Address: | Department of Mathematics Princeton University Fine Hall, Washington Road Princeton, NJ 08544 United States |
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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, a Hedrick Assistant Professor at UCLA.
My research is partially supported by NSF grant DMS-1801385.
For more details, please see my CV (as of September 2018).
Research Interests: Number Theory and Arithmetic Geometry.
More specifically: p-adic L-functions, Euler systems and Iwasawa theory.
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) | ||
Preprint. | ||
▪ | Class groups and local indecomposability of non-CM forms. | |
(joint with Carl Wang-Erickson) | ||
Preprint. | ||
▪ | 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] | ||
▪ | 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. | ||
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 |