Francesc Castella


I am a Hedrick Assistant Adjunct Professor in the Department of Mathematics at UCLA.

Email: castella at math dot ucla dot edu
Office: Math Science 6939


My CV as of December 2015.

Research Interests: p-adic L-functions, Euler systems, and their variation in p-adic families,
with a special emphasis on their applications to the arithmetic of elliptic curves and modular forms.


Courses

Spring 2016 Math 132
Winter 2016 Math 132
Fall 2015 Math 33A
Fall 2015 Math 132
Spring 2015 Math 117
Winter 2015 Math 31B
Winter 2015 Math 110A
Fall 2014 Math 207
Spring 2014 Math 33A
Fall 2013 Math 31A
Fall 2013 Math 115A

Preprints and Publications

Note: Papers here may differ slightly from the published versions.

  • Lambda-adic Gross-Zagier formula for elliptic curves at supersingular primes.
    F. Castella and X. Wan
    preprint.
  • A geometric perspective on p-adic properties of mock modular forms.
    L. Candelori and F. Castella
    submitted. [pdf]
  • p-adic heights of Heegner points and Beilinson-Flach elements.
    F. Castella
    submitted. [pdf]
  • Heegner cycles and p-adic L-functions.
    F. Castella and M.-L. Hsieh
    submitted. [pdf]
  • Iwasawa main conjecture for Heegner points: supersingular case.
    F. Castella and X. Wan
    preprint. [pdf]
  • Variation of anticyclotomic Iwasawa invariants in Hida families.
    F. Castella, C.-H. Kim and M. Longo
    submitted. [pdf]
  • Big Heegner points and special values of L-series.
    F. Castella and M. Longo
    Annales Mathématiques du Québec, special issue: Glenn Stevens 60th birthday, to appear. [pdf], [journal]
  • On the exceptional specializations of big Heegner points.
    F. Castella
    Journal de l'Institut Mathématique de Jussieu, to appear. [pdf], [journal]
  • On the p-adic variation of Heegner points.
    F. Castella
    submitted. [pdf]
  • Heegner cycles and higher weight specializations of big Heegner points.
    F. Castella
    Mathematische Annalen 356 (2013), 1247-1282. [pdf], [journal]
  • Euler systems and p-adic L-functions: a tale in two trilogies.
    M. Bertolini, F. Castella, H. Darmon, S. Dasgupta, K. Prasanna and V. Rotger
    LMS Lecture Note Series 414 (2014), 52-101. [pdf]

    Other Writings

  • On the p-adic variation of Heegner points.
    F. Castella
    PhD thesis (adviser: Prof. Henri Darmon). [pdf]
  • Ordinary CM forms and local Galois representations.
    F. Castella
    MSc thesis (adviser: Prof. Victor Rotger). [pdf]

    10201225.jpg