About me

I'm a postdoc (EPSRC Doctoral Prize Fellow) in the Number Theory group at University College London.
Previously, I was a postdoc at King's College London, where I also did my PhD under the supervision of David Burns. During my PhD I was a member of the 2018 cohort of the London School of Number Theory and Geometry (LSGNT). Prior to that, I was at LMU Munich.

My primary mathematical interests are:

• Special values of \(L\)-functions, particularly the Tamagawa Number Conjecture of Bloch and Kato and its equivariant refinement (the `eTNC').
• Stark's Conjecture and its integral refinements.
• Euler systems
• Iwasawa theory

Jointly with Luis García, I am organising the London number theory seminar in the 2025 spring term. For more information on the seminar, including the schedule, see here.

Jointly with Daniel Macías Castillo, I organised a conference on the arithmetic of \(L\)-functions, which took place 22 -- 26 May 2023 at ICMAT in Madrid. The webpage for the conference can be found here and the conference booklet can be downloaded here.

Preprints

• Dominik Bullach, Daniel Macías Castillo:
  Annihilating class groups in \(p\)-elementary extensions,
  Preprint. arxiv pdf
• Dominik Bullach, David Burns, Alexandre Daoud, Soogil Seo:
  On Euler systems and a conjecture of Coleman,
  Preprint. pdf
• Dominik Bullach, David Burns, Alexandre Daoud, Soogil Seo:
  Dirichlet \(L\)-series at \(s = 0\) and the scarcity of Euler systems,
  Preprint. arxiv pdf

Published research articles

• Dominik Bullach, David Burns, Takamichi Sano:
  On \(p\)-adic families of special elements for rank-one motives,
  Trans. Amer. Math. Soc. 376 (2023), pp. 5377--5407. arXiv journal pdf
• Dominik Bullach, Martin Hofer:
  The equivariant Tamagawa Number Conjecture for abelian extensions of imaginary quadratic fields,
  Documenta Mathematica 28 (2023), no. 2, pp. 369–-418. arXiv journal () pdf
• Dominik Bullach, Alexandre Daoud:
  On universal norms for \(p\)-adic representations in higher-rank Iwasawa theory,
  Acta Arithmetica 201.1 (2021), pp. 63--108. arXiv journal pdf

Edited volumes

• Dominik Bullach, Daniel Macías Castillo (editors): Arithmetic of \(L\)-series. Proceedings of an international conference held at ICMAT, Madrid, May 2023. To appear in EMS series of congress reports.

Textbooks

• Dominik Bullach, Johannes Funk:
  Vorbereitungskurs Staatsexamen Mathematik.
  Aufgabenbereiche Algebra und Analysis mit umfassenden Lösungen.
  Second edition. Springer Spektrum, 2021.
  Available here. There are also lists of errata for the first edition and second edition, and a document of material that was contained in the first edition but cut from the second edition.

Past research talks

• On leading terms of \(L\)-series and Euler systems, mini-course at the conference Algebraic Number Theory -- a workshop for young researchers, Universität der Bundeswehr München, 2 -- 6 September 2024.
• On the refined `Birch--Swinnerton-Dyer type’ conjectures of Mazur and Tate, Sugimoto Algebra Seminar, Osaka Metropolitan University, 19 July 2024.
• On the refined `Birch--Swinnerton-Dyer type’ conjectures of Mazur and Tate, Recent progress on Hilbert's 12th problem, International Centre for Mathematical Sciences, Edinburgh, 24 -- 28 June 2024.
• On some recent developments in the theory of Euler systems, London Number Theory Seminar, 17 January 2024.
• Euler systems and refined conjectures of Birch and Swinnerton-Dyer type, Algebra, Arithmetic and their Geometries seminar, Nottingham, 6 December 2023.
• Euler systems and refined conjectures of Birch and Swinnerton-Dyer type, workshop on Iwasawa theory and cohomology of arithmetic groups, Bielefeld, 27--28 November 2023.
• Euler systems and refined conjectures of Birch and Swinnerton-Dyer type, ICMAT Number Theory Seminar, Madrid, 14 November 2023
• Dirichlet \(L\)-series at \(s = 0 \) and the scarcity of Euler systems, King's College London Internal Number Theory Seminar, 22 June 2023.
• The minus part of the equivariant Tamagawa Number Conjecture, London Junior Number Theory Seminar, 13 June 2023.
• The minus part of the equivariant Tamagawa Number Conjecture, ICMAT Number Theory Seminar, Madrid, 19 May 2023
• Cyclotomic units and the scarcity of Euler systems, Young Researchers in Algebraic Number Theory, Glasgow, 23 August 2022
• Cyclotomic units and the scarcity of Euler systems, Number Theory Seminar, Korea Institute for Advanced Studies (KIAS), Seoul, 27 July 2022
• Cyclotomic units and the scarcity of Euler systems, Number Theory Seminar, Yonsei University, Seoul, 26 July 2022
• Dirichlet \(L\)-series at \(s = 0 \) and the scarcity of Euler systems, Oberseminar Arithmetische und Algebraische Geometrie, LMU Munich, 12 July 2022
• Cyclotomic units and the scarcity of Euler systems, Algebra and Number Theory Seminar, University College Dublin, 25 May 2022
• Dirichlet \(L\)-series at \(s = 0 \) and the scarcity of Euler systems, Number Theory Seminar at Università degli Studi, Padova, 12 May 2022
• Dirichlet \(L\)-series at \(s = 0 \) and the scarcity of Euler systems, Algebra and Number Theory seminar, Exeter, 17 March 2022
• Dirichlet \(L\)-series at \(s = 0 \) and the scarcity of Euler systems, Oberseminar Algebraische Geometrie und Arithmetik, Essen, 25 November 2021
• Dirichlet \(L\)-series at \(s = 0 \) and the scarcity of Euler systems, ICMAT Number Theory Seminar, Madrid, 15 November 2021
• The equivariant Tamagawa Number Conjecture for abelian extensions of imaginary quadratic fields, Young Researchers in Algebraic Number Theory Conference, Bristol (online), 20 August 2021
• Universal norms for \(p\)-adic representations in higher-rank Iwasawa theory, Oberseminar Arithmetische und Algebraische Geometrie, LMU Munich (online), 8 June 2021
• The equivariant Tamagawa Number Conjecture for abelian extensions of imaginary quadratic fields, Luxembourg Number Theory Seminar (online), 4 May 2021
• The equivariant Tamagawa Number Conjecture for abelian extensions of imaginary quadratic fields, ICMAT Number Theory Seminar, Madrid (online), 13 April 2021

Notes / Miscellaneous

Maybe the following are useful:

• My PhD thesis: Tamagawa Number Conjectures and the scarcity of Euler systems
• My Master's thesis: Classification of weakly ramified extensions of the p-adic numbers
• Notes for David Burns's lecture at the 2018 Topics in Number Theory course: Introduction to Iwasawa Theory

Contact

Department of Mathematics, University College London,
25 Gordon Street, WC1H 0AY, London, United Kingdom.

dominik.bullach@ucl.ac.uk