About me

I am currently a postdoc in the Number Theory group at King's College London. From October 2023 I will be an EPSRC Doctoral Prize Fellow at University College London.
Previously, I was a PhD student supervised by David Burns and 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 Stark-type conjectures and the equivariant Tamagawa number conjecture (eTNC)
• Euler systems
• Iwasawa theory

Jointly with Daniel Macias 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.


During the 2019-20 academic year, Gabriel Micolet and I organised the London Junior Number Theory seminar. More information on the seminar can be found here.

Publications / Preprints

• 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
• 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
• 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.

Research talks

• 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 first year mini-projects (contain mistakes): On the Gross-Stark Conjecture , A very personal introduction to the equivariant Tamagawa Number Conjecture
• 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