PhD Studentship: Automorphic forms, L-functions and trace formulas

University of Bristol - School of Mathematics

Location School of Mathematics http://bristol.ac.uk/maths/
Funding for (UK/EU/o’seas) Uk/EU
Funding amount Includes tuition fees, research travel grant and a full stipend at the EPSRC DTA rate (£14,553 2017/18) for 3.5 years
Hours Full time
Contract (temp/perm) Contract/temporary
Closing date 8 January 2018

The project:

More than a century, L-functions have played an important role in number theory. The goal of my project is to understand L-functions by looking at many concrete examples. In particular, we are focusing on L-functions associated with automorphic forms.

Automorphic forms/representations have been another important piece in number theory. Several significant conjectures (e.g. BSD conjecture, and the biggest of all, Langlands programme) are related with automorphic forms and their L-functions. There are only a few concrete methods to study automorphic forms and their L-functions, and trace formulas are one of them.

In 1956, Selberg introduced his famous trace formula, now called the Selberg trace formula, to obtain Weyl’s law, which implies the existence of infinitely many Maass forms (automorphic forms for GL(2)). For almost 60 years, Selberg’s ideas have been generalised, and various trace formulas have been constructed and studied. However, there are few numerical results from trace formulas. The main obstacle is the complexity of trace formulas. Many trace formulas (Selberg, Arthur-Selberg, Bruggeman-Kuznetsov, etc) are investigated, constructed and used to understand automorphic forms and their L-functions from a theoretical point of view, but most of them are not explicit enough to implement in computer code. One particular purpose of my projects is to make some of them explicit and apply numerical methods to them.

How to apply:

Please make an online application  for this project selecting Mathematics (PhD) as the programme choice http://www.bristol.ac.uk/maths/study/postgraduate/apply/. When prompted in the Funding and Research Details sections of the form, specify that you wish to be considered  for the Number Theory DTA Studentship

Candidate requirements:  To be considered for this funded PhD studentship, applicants must hold (or expect to receive) a First Class degree (or equivalent) in Mathematics.

Funding:  Includes tuition fees, research travel grant and a full stipend at the EPSRC DTA rate (£14,553 2017/18) for 3.5 years

Contacts:  Dr Min Lee http://bristol.ac.uk/maths/people/person/min-lee/overview.html

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