Mathematics Department
Number Theory Group


Professor D Burns

Department of Mathematics
King's College London
Strand, London WC2R 2LS
United Kingdom

Room 413, Strand Building
Tel: +44-(0)20-7848 2863 (direct)
Tel: +44-(0)20-7848 2217 (general office)
Fax: +44-(0)20-7848 2017

Head of the Number Theory Group

Principal research interests

-- The Tamagawa Number Conjecture of Bloch and Kato (and its equivariant refinement).

-- Iwasawa Theory (including aspects of non-commutative Iwasawa Theory).

-- Stark's Conjecture (and various natural integral refinements of this conjecture).

-- Epsilon constants and de Rham structure invariants associated to arithmetic schemes with a finite group action.

-- Algebraic K-theory and homological algebra.

Research Publications

For publications and preprints since 2000 see here.

For a full list of publications see MathSciNet.

Ph.D. Theses Supervised

Sey Kim: "On the equivariant Tamagawa number conjecture for Quaternion fields", 2001
Anthony Hayward: "Congruences satisfied by Stark units", 2004
Manuel Breuning: "Equivariant epsilon constants for Galois extensions of number fields and p-adic fields", 2004
Andrew Jones: "Dirichlet L-functions at s = 1", 2007
Andrew Parker: "Equivariant Tamagawa numbers and non-commutative Fitting invariants" (PDF), 2007
James Barrett: "Annihilating the Tate-Shafarevic groups of Tate motives", 2009
Claire Ward: "On geometric Zeta functions, epsilon constants and canonical classes", 2011
Daniel Macias-Castillo: "On the values of derivatives of Dirichlet and Hasse-Weil L-functions", 2011
Carl Hahn: "On the square root of the inverse different via relative algebraic K-theory", 2016
Yasin Zaehringer (jointly supervised with Mahesh Kakde): "Non-commutative Iwasawa Theory with (phi,gamma)-local conditions over distribution algebras", 2017
Asuka Kumon: "Derivatives of L-series, p-adic cohomology and ray class groups", 2017.
Alice Livingstone Boomla: "Selmer groups, zeta elements and refined Stark conjectures", 2018.
Kwok-Wing Tsoi: "On special elements for p-adic representations and higher rank Iwasawa theory at arbitrary weights", 2018
Rob Evans (jointly supervised with Vladimir Dokchitser): "Artin-twists of Abelian Varieties: Periods, L-values and Arithmetic", 2021.
Alexandre Daoud: "On modules of Euler systems", 2021.
Yu Kuang: expected 2021
Matthew Honnor (jointly supervised with Mahesh Kakde): expected 2022.
Dominik Bullach: expected 2022.
Daniel Puignau (jointly supervised with Daniel Macias Castillo): expected 2025.
Dingli Liang: expected 2025.
Hassan Mahmoodzadeh Vaziry: expected 2025.

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Department of Mathematics - King's College London