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Thường trực Hội đồng Giáo sư cơ sở

Hội thảo và tọa đàm với chủ đề: “Khoa học cơ bản cho phát triển bền vững” nhân ngày Khoa học và Công nghệ Việt Nam

Hội đồng Giáo sư cơ sở Viện Toán học năm 2025

Hội thảo sắp diễn ra

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21/07/25, Hội nghị, hội thảo:

International conference on commutative algebra to the memory of Jürgen Herzog

Xuất bản mới

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Đoàn Nhật Minh, Sang-Hyun Kim, Mong Lung Lang, Ser Peow Tan, Optimal Special Polygons for the Congruence Subgroups

Γ_{0} (p)

and

Γ_{0} (p q)

, The Journal of Geometric Analysis, Volume 35, article number 216, (2025) (SCI-E, Scopus) .

Hà Đức Thái, Hoàng Thế Tuấn, The oscillatory solutions of multi-order fractional differential equations, Fractional Calculus and Applied Analysis 28, 1282–1323 (2025) (SCI-E, Scopus) .

Võ Quốc Bảo, Phùng Hồ Hải, Đào Văn Thịnh, 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) .

Integrality in topology stemming from complex algebraic varieties

Người báo cáo: Hélène Esnault

Thời gian: Bắt đầu từ 9h30, thứ Sáu, ngày 13/6/2025

Địa điểm: Hội trường Hoàng Tụy, Tầng 2, Nhà A6, Viện Toán học

Tóm tắt báo cáo: A smooth complex quasi-projective variety

X

is, as a topological space, homotopic to a bouquet of spheres. In particular its fundamental group

π_{1}^{t o p} (X)

is finitely presented, thus finitely generated and the relations themselves are finitely generated. For example, if

X

is an affine curve,

π_{1}^{t o p} (X)

is a free group. Free groups possess linear integral representations into

G L_{r} (r, \bar{Z})

for all

r

. Not every finitely presented group possesses linear integral representations. So we could ask whether this property is an obstruction for a finitely presented group to come from geometry, that is to be isomorphic to

π_{1}^{t o p} (X)

for some

X

as above. While we have at disposal obstructions which stem from Hodge theory, such as harmonic analysis, when

X

is projective (or proper), they do not apply for

X

quasi-projective.

We showed (with Johan de Jong, partially based on earlier work with Michael Groechenig), that a weaker integrality notion, which we called weak integrality, is an obstruction for a finitely presented group to be geometric. The proof is now purely arithmetic (with some algebraic geometry) and relies on the Langlands correspondence. It would be of interest to know whether integrality itself (without ‘weak’) is an obstruction, we do not know this.