Francesc Castella

Address: Department of Mathematics
University of California, Santa Barbara
South Hall, Room 6511
Santa Barbara, CA 93106
United States
Email: castella at ucsb dot edu

I am an Assistant 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: October 2019).

My research is partially supported by the NSF grant DMS #1801385 and #1946136.


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.

On the non-vanishing of generalized Kato classes for elliptic curves of rank two, (with M.-L. Hsieh). Submitted.
On anticyclotomic variants of the p-adic Birch-Swinnerton-Dyer conjecture, (with A. Agboola). Preprint.
A proof of Perrin-Riou's Heegner point main conjecture, (with A. Burungale and C.-H. Kim). Submitted.
The Iwasawa main conjectures for GL2 and derivatives of p-adic L-functions, (with X. Wan). Preprint.
On the Iwasawa main conjectures for modular forms at non-ordinary primes, (with M. Çiperiani, C. Skinner, and F. Sprung). Submitted.
Perrin-Riou's main conjecture for elliptic curves at supersingular primes, (with X. Wan). Submitted.
Class groups and local indecomposability of non-CM forms, (with C. Wang-Erickson). With an appendix by Haruzo Hida.
J. Eur. Math. Soc. (JEMS), to appear.
On the p-adic variation of Heegner points.
J. Inst. Math. Jussieu, to appear.
On the p-part of the Birch-Swinnerton-Dyer formula for multiplicative primes.
Cambridge J. Math. 6 (2018), no. 1, 1-23.
On the exceptional specializations of big Heegner points.
J. Inst. Math. Jussieu 17 (2018), no. 1, 207-240.
Heegner cycles and p-adic L-functions, (with M.-L. Hsieh).
Math. Annalen 370 (2018), no. 1-2, 567-628. erratum
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).
Res. 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.
Project descriptions for the course by Christopher Skinner in AWS 2018.
On the p-adic variation of Heegner points.
PhD thesis, McGill, 2013, under the direction of Henri Darmon.
Ordinary CM forms and local Galois representations.
MSc thesis, Barcelona, 2009, under the direction of Victor Rotger.

Teaching

Spring 2019 MAT 419: Algebraic Number Theory
Fall 2018 MAT 419: Arithmetic of Elliptic Curves
Spring 2018 MAT 202: Linear Algebra with Applications
Fall 2017 MAT 511: Class Field Theory
Spring 2017 MAT 175: Multivariable Calculus for Economics and Life Sciences
Fall 2016 MAT 175: Multivariable Calculus for Economics and Life Sciences
Spring 2016 Math 132: Complex Analysis for Applications
Winter 2016 Math 132: Complex Analysis for Applications
Fall 2015 Math 33A: Linear Algebra and Applications
Fall 2015 Math 132: Complex Analysis for Applications
Spring 2015 Math 117: Algebra for Applications
Winter 2015 Math 31B: Integration and Infinite Series
Winter 2015 Math 110A: Algebra
Fall 2014 Math 207: Topics in Number Theory
Spring 2014 Math 33A: Linear Algebra and Applications
Fall 2013 Math 31A: Differential and Integral Calculus
Fall 2013 Math 115A: Linear Algebra

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