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: "On the Galois-Gauss sums of weakly ramified characters", 2022.
Matthew Honnor (jointly supervised with Mahesh Kakde): "Formulas for Brumer-Stark units", 2022.
Dominik Bullach: "Tamagawa number conjectures and the scarcity of Euler systems", 2023.
Daniel Puignau (jointly supervised with Daniel Macias Castillo): expected 2025.
Dingli Liang: expected 2025.
Diego Gordo Chicharro (jointly supervised with Owen Patashnick), expected 2025.
Wenhan Zhang: expected 2028.
