• Sey Kim, 2001
  - On the equivariant Tamagawa number conjecture for Quaternion fields
--- An elementary proof of the quadratic reciprocity law, Amer. Math. Monthly 111 (2004) 48-50.
--- On congruence relations between the fundamental units of biquadratic fields, J. Number Theory 121 (2006) 7–29.
--- On the Iwasawa invariants of prime cyclotomic fields, Res. Number Theory 9 (2023) Paper No. 29.

• Anthony Hayward, 2004
  - Congruences satisfied by Stark units
--- A class number formula for higher derivatives of abelian L-functions, Compositio Math. 140 (2004) 99-129.
--- Explicit units and the equivariant Tamagawa number conjecture, II (with D. Burns), Comment. Math. Helv. 82 (2007) 477-497.

• Manuel Breuning, 2004
  - Equivariant epsilon constants for Galois extensions of number fields and \(p\)-adic fields
--- On equivariant global epsilon constants for certain dihedral extensions, Math. Comp. 73 (2004) 881-898.
--- Equivariant local epsilon constants and étale cohomology, J. London Math. Soc. 70 (2004) 289-306.
--- Exact algorithms for \(p\)-adic fields and epsilon constant conjectures (with W. Bley), Illinois J. Math. 52 (2008) 773-797.

• Andrew Jones, 2007
  - Dirichlet \(L\)-functions at \(s = 1\)
--- On the values of Artin \(L\)-series at \(s=1\) and annihilation of class groups (with H. Castillo), Acta Arith. 160 (2013) 67-93.

• Andrew Parker, 2007
  - Equivariant Tamagawa numbers and non-commutative Fitting invariants
• James Barrett, 2009
  - Annihilating the Tate-Shafarevic groups of Tate motives
--- Annihilating Selmer Modules (with D. Burns), J. reine u. angew. Math. 675 (2013) 191-222.

• Claire Ward, 2011
  - On geometric Zeta functions, epsilon constants and canonical classes
• Daniel Macias-Castillo, 2011
  - On the values of derivatives of Dirichlet and Hasse-Weil \(L\)-functions
--- On higher-order Stickelberger-type theorems for multi-quadratic extensions, Int. J. Number Theory 8 (2012) 95-110.
--- On higher order Stickelberger-type theorems, J. Number Theory 133 (2013) 3007-3032.
--- Organizing matrices for arithmetic complexes (with D. Burns), Int. Math. Res. Not. (2014) 2814-2883.
--- On the Galois structure of Selmer groups (with D. Burns and C. Wuthrich), Int. Math. Res. Not. (2015) 11909-11933.
--- Congruences for critical values of higher derivatives of twisted Hasse-Weil \(L\)-functions (with W. Bley), J. Reine Angew. Math. 722 (2017) 105-135.

• Carl Hahn, 2016
  - On the square root of the inverse different via relative algebraic \(K\)-theory
--- On refined metric and hermitian structures in arithmetic, I: Galois-Gauss sums and weak ramification (with W. Bley and D. Burns), Ann. \(K\)-theory 5 (2020) 79-140.

• Yasin Zaehringer, 2017 -- jointly supervised with Mahesh Kakde
- Non-commutative Iwasawa Theory with \((\varphi,\gamma)\)-local conditions over distribution algebras

• Asuka Kumon, 2017
  - Derivatives of \(L\)-series, \(p\)-adic cohomology and ray class groups
--- On the Galois structure of arithmetic cohomology II: ray class groups (with D. Burns), J. Math. Soc. Japan 70 (2018) 481-517.
--- On the Krull-Schmidt decomposition of unit groups of number fields (with D. Lim), Acta Arith. 218 (2025) 77-96.

• Alice Livingstone Boomla, 2018
  - Selmer groups, zeta elements and refined Stark conjectures
--- On zeta elements and refined abelian Stark conjectures, Tokyo J. Math. 40 (2017) 123-151.
--- On Selmer groups and refined Stark conjectures (with D. Burns), Bull. Lond. Math. Soc. 50 (2018) 845-862.

• Kwok-Wing Tsoi, 2018 -- Winner of an Elsevier Outstanding PhD Thesis Prize
- On special elements for \(p\)-adic representations and higher rank Iwasawa theory at arbitrary weights
--- On generalised Kummer congruences and higher rank Iwasawa theory at arbitrary weights, Tokyo J. Math. 42 (2019) 585-610.
--- On higher special elements of \(p\)-adic representations (with D. Burns and T. Sano), Int. Math. Res. Not. (2021) 15337-15411.
--- On non-abelian higher special elements of \(p\)-adic representations (with D. Macias Castillo), Israel J. Math. 248 (2022) 95-147.
--- On a Birch and Swinnerton-Dyer type conjecture for Hasse-Weil-Artin \(L\)-functions in characteristic \(p > 0\) (with W. Kim, K-S. Tan and F. Trihan) - Submitted.

• Rob Evans, 2021 -- jointly supervised with Vladimir Dokchitser
  - Artin-twists of Abelian Varieties: Periods, \(L\)-values and Arithmetic
--- On a BSD-type formula for \(L\)-values of Artin twists of elliptic curves (with V. Dokchitser and H. Wiersema), J. Reine Angew. Math. 773 (2021) 199-230.
--- Numerical evidence for a refinement of Deligne's Period Conjecture for Jacobians of curves (with D. Macias Castillo and H. Wiersema), Exp. Math. 34 (2025) 366-383.

• Alexandre Daoud, 2021
  - On modules of Euler systems
--- On universal norms for p-adic representations in higher-rank Iwasawa theory (with D. Bullach), Acta Arith. 201 (2021) 63-108.
--- On the structure of the module of Euler systems for a \(p\)-adic representation, New York J. Math. 28 (2022) 993-1041.

• Yu Kuang, 2022
  - On the Galois-Gauss sums of weakly ramified characters
--- On the Galois-Gauss sums of weakly ramified characters, New York J. Math. 29 (2023) 417-440.
--- On Galois-Gauss sums and the square root of the inverse different, Acta Arith. 209 (2023) 319-355.
--- On the square root of the inverse different (with A. Agboola, D. Burns and L. Caputo), Canad. J. Math. 76 (2024) 283-318.

• Matthew Honnor, 2022 -- jointly supervised with Mahesh Kakde.
  - Formulas for Brumer-Stark units
--- Comparing two formulas for the Gross-Stark units, J. Number Theory 248 (2023) 368-419.
--- On the root of unity ambiguity in a formula for the Brumer-Stark units, Canad. Math. Bull. 67 (2024) 611-623.
--- On the equality of three formulas for Brumer-Stark units (with S. Dasgupta and M. Spiess), J. Lond. Math. Soc 112 (2025), Paper No. e70296.

• Dominik Bullach, 2023 -- Winner of an Elsevier Outstanding PhD Thesis Prize
  - Tamagawa number conjectures and the scarcity of Euler systems
--- The equivariant Tamagawa Number Conjecture for abelian extensions of imaginary quadratic fields (with M. Hofer), Doc. Math. 28 (2023) 369-418.
--- Annihilating class groups in \(p\)-elementary abelian extensions (with D. Macias Castillo), Math. Proc. Camb. Philos. Soc. 179 (2025) 145-166.
--- On Euler systems and a conjecture of Coleman (with D. Burns, A. Daoud and S. Seo) - Submitted.
--- Dirichlet \(L\)-series at \(s=0\) and the scarcity of Euler systems (with D. Burns, A. Daoud and S. Seo) - Submitted.
--- On the refined `Birch–Swinnerton-Dyer type' conjectures of Mazur and Tate (with M. Honnor) - Submitted.

• Daniel Puignau, -- jointly supervised with Daniel Macias Castillo
  - withdrew from thesis
--- Congruences between derivatives of Artin \(L\)-Series at \(s = 0\) (with D. Burns, T. Sano and S. Seo), Int. Math. Res. Not. 2026 (2026) 1-26.

• Dingli Liang, 2025
  - On non-Noetherian Iwasawa theory
--- On the coherency of completed group algebras (with D. Burns and Y. Kuang), J. Algebra 661 (2025) 757-777.
--- On non-Noetherian Iwasawa theory (with D. Burns and A. Daoud) - Submitted.

• Wenhan Zhang, expected 2028
• Eva Brenner, expected 2028 -- jointly supervised with Werner Bley
• Philipp Weidemann, expected 2029 -- jointly supervised with Dominik Bullach

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