This summer I did a research internship in the Theory group at the Computer Science department at ETH Zurich (Switzerland), supervised by Rasmus Kyng. I worked on iterative algorithms for solving sparse linear systems using p-adic numbers, and we improved the running time for inverting and for computing the rank of sparse matrices over finite fields (arXiv preprint). It is a fascinating topic in Theoretical Computer Science and Number Theory that dates back to Dixon’s algorithm. I gave a talk on this research topic at the Harvard Math Table (poster, slides).
In the end, due to the impossibility to return to the US with the pandemic, I am taking a gap year to do research in Theoretical Computer Science. I stayed in Rasmus Kyng’s group until December (see also his seminar on Algorithms and Complexity), and I am joining the Security and Privacy group at IBM Research Zurich next spring to work in cryptography (more concretely, on Oblivious Pseudorandom Functions) supervised by Julia Hesse.
During the summer I was a mentor of abstract algebra for the math program for high school students MORPH. This is an online reading program offered to students to introduce them to college-level Mathematics. The program has been organized by Harvard undergraduates after seeing how many wonderful math and science summer camps have been canceled due to the Covid-19 situation. My (first!) mathematics research paper, entitled On the Divisibility of Binomial Coefficients, has been accepted for publication at the journal Ars Mathematica Contemporanea (to appear in 2020). The work primarily took place at the Research Science Institute at MIT in the summer of 2017 under the supervision of Oscar Mickelin.
During the spring semester, I was a Teaching Assistant for the class CS 124: Data Structures and Algorithms with Michael Mitzenmacher, for which I received the Special Commendation for Extraordinary Teaching in Extraordinary Times (one of 281 instructors out of 2,500 named by Harvard undergraduates). I also continued my work as Research Assistant in Natural Language Processing for Damián Blasi along with Karina Halevy at the Radcliffe Institute of Advanced Study at Harvard. We worked on analyzing the cross-linguistic emerging semantics of multilingual word embeddings (FastText and MUSE) using modularity tools (arXiv, GitHub). During the fall semester in Zurich, I took German classes and I re-took violin classes under the guidance of Elena Tanski.
As for the course-work, I learnt a lot of abstract algebra and number theory, along with Galois Theory, being very fortunate to take Algebraic Number Theory with Barry Mazur. Here is a small write-up on p-adic numbers for the class notes. I also became interested in logic programming in the class on Programming Languages by Nada Amin. Here is a small write-up on Prolog and Answer Set Programming for the class. I discovered the world of Early Modern Philosophy and Analytic Philosophy with Alison Simmons (and all its connections with pure math and logic! Also, reading Wittgenstein while learning NLP has been a very interesting experience). Here is a small commentary on Hume’s Uniformity principle. Finally, here is a short essay on religious conversions for a class on revolution and reform movements across history. At ETH they allowed me to audit a class on p-adic numbers by Paloma Bengoechea and a graduate class on advanced algorithms by Mohsen Ghaffari.
I re-joined the board of the student group Harvard Gender Inclusivity in Mathematics (GIIM) and started the social media project “Women of the Math Department”, for which I interview women who integrate Harvard’s math department (from undergraduates to professors) on their personal journeys and perspectives of Mathematics. You can find all of the interviews on our Instagram page and in our Facebook page. I am the Academics co-director for the group Harvard Women in Computer Science (WiCS) for the upcoming academic year, where we started several Computer Science research reading groups for undergraduates mentored by PhD students. I am the vice-president of ACFAEC, which is an association for families and alumni of math and science programs in Catalonia. I also joined the Multimedia board of the Harvard Crimson, the student newspaper on campus (here are some pictures). With the Mozart Society Orhcestra we prepared a virtual Zoom concert (e.g., Bach Air on G String).