Introduction to Singularity Theory
Singularity theory is a field of intensive study in modern mathematics with fascinating relations to algebraic geometry, complex analysis, commutative algebra, representation theory, the theory of Lie groups, topology, dynamical systems, and many more, and with numerous applications in the natural and
technical sciences. In this lecture, we develop the relevant techniques, the basic theory of complex spaces and their germs and sheaves on them, including the key ingredients - the Weierstraß preparation theorem and its other forms (division theorem and finiteness theorem), and the finite coherence theorem.
Then we pass to the main object of study, isolated hypersurface and plane curve singularities. Isolated hypersurface singularities and especially plane curve singularities form a classical research area which still is in the centre of current research. In many aspects they are simpler than general singularities,
but on the other hand they are much richer in ideas, applications, and links to other branches of mathematics. Furthermore, they provide an ideal introduction to the general singularity theory. Particularly, we treat in detail the classical topological and analytic invariants, finite determinacy, resolution of singularities, and classification of simple singularities.
technical sciences. In this lecture, we develop the relevant techniques, the basic theory of complex spaces and their germs and sheaves on them, including the key ingredients - the Weierstraß preparation theorem and its other forms (division theorem and finiteness theorem), and the finite coherence theorem.
Then we pass to the main object of study, isolated hypersurface and plane curve singularities. Isolated hypersurface singularities and especially plane curve singularities form a classical research area which still is in the centre of current research. In many aspects they are simpler than general singularities,
but on the other hand they are much richer in ideas, applications, and links to other branches of mathematics. Furthermore, they provide an ideal introduction to the general singularity theory. Particularly, we treat in detail the classical topological and analytic invariants, finite determinacy, resolution of singularities, and classification of simple singularities.
Lecturer
Date
25th March ~ 27th May, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday | 15:20 - 17:50 | A3-4-312 | Zoom 16 | 468 248 1222 | BIMSA |
| Wednesday | 15:20 - 16:55 | A3-4-312 | Zoom 16 | 468 248 1222 | BIMSA |
Reference
Introduction to Singularities and Deformations,G.-M. Greuel • C. Lossen • E. Shustin
Audience
Undergraduate
, Advanced Undergraduate
, Graduate
Video Public
Yes
Notes Public
Yes
Language
Chinese
Lecturer Intro
Hu chuangqiang joined Bimsa in the autumn of 2021. The main research fields include: coding theory, function field and number theory, singularity theory. In recent years, he has made a series of academic achievements in the research of quantum codes, algebraic geometric codes, Drinfeld modules, elliptic singular points, Yau Lie algebras and other studies. He has published 13 papers in famous academic journals such as IEEE Trans. on IT., Final Fields and their Applications, Designs, Codes and Cryptography. He has been invited to attend domestic and international academic conferences for many times and made conference reports.