### 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.