About me

I am a final year PhD student supervised by David Burns and a member of the 2018 cohort of the London School of Number Theory and Geometry (LSGNT). Previously, 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

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: Dirichlet \(L\)-series at \(s = 0\) and the scarcity of Euler systems, submitted. arxiv pdf
• Dominik Bullach, David Burns, Takamichi Sano: On \(p\)-adic families of special elements for rank-one motives, submitted. arXiv pdf
• Dominik Bullach, Martin Hofer: The equivariant Tamagawa Number Conjecture for abelian extensions of imaginary quadratic fields, submitted. arXiv pdf
• Dominik Bullach, Alexandre Daoud: On universal norms for \(p\)-adic representations in higher-rank Iwasawa theory,
  Acta Arithmetica 200.1 (2021), pp. 63--108. arXiv 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

• 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 (use at own risk):

• My first year mini-projects: 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