Representations of complex reflection groups and related objects

Program Overview

This PhD program delves into the theory and applications of complex reflection groups, providing advanced research skills in this area. Students explore the structure, representations, and applications of these mathematical objects, contributing to the advancement of knowledge and pursuing careers in academia, research, or industry.

Program Outline

PhD in Mathematics: Representations of Complex Reflection Groups and Related Objects

Degree Overview:

This program delves into the fascinating world of complex reflection groups and their associated objects.

Objectives:

• Deepen understanding of complex reflection groups and related objects.
• Develop advanced research skills in this area.
• Contribute to the advancement of knowledge in complex reflection groups and related areas.
• Become a skilled researcher, capable of independent and collaborative work.

Program Description:

The program is designed to provide a comprehensive and rigorous education in the theory and applications of complex reflection groups. It combines theoretical foundations with practical applications, equipping students with the necessary skills to become successful researchers in this field.

Outline:

The program curriculum covers a wide range of topics, including:

• Complex reflection groups and their properties
• Representations of complex reflection groups
• Hecke and Cherednik algebras
• Applications to other areas of mathematics, such as topology and number theory

Modules:

• Complex Reflection Groups: An in-depth exploration of the structure and properties of complex reflection groups.
• Representations of Complex Reflection Groups: A study of the different types of representations of complex reflection groups and their applications.
• Hecke and Cherednik Algebras: A comprehensive examination of these important mathematical objects and their connections to complex reflection groups.
• Applications of Complex Reflection Groups: An exploration of the diverse applications of complex reflection groups in various areas of mathematics.

Assessment:

Assessment methods include:

• Written examinations
• Oral presentations
• Research thesis
• Research proposal
Assessment criteria include:
• Depth of understanding of the subject matter
• Originality and creativity in research
• Clarity and effectiveness of communication

Teaching:

The program is taught by a team of internationally recognized experts in complex reflection groups and related fields. The teaching methods include:

• Lectures
• Seminars
• Group discussions
• Individual supervision

Careers:

Graduates of the program are well-positioned for careers in academia, research, and industry. Potential career paths include:

• Research fellow
• Postdoctoral researcher
• Lecturer
• Professor
• Data scientist
• Quantitative analyst

Other:

• The program offers the opportunity to participate in research conferences and workshops.
• Students have access to a dedicated research library and computing facilities.
• The program provides a supportive and stimulating environment for research.

UK fee: £4,712 Full-time degree per annum International fee: £20,250 Full-time degree per annum University fees and charges can be paid in advance and there are several methods of payment, including online payments and payment by instalment. Fees are reviewed annually and are likely to increase to take into account inflationary pressures.