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I'm a CSIC researcher at the Instituto de Ciencias Matemáticas (ICMAT) in Madrid. You may contact me at daniel dot macias at icmat dot es .

Between early 2016 and early 2024, I held different positions at the Universidad Autónoma de Madrid. I had been a postdoctoral researcher at ICMAT between October of 2012 and December of 2015.

Before that, I had been a postdoctoral researcher at the Ludwig-Maximilians-Universität in Munich during the academic year 2011-2012.

I obtained my PhD from King's College London in the fall of 2011.

My research is in algebraic number theory and arithmetic geometry. I am particularly interested in the arithmetic properties of the leading terms and values of L-functions.

Registration is open for the Tenth Number Theory Days, to take place in Madrid in July 2024.

PUBLICATIONS AND PREPRINTS

17. (with M. I. de Frutos-Fernández and D. Martínez Marqués) The refined class number formula for Drinfeld modules, submitted. pdf

16. (with D. Bullach) Annihilating class groups in p-elementary extensions, submitted. pdf

15. (with R. Evans and H. Wiersema) Numerical evidence for a refinement of Deligne's Period Conjecture for Jacobians of curves, submitted. pdf

14. (with D. Burns and S. Seo) On Weil-Stark elements, II: refined Stark conjectures, to appear in Transactions of the Amer. Math. Soc. pdf

13. (with D. Burns and S. Seo) On Weil-Stark elements, I: general properties, submitted. pdf

12. (with W. Bley) Congruences for critical values of higher derivatives of twisted Hasse-Weil L-functions, III, Math. Proc. Camb. Phil. Soc., Vol. 173 (2022), 431-456. pdf

11. (with K.-W. Tsoi) On non-abelian higher special elements of p-adic representations, Isr. J. Math., Vol. 248 (2022), 95-147. pdf

10. (with D. Burns) On refined conjectures of Birch and Swinnerton-Dyer type for Hasse-Weil-Artin L-series, to appear in Memoirs of the Amer. Math. Soc. pdf

9. Congruences for critical values of higher derivatives of twisted Hasse-Weil L-functions, II, Acta Arith., Vol. 195 (2020), 327-365. pdf

8. On the Krull-Schmidt decomposition of Mordell-Weil groups, Tokyo J. Math., Vol. 40 (2017), 353-378. pdf

7. (with W. Bley) Congruences for critical values of higher derivatives of twisted Hasse-Weil L-functions, J. reine angew. Math., Vol. 722 (2017), 105-136. pdf

6. (with D. Burns and C. Wuthrich) On Mordell-Weil groups and congruences between derivatives of twisted Hasse-Weil L-functions, J. reine angew. Math., Vol. 734 (2018), 187-228. pdf

5. (with D. Burns) On p-adic L-series, p-adic cohomology and class field theory, J. reine angew. Math., Vol. 732 (2017), 55-84. pdf

4. (with D. Burns and C. Wuthrich) On the Galois structure of Selmer groups, Int. Math. Res. Notices, Vol 2015, No. 22 (2015), 11909-11933. pdf

3. (with D. Burns) Organising matrices for arithmetic complexes, Int. Math. Res. Notices, Vol 2014, No. 10 (2014), 2814- 2883. pdf

2. On higher order Stickelberger-type theorems, J. Number Theory, Vol 133, No. 9 (2013), 3007-3032. pdf

1. On higher order Stickelberger-type theorems for multi-quadratic extensions, Int. J. Number Theory, Vol. 8, No. 1 (2012), 95-110. pdf

0. PhD Thesis: On the values of derivatives of Dirichlet and Hasse-Weil L-functions, King's College London, 2011. pdf

Postdocs:

Oliver Bräunling, from October 2023.
María Inés de Frutos Fernández, from February 2023.

PhD Students:

Daniel Martínez Marqués, UAM, ongoing.
Daniel Puignau Chacón, KCL, jointly supervised with D. Burns, ongoing.

Masters' theses supervised:

Ignacio Muñoz Jiménez, Goss L-functions of Drinfeld modules, 2023.
Victor Mialdea Molina, Modularity theorems, 2023.
Pablo García Fernández, Projective modules over group-rings and an application to algebraic K-theory, 2023.
Alberto Angurel Andrés, Mazur's control theorem, 2022.
Daniel Puignau Chacón, The weak Mordell-Weil theorem, 2021.
Enrique Martínez Cardenal, Local class field theory, 2020.
Xabier Echeberria Barrio, Drinfeld modules, 2019.
Carlos Alonso Gómez, Elliptic curves over local fields, 2018.
Antonio Mejías Gil, Iwasawa's main conjecture, 2018.
Ana Ruiz Lanau, The equivariant Birch and Swinnerton-Dyer rank conjecture, 2017.