Quantum Groups
Project Description
Quantum groups are quantizations of universal enveloping algebras of Lie algebras discovered by Drinfeld and Jimbo in the study of exactly solvable models in statistical mechanics in the middle of 80s. Quantum groups have applications in many areas of mathematics and physics, and had profound impact on representation theory, low dimensional topology, the theory of Yang-Baxter type exactly soluble models and conformal field theory, among other subjects.
The projects aim to introduce the basics of the representation theory of quantum groups and explore its various applications through the solution of the Yang-Baxter equation. Students who have excellent performances will be invited to continue on the project for more original research.
The projects aim to introduce the basics of the representation theory of quantum groups and explore its various applications through the solution of the Yang-Baxter equation. Students who have excellent performances will be invited to continue on the project for more original research.
Supervisor
IP, Ivan Chi Ho
Quota
10
Course type
UROP1100
UROP2100
UROP3100
UROP3200
UROP4100
Applicant's Roles
The students will be introduced to the theory of quantum groups under the guidance of the supervisor. Students should have a solid background in linear algebra and abstract algebra (group and ring theory). Familiarity with Lie algebra and representation theory is a bonus, but not required. At the end of the project, students in UROP 1100 are expected to write an expository article on the subject. For students in UROP 2100 or higher, some original research works are expected.
Applicant's Learning Objectives
1) Be familiar with Lie algebras and representation theory.
2) Improve critical thinking skills through reading research-level mathematics books.
3) Learn to search for references during research
4) Prepare themselves for postgraduate studies in mathematics or physics.
2) Improve critical thinking skills through reading research-level mathematics books.
3) Learn to search for references during research
4) Prepare themselves for postgraduate studies in mathematics or physics.
Complexity of the project
Moderate