Canceled - Mini-course on “Positive Characteristic and Homological Methods in Commutative Algebra”

Thời gian: 09:00:16/03/2020 đến 16:30:18/03/2020

Địa điểm: B4-705, VIASM

Báo cáo mời/Giảng viên

Prof. Ilya Smirnov ( Stockholm University, Sweden). 

Prof. Marc Chardin (CNRS and Sorbonne Université , France).

Mục tiêu/ Nội dung:

Lecture 1: Geometry of syzygies (Marc Chardin). This course will explore some advanced notions and tools of homological nature that are used in commutative algebra and algebraic geometry, namely complexes, spectral sequences associated to a double complex, Tor and Ext modules, local cohomology, local duality and Castelnuovo-Mumford regularity. From these tools, basic properties and examples from geometry will be derived, especially in the case of curves. Other applications of these tools will be the study of powers of ideals, the asymptotic behavior of regularity, local cohomology, Betti tables, Rees algebras, symmetric algebras, geometric interpretation of the asymptotic behavior of regularity. Finally, Koszul homology, approximation complexes and applications to the study of rational maps will also be discussed.

Lecture 2: An introduction to positive characteristic method in Commutative Algebra (Ilya Smirnov). The lectures will focus on Hilbert-Kunz multiplicity, which is a multiplicity theory native to rings of positive characteristic. I will cover the basic properties of Hilbert-Kunz multiplicity and connections with the classical Hilbert-Samuel theory.

Đối tượng tham dự: Học viên cao học, nghiên cứu sinh, nghiên cứu viên trong lĩnh vực Đại số giao hoán.

Ngôn ngữ: Tiếng Anh

Liên hệ: 

Tran Quang Hoa (Hue University of Education),

Pham Hung Quy (FPT University),