁱ_I(M) is not Artinian} g-depth(I, M) = inf{i ∈ ℕ | Supp_R Hⁱ_I(M) is infinite}Regular, f-, and g-sequences are very useful for studying unmixed finitely generated modules, but they are less effective for modules that are not unmixed. For example, M is Cohen–Macaulay if and only if M/xM is Cohen–Macaulay for any regular element x of M. However, while M being sequentially Cohen–Macaulay implies M/xM is so, the converse does not hold generally.
In this talk, we introduce some extensions of the regular sequence concept suitable for studying modules not necessarily unmixed. We clarify the structure of certain classes of modules that include all sequentially Cohen–Macaulay modules.References:
- [CST] N. T. Cuong, P. Schenzel, N. V. Trung, Verallgemeinerte Cohen–Macaulay Moduln, Math. Nachr. 85 (1978), 57–73.
- [LT] R. Lü, Z. Tang, The f-depth of an ideal on a module, Proc. Amer. Math. Soc. 130 (2001), 1905–1912.
- [Nh] L. T. Nhan, On generalized regular sequences and the finiteness for associated primes of local cohomology modules, Comm. Algebra 33 (2005), 793–806.
- [NM] L. T. Nhan, M. Morales, Generalized f-modules and the associated primes of local cohomology modules, Comm. Algebra 34 (2006), 863–878.
- [LN] N. X. Linh, L. T. Nhan, On sequentially Cohen–Macaulay modules and sequentially generalized Cohen–Macaulay modules, J. Algebra 678 (2025), 635–653.
- [LLN] N. X. Linh, N. T. H. Loan, L. T. Nhan, An extension of the class of sequentially Cohen–Macaulay modules, Preprint.
- [Serr] J. P. Serre, Sur la dimension cohomologique des anneaux et des modules noetheriens, Proc. Intern. Symp. on Alg. Number Theory, Tokyo–Nikko (1955), 176–189.
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Title: Cohen-Macaulayness of Powers of Edge Ideals of Weighted Oriented Graphs
(This is a joint work with Truong Thi Hien, Jiaxin Li and Guangjun Zhu)
Abstract: An oriented graph D=(V(D), E(D)) consists of a simple underlying graph G in which each edge is oriented, i.e., it is a directed graph with no multiple edges or loops. The elements of E(D) are denoted by ordered pairs to reflect the orientation. A vertex-weighted (or simply weighted) oriented graph D is a graph equipped with a weight function ω : V(D) → ℤ>0. The pair (D,ω) is called a weighted oriented graph.
Let R=K[x1, …, xn] be a polynomial ring with n variables over a field K. Assume that V(D)={1,2,…,n}. The edge ideal of D is defined as I(D) = (xixjω(j) | (i,j)∈E(D)). We prove that its symbolic powers I(D)(t) are Cohen-Macaulay for all t ≥1 if and only if the underlying graph G is a disjoint union of complete graphs. We also characterize the Cohen-Macaulayness of the ordinary powers I(D)t for all t≥2 and provide a criterion for when I(D)t=I(D)(t).
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Title: Groebner bases of Rees algebras
Abstract: Let R be a standard graded algebra over a field and I a graded ideal generated in a single degree. The Rees algebra R[It] is a standard bigraded algebra. If we know the bigeneric initial ideal of the defining ideal of R[It], we can compute the regularity function reg In. In this talk I will present a class of graded ideals I for which Groebner bases of the defining ideal of R[It] can be computed. This result can be used to construct ideals I with given regularity functions.
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Title: Classifying subcategories closed under kernels and extensions
(This is joint work with Shunya Saito.)
Abstract: Let R be a commutative noetherian ring.
A subcategory X of the category of finitely generated R-modules is called KE-closed if it is closed under taking kernels and extensions. We aim to classify KE-closed subcategories of mod R.
We associate a function on Spec R with each KE-closed subcategory of mod R, and show that this function completely determines the original subcategory.
In the case where R is (S2)-excellent, we obtain a bijection between the set of KE-closed subcategories and the set of functions satisfying certain properties.
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Title: Bergman kernel functions associated to measures supported on totally real submanifolds
Abstract: I will talk about my recent joint work with George Marinescu on Christofell-Darboux kernel on ℂn, or more generally, Bergman kernel on compact Kähler manifolds. Applications to the equidistribution of zeros of random polynomials will also be discussed.
Programs
| Time | Monday November 3, 2025 |
Tuesday November 4, 2025 |
Wednesday November 5, 2025 |
|---|---|---|---|
| 8:30-8:55 | Registration | ||
| 8:55-9:00 | Opening Ceremony | ||
| 9:00-9:45 | Ngo Viet Trung | Ivan Arzhantsev | Pham Hoang Hiep |
| 9:55-10:40 | Le Van Dinh | Sergei Gaifullin | Le Mau Hai |
| 10:50-11:35 | Le Xuan Dung | Nguyen Quang Dieu | Vu Duc Viet |
| 12:00-13:30 | Lunch | ||
| 13:30-14:15 | Do Trong Hoang | Do Van Kien | Le Tuan Hoa |
| 14:25-15:10 | Toshinori Kobayashi | Tran Quang Hoa | Tran Nam Trung |
| 15:20-16:05 | Kazuho Ozeki | Le Thi Thanh Nhan | Sudeshna Roy |
| 17:30-20:30 | Banquet | ||
Participants
- Cao Huy Thinh, Hanoi University of Science and Technology
- Cao Phuong, Hanoi University of Science and Technology
- Do Hoang Viet, Institute of Mathematics, VAST
- Do Thai Duong, University of Engineering and Technology, VNU, Hanoi
- Do Trong Hoang, Hanoi University of Science and Technology
- Do Van Kien, Hanoi Pedagogical University 2
- Gede Adhitya Wisnu Wardhana, University of Mataram
- Gusti Yogananda Karang, University of Mataram
- Ha Minh Lam, Institute of Mathematics, VAST
- Hoang Le Truong, University of Engineering and Technology, VNU, Hanoi
- Hoang Ngoc Yen, Thai Nguyen University of Education
- Hoang Phi Dung, Posts and Telecommunications Institute of Technology, Vietnam
- Ivan Arzhantsev, HSE University
- Kazuho Ozeki, Nihon University
- Le Lam, Vietnam National University
- Le Mau Hai, Hanoi National University of Education
- Le Thi Thanh Nhan, Institute of Mathematics, VAST
- Le Tien Nghaa, Institute of Artificial Intelligence, University of Engineering and Technology, Vietnam National University
- Le Tuan Hoa, Institute of Mathematics, VAST
- Le Van Dinh, FPT University, Vietnam
- Le Xuan Dung, Hong Duc University
- Nguyen Bich Van, University of Engineering and Technology, VNU, Hanoi
- Nguyen Cong Minh, Hanoi University of Science and Technology
- Nguyen Dang Hop, Institute of Mathematics, VAST
- Nguyen Duy Duc, Tsinghua University
- Nguyen Nhat Minh, University of Engineering and Technology - VNU
- Nguyễn Quang Diệu, Hanoi National University of Education
- Nguyen Tan Phat, VNU University of Engineering and Technology
- Nguyen Thi Anh Hang, Thai Nguyen University of Education
- Nguyen Thi Thanh Tam, Hung Vuong University
- Nguyen Thi Tra, Hanoi Pedagogical University 2
- Nguyen Thu Hang, Thai Nguyen University of Sciences
- Nguyen Van Hoang, University of Transport and Communications
- Nguyen Van Ninh, Thai Nguyen University of Education
- Nguyen Viet Phuong,University of Engineering and Technology - VNU
- Nguyen Xuan Linh, Hanoi University of Civil Engineering
- Nguyen Xuan Linh, Hanoi University of Civil Engineering
- Pham Hoang Hiep, University of Engineering and Technology, VNU, Hanoi
- Pham Hong Nam, Thai Nguyen University of Sciences
- Pham Hung Quy, FPT University, Vietnam
- Pham My Hanh, An Giang University
- Phan Thi Thuy, Hanoi National University of Education
- Sergey Gaifullin, HSE University
- Sudeshna Roy, Indian Institute of Technology Gandhinagar
- Toshinori Kobayashi, Meiji University
- Tran Dai Tan, Institute of Mathematics, VAST
- Tran Do Minh Chau, Thai Nguyen University of Education
- Tran Minh, University of Engineering and Technology - VNU
- Tran Nam Trung, Institute of Mathematics, VAST
- Tran Nguyen An, Thai Nguyen University of Education
- Tran Quang Hoa, Hue University
- Truong Thi Hien, Hong Duc University
- Vu Duc Viet, University of Cologne
