Phd Representation Theory And Categorification Miemietzvu27Empsfp

The deadline to apply for the Oct 2027 intake is Jul 31, 2027.

At the heart of modern algebra lies the transition from classical representation theory—where an algebra acts on a vector space via linear maps—to the richer, higher-dimensional landscape of categorification. By replacing vector spaces with categories and linear maps with functors, this field allows mathematicians to uncover profound new structures, most notably through the study of natural transformations between functors. This PhD project, supervised by Professor Vanessa Miemietz, invites candidates to push the boundaries of this transition, which has already been instrumental in solving landmark problems such as Broué’s abelian defect group conjecture and the Kazhdan—Lusztig conjectures.

Research Focus

The research is dedicated to exploring specific, advanced examples of categorifications. By examining how monoidal categories act on other categories, or how 2-categories interact with collections of categories, students will investigate the underlying mechanics that have propelled major advances in mathematics over the last three decades. This is an ideal destination for a researcher looking to engage with the deep interplay between algebra, category theory, and the geometric insights that categorification provides.

University of East Anglia, Norwich is a university in the United Kingdom, founded in 1963, with 2820 international students among its 16872 total students.

The university has 400 programs, covering various subjects and research areas, allowing students to explore their interests.

Norwich provides a great location for students, with a rich history and cultural events to enjoy outside of campus.