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 at Princeton,
and before that, I was a Hedrick Assistant Professor at UCLA.

My research is partially supported by NSF grant DMS-1801385.

Here is my CV (as of September 2018).


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 2.
(joint with Ming-Lun Hsieh)
Submitted.
Class groups and local indecomposability of non-CM forms, with an appendix by Haruzo Hida.
(joint with Carl Wang-Erickson)
Submitted.
Indivisibility of Heegner points and arithmetic applications.
(joint with Ashay Burungale and Chan-Ho Kim)
Submitted.
Rankin-Eisenstein classes, big Heegner points, and main conjectures for GL2.
(joint with Xin Wan)
Preprint.
On the Iwasawa main conjectures for modular forms at non-ordinary primes.
(joint with Mirela Çiperiani, Christopher Skinner, and Florian Sprung)
Submitted.
Perrin-Riou's main conjecture for elliptic curves at supersingular primes.
(joint with Xin Wan)
Submitted.
On the p-part of the Birch-Swinnerton-Dyer formula for multiplicative primes.
Cambridge Journal of Mathematics, 6 (2018), no. 1, 1-23. [journal]
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.
(joint with Chan-Ho Kim and Matteo Longo)
Algebra & Number Theory, 11 (2017), no. 10, 2339-2368. [journal]
Heegner cycles and p-adic L-functions.
(joint with Ming-Lun Hsieh)
Mathematische Annalen, 370 (2018), no. 1-2, 567-628. [journal] erratum
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.
(joint with Luca Candelori)
Research in the Mathematical Sciences, 4:5 (2017), 15 pp. [journal]
Big Heegner points and special values of L-series.
(joint with Matteo 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.
(joint with Massimo Bertolini, Henri Darmon, Samit Dasgupta, Kartik Prasanna, and Victor Rotger)
London Mathematical Society Lecture Note Series, 414 (2014), 52-101. [chapter]

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

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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