Francesc Castella

Address: Department of Mathematics
Princeton University
Fine Hall, Washington Road
Princeton, NJ 08544
United States
Email: fcabello at math dot princeton dot edu

I am an Instructor at Princeton University. Previously, I was an Associate Research Scholar here,
and before that, a Hedrick Assistant Professor at UCLA.

For more details, please see my CV (as of November 2017).


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 Iwasawa main conjectures for modular forms at non-ordinary primes.
(with M. Çiperiani, C. Skinner, and F. Sprung). Preprint.
On the p-part of the Birch-Swinnerton-Dyer formula for multiplicative primes.
Cambridge Journal of Mathematics, to appear.
Perrin-Riou's main conjecture for elliptic curves at supersingular primes.
(with X. Wan). Submitted.
p-adic heights of Heegner points and Beilinson-Flach classes.
Journal of the London Mathematical Society, 96 (2017), no. 1, 156-180. [journal]
On the p-adic variation of Heegner points.
Journal de l'Institut Mathématique de Jussieu, to appear.
Variation of anticyclotomic Iwasawa invariants in Hida families.
(with C.-H. Kim and M. Longo). Algebra & Number Theory, 11 (2017), no. 10, 2339-2368. [journal]
Heegner cycles and p-adic L-functions.
(with M.-L. Hsieh). Mathematische Annalen, 370 (2018), no. 1-2, 567-628. [journal]
On the exceptional specializations of big Heegner points.
Journal de l'Institut Mathématique de Jussieu, 17 (2018), no. 1, 207-240. [journal]
A geometric perspective on p-adic properties of mock modular forms.
(with L. Candelori). Research in the Mathematical Sciences, 4:5 (2017), 15 pp. [journal]
Big Heegner points and special values of L-series.
(with M. Longo). Annales Mathématiques du Québec, 40 (2016), no. 2, 303-324. [journal]
Heegner cycles and higher weight specializations of big Heegner points.
Mathematische Annalen, 356 (2013), no. 4, 1247-1282. [journal]
p-adic L-functions and Euler systems: a tale in two trilogies.
(with M. Bertolini, H. Darmon, S. Dasgupta, K. Prasanna, and V. Rotger).
London Mathematical Society Lecture Note Series, 414 (2014), 52-101. [chapter]

Other Writings

On the p-adic variation of Heegner points.
PhD thesis (advisor: Prof. Henri Darmon).
Ordinary CM forms and local Galois representations.
MSc thesis (advisor: Prof. Victor Rotger).
Propagating the Iwasawa main conjecture via congruences.
Project descriptions for AWS 2018 (course leader: Prof. Chris Skinner).

Teaching

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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