This year I was very fortunate to participate in the Research Science Institute (RSI) at the Massachusetts Institute of Technology (MIT) as part of my second summer scientific research stay with Joves i Ciència. This was a superb program that I could attend thanks to the funding provided by the Center for Excellence for Education and la Fundació Catalunya la Pedrera. The program gathers 80 students from the US and around the world and guides them through the production of a scientific paper, while also organizing talks with extremely interesting guests (including Nobel Laureates). I worked on a project related to number theory entitled On the Divisibility of Binomial Coefficients and my supervisor was Oscar Mickelin, a graduate student at the department of Mathematics at MIT (see here for all the math RSI papers). I obtained the Research Science Institute Student Award for the final presentation of the project (see the video here). Also, I hadn’t even considered doing my undergraduate in the US until I participated in RSI, so I am very grateful to the program. Here we talk more about this experience (and picture at the radio). Picture of all the people in RSI’17. Picture with my mentor. Picture from my talk. Picture of when I finished writing the paper!
After some months of editing I posted my paper on arXiv (see here). I also posted on arXiv a short paper entitled Irrationality of the Sum of a p-Adic Series (see here). These two papers, along with some other materials, configured my high school senior thesis, entitled Open Problems with Factorials, which you can download here. From this research originated two new series that I posted in the Online Encyclopedia of Integer Sequences (OEIS): A290203 and A290290 I created a webpage for the thesis, which you can find here, which contains a lot of Number Theory and Group Theory, along with many C++ codes that I programmed during the thesis. This webpage also includes information about another math research project that I carried out during high school about methods for finding primitive roots, which you can read here.
Here is a talk in Spanish about the project that I gave at the research congress for youth Certamen de Jóvenes Investigadores, and here a short review given at the same congress. Here is a talk in Catalan about the project that I gave at the prize ceremony of the Premi Poincaré (UPC). Finally, here is a short talk in Catalan about the project for the prize Premis Ramon Llull (URL). Some news here and here.
Finally, the thesis obtained the following prizes: Premi Poincaré (Universitat Politècnica de Catalunya), Premis Ramon Llull in Science and Technology (Universitat Ramon Llull), Premi Argó (Universitat Autònoma de Barcelona), Premi UPF (Universitat Pompeu Fabra), Premi Recerca Jove (by the Catalan Government – former Premis Cirit), Alpha Mu Theta Award from the Mathematical Honors Society at the Exporecerca Science Fair, and the special prize at the Certamen de Jóvenes Investigadores (by the Spanish Government), which also selected it to represent Spain at the EU Contest for Young Scientists organized by the European Comission (which I could not attend). Picture of my presentation at the Poincaré ceremony and another here. Picture of everyone who attended the congress Certamen de Jóvenes Investigadores and picture of its closing ceremony. Picture at the stand during the Exporecerca science fair.
On a more literary note, I wrote a math short story called Desigualtats about the impossible love between a digit in binary and a digit in decimal for the contest Concurs de Relats. Read it here. Picture from the ceremony.
I also wrote a longer story entitled La Divina Literatura based on Dante’s Divine Comedy, which you can read here. Here is also a short story about a man fooled by music, entitled Les Tecles.
Also, with three of my classmates we elaborated a statistics project about the relationship between nationalism and classical music, by analyzing how often different European countries play their own authors compared to foreign composers. You can read the results here. We then presented this project to the Planter Statistics Competition in Catalonia (results).
This year I was selected to represent Spain at the European Girls’ Mathematical Olympiad in Zurich, Switzerland. Picture with the Spanish team here. I also participated in the telematic competition for math problem solving, Olitele.
Finally, I participated with two classmates in the Fisidabo physics activity at the Barcelona theme park Tibidabo, were we carried out a physics experiment about the aerodynamic or drag coefficient of spheres at one of the attractions. Here is a video explaining it at the park, and here is the written report.
Sílvia Casacuberta Puig 
