Dr Thomas Oliver
PhD, MMath(Dunelm)
Status:
Research Fellow
Personal website:
+44 1865 611509
Research groups:
Address
Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Recent Publications:
A conjectural extension of Hecke’s converse theorem
A conjectural extension of Hecke’s converse theorem
The Ramanujan Journal
issue 3
volume 47
page 659-684
(10 December 2018)
Research interests:
I'm interested in the analytic properties of L-functions. In particular:
- How are they established? My recent research is concerned with extensions of the Langlands--Shahidi method;
- What do they mean? I am very interested in so-called "converse theorems" (they are converse to the well-known fact that if V is an automorphic representation, then L(V,s) has nice analytic properties).
My latest work studies the orders of and cancellation between zeros of L-functions. In particular:
- Constraints on the orders of non-real zeros (which are expected to be simple);
- Poles of quotients of L-functions.
Prizes, awards, and scholarships:
- Oxford University Innovation - "John Fell Fund", small award
- LMS grant scheme 4 - "Research in pairs", joint with Michalis Neururer.
- HIMR focused research grant (2016) - "Kac--Moody groups and L-functions", joint with Sergey Oblezin.
- LMS grant scheme 1 (2016) - "Algebraisation and geometrisation in the Langlands programme", joint with Robert Kurinczuk.
- University of Nottingham: Graduate school travel prize (2014).
- University of Durham: Collingwood memorial prize (2010); Charles Holmes prize (2010); Nuffield Foundation undergraduate research bursary (2009); Norton prize (2008).
Major / recent publications:
- "Cancellation of zeros between automorphic L-functions and converse theorems for Maass forms". Joint with Michalis Neururer. arXiv:1809.06586.
- "Notes on low degree L-data", survey article for RIMS Kôkyûroku, no. 2014, "Analytic Number Theory and Related Areas". arXiv:1601.05009.