Professor David Burns

Professor David Burns - PhD thesis supervision

The following list gives information (including title of thesis, name of student, year of graduation and details of all thesis-related publications) for each of the theses that I have supervised so far.

On the equivariant Tamagawa number conjecture for Quaternion fields, Sey Kim (2001)
-- 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.

Congruences satisfied by Stark units, Anthony Hayward (2004)
--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.

Equivariant epsilon constants for Galois extensions of number fields and p-adic fields, Manuel Breuning (2004)
--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.

Dirichlet L-functions at s = 1, Andrew Jones (2007)
--On the values of Artin L-series at s=1* and annihilation of class groups* (with H. Castillo), Acta Arith. 160 (2013) 67-93.
Equivariant Tamagawa numbers and non-commutative Fitting invariants, Andrew Parker (2007)

Annihilating the Tate-Shafarevic groups of Tate motives, James Barrett (2009)
--Annihilating Selmer Modules (with D. Burns), J. reine u. angew. Math. 675 (2013) 191-222.

On geometric Zeta functions, epsilon constants and canonical classes, Claire Ward (2011)

On the values of derivatives of Dirichlet and Hasse-Weil L-functions, Daniel Macias-Castillo (2011)
--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 square root of the inverse different via relative algebraic K-theory, Carl Hahn (2016)
--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.

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

Derivatives of L-series, p-adic cohomology and ray class groups, Asuka Kumon (2017)
--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), to appear in Acta Arith.

Selmer groups, zeta elements and refined Stark conjectures, Alice Livingstone Boomla (2018)
--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.

On special elements for p-adic representations and higher rank Iwasawa theory at arbitrary weights, Kwok-Wing Tsoi (2018) -- Winner of an Elsevier Outstanding PhD Thesis Prize
--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.

Artin-twists of Abelian Varieties: Periods, L-values and Arithmetic, Rob Evans (2021) -- jointly supervised with Vladimir Dokchitser
--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), to appear in Exp. Math.

On modules of Euler systems, Alexandre Daoud (2021).
--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.

On the Galois-Gauss sums of weakly ramified characters, Yu Kuang (2022).
--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.

Formulas for Brumer-Stark units, Matthew Honnor (2022) -- jointly supervised with Mahesh Kakde.
--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.

Tamagawa number conjectures and the scarcity of Euler systems, Dominik Bullach (2023) -- Winner of an Elsevier Outstanding PhD Thesis Prize
--The equivariant Tamagawa Number Conjecture for abelian extensions of imaginary quadratic fields (with M. Hofer), Doc. Math. 28 (2023) 369-418.
--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.

Title to be confirmed, Daniel Puignau (expected 2025) -- jointly supervised with Daniel Macias Castillo

Title to be confirmed, Dingli Liang (expected 2025)

Title to be confirmed, Wenhan Zhang (expected 2028)

Title to be confirmed, Eva Brenner (expected 2028) -- jointly supervised with Werner Bley