Francesc Castella

I am an Associate Professor in the Department of Mathematics at UCSB.

Previously, I was an Instructor at Princeton University, and before that, a Hedrick Assistant Professor at UCLA.
Here is my CV (last updated: December 2023).

My research is partially supported by the NSF grant DMS-2401321 and by the 2024-2025 AMS Centennial Research Fellowship.

I help organize the Seminar on Geometry and Arithmetic

Research Interests: Number Theory and Arithmetic Geometry.
More specifically: p-adic L-functions, Euler systems and Iwasawa theory.

Preprints and Publications

Note: Preprints posted here (click on title) may be more up to date than the arXiv versions.

• Tamagawa number conjecture for CM modular forms and Rankin-Selberg convolutions.
  preprint.  
• Exceptional zeros for Heegner points and p-converse to the theorem of Gross-Zagier and Kolyvagin.
  preprint.  
• Base change and Iwasawa Main Conjectures for GL2.
  (with A. Burungale and C. Skinner)
  preprint.  
• Critical Lambda-adic modular forms and bi-ordinary complexes.
  (with C. Wang-Erickson)
  preprint.  
• Nonvanishing of Kolyvagin systems and Iwasawa theory.
  (with A. Burungale, G. Grossi, and C. Skinner)
  preprint.  
• Derived p-adic heights and the leading coefficient of the Bertolini-Darmon-Prasanna p-adic L-function.
  (with C.-Y. Hsu, D. Kundu, Y.-S. Lee, and Z. Liu)
  preprint.  
• On the Iwasawa theory of elliptic curves at Eisenstein primes.
  Proceedings of the 2022 ICTS workshop Elliptic curves and the special values of L-functions, to appear.  
• Nonvanishing of generalised Kato classes and Iwasawa main conjectures.
  Elliptic curves and modular forms in arithmetic geometry (Massimo Bertolini's 60th birthday proceedings), to appear.  
• Diagonal cycles and anticyclotomic Iwasawa theory of modular forms.
  (with K. T. Do)
  preprint.  
• Generalised Kato classes on CM elliptic curves of rank 2.
  preprint.  
• Mazur's main conjecture at Eisenstein primes.
  (with G. Grossi and C. Skinner)
  preprint.  
• On the Iwasawa main conjectures for modular forms at non-ordinary primes.
  (with M. Çiperiani, C. Skinner, and F. Sprung)
  preprint.  
• Perrin-Riou's main conjecture for elliptic curves at supersingular primes.
  (with X. Wan) Math. Annalen, 389 (2024), no. 3, 2595-2636.  
• An anticyclotomic Euler system for adjoint modular Galois representations.
  (with R. Alonso and Ó. Rivero) Ann. Inst. Fourier, to appear.  
• The diagonal cycle Euler system for GL2 × GL2.
  (with R. Alonso and Ó. Rivero) J. Inst. Math. Jussieu, to appear.  
• Iwasawa-Greenberg main conjecture for non-ordinary modular forms and Eisenstein congruences on GU(3,1).
  (with Z. Liu and X. Wan) Forum Math. Sigma, 10 (2022), e110, 90 pp. addendum  
• On the anticyclotomic Iwasawa theory of rational elliptic curves at Eisenstein primes.
  (with G. Grossi, J. Lee, and C. Skinner) Invent. Math., 227 (2022), no. 2, 517-580.  
• Class groups and local indecomposability of non-CM forms. With an appendix by Haruzo Hida.
  (with C. Wang-Erickson) J. Eur. Math. Soc. (JEMS), 24 (2022), no. 4, 1103-1160.  
• The Iwasawa Main Conjectures for GL2 and derivatives of p-adic L-functions.
  (with X. Wan) Adv. Math., 400 (2022), 108266, 45 pp.  
• On the nonvanishing of generalised Kato classes for elliptic curves of rank 2.
  (with M.-L. Hsieh) Forum Math. Sigma, 10 (2022), e12, 32 pp.  
• p^∞-Selmer groups and rational points on CM elliptic curves.
  (with A. Burungale, C. Skinner, and Y. Tian) Annales Math. Québec, Special issue in honor of Bernadette Perrin-Riou, 46 (2022), no. 2, 324-346.  
• On anticyclotomic variants of the p-adic Birch-Swinnerton-Dyer conjecture.
  (with A. Agboola) J. Théor. Nombres Bordeaux, Iwasawa 2019 special issue, 33 (2021), no. 3.1, 629-658.  
• A proof of Perrin-Riou's Heegner point main conjecture.
  (with A. Burungale and C.-H. Kim) Algebra Number Theory, 15 (2021), no. 7, 1627-1653.  
• On the p-adic variation of Heegner points.
  J. Inst. Math. Jussieu, 19 (2020), no. 6, 2127-2164.  
• On the p-part of the Birch-Swinnerton-Dyer formula for multiplicative primes.
  Cambridge J. Math., 6 (2018), no. 1, 1-23. erratum  
• Heegner cycles and p-adic L-functions.
  (with M.-L. Hsieh) Math. Annalen, 370 (2018), no. 1-2, 567-628. erratum  
• On the exceptional specializations of big Heegner points.
  J. Inst. Math. Jussieu, 17 (2018), no. 1, 207-240.  
• p-adic heights of Heegner points and Beilinson-Flach classes.
  J. Lond. Math. Soc., 96 (2017), no. 1, 156-180.  
• Variation of anticyclotomic Iwasawa invariants in Hida families.
  (with C.-H. Kim and M. Longo) Algebra Number Theory, 11 (2017), no. 10, 2339-2368.  
• A geometric perspective on p-adic properties of mock modular forms.
  (with L. Candelori) Research Math. Sci., 4 (2017), paper no. 5, 15 pp.  
• Big Heegner points and special values of L-series.
  (with M. Longo) Annales Math. Québec, Special issue in honor of Glenn Stevens' 60th birthday, 40 (2016), no. 2, 303-324.  
• p-adic L-functions and Euler systems: a tale in two trilogies.
  (with M. Bertolini, H. Darmon, S. Dasgupta, K. Prasanna, and V. Rotger) Automorphic Forms and Galois Representations, Lond. Math. Soc. Lecture Note Ser., 414 (2014), 52-101.  
• Heegner cycles and higher weight specializations of big Heegner points.
  Math. Annalen, 356 (2013), no. 4, 1247-1282.  

Other Writings

• Propagating the Iwasawa main conjecture via congruences.
  Projects for the course by Christopher Skinner in AWS 2018.  
• On the p-adic variation of Heegner points.
  My PhD thesis (McGill, 2013), under the direction of Henri Darmon.  
• Ordinary CM forms and local Galois representations.
  My MSc thesis (UPC, 2009), under the direction of Victor Rotger.  

Teaching