About me

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Hey there! I am Marta, graduated in Mathematics. My main interests are abstract algebra, number theory and arithmetic geometry, especially the theory of elliptic curves and Galois representations. You can find my CV here.

Pronouns: she/her.

Talks and slides

  1. A trip through elliptic curves and Fermat’s Last Theorem. Slides in English and Spanish. This is a talk I prepared for the cultural week we celebrate in university because of the Pi Day. I talk about motivation for defining elliptic curves, the key role that they play in the proof of Fermat’s Last Theorem, and their connection to modular forms. I would like to improve the slides and the talk itself in the future, though.
  2. Entering the tower with Iwasawa theory. Slides in English. Proving Fermat’s Last Theorem has been one of the most famous mathematical challenges during the last years. Most importantly, it served as a key starting point for developing deep theories in arithmetic geometry; and Iwasawa theory has been one of such. The fundamental idea of Iwasawa theory is studying the growth of arithmetic objects (such as the ideal class group of number fields or Selmer groups of elliptic curves and abelian varieties) over the tower of a p-adic extension. Furthermore, much of the recent progress in the Birch and Swinnerton-Dyer conjecture is due to these methods. In this talk I give an introduction to Iwasawa theory with an eye on its application to elliptic curves.
  3. Los secretos de los números primos. Slides in Spanish. This is a friendly talk about prime numbers and cryptography, and how the are related. It was due to an invitation from the STEM Talent Girl organizers in León (Spain).
  4. La conjetura de modularidad de Serre. Slides in Spanish. My Final Degree Project, which you can find here.

Conferences I attended

  1. Novenas Jornadas de Teoría de Números - 2022, Logroño (Spain).
  2. Décimas Jornadas de Teoría de Números - 2024, Madrid (Spain).
  3. 9th European Congress of Mathematics (as volunteer) - 2024, Sevilla (Spain).

Misc

Two of my favorite things together: my cat Salem and elliptic curves.

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“It is possible to write endlessly about elliptic curves. (This is not a threat.)” - Serge Lang.