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, (with M.-L. Hsieh). Submitted.
Class groups and local indecomposability of non-CM forms, (with C.-W. Erickson). With an appendix by Haruzo Hida. Submitted.
Indivisibility of Heegner points and Perrin-Riou's main conjecture, (with A. Burungale and C.-H. Kim). Submitted.
Rankin-Eisenstein classes, big Heegner points, and main conjectures for GL2, (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.
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 for 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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