Main areas of research: p-adic eigenvarieties, PEL Shimura varieties, Mazur’s Galois deformation theory, p-adic Hodge theory, Iwasawa theory and p-adic L-functions. 

Preprints

1) CM congruence and trivial zeros of the Katz p-adic L-functions for CM fields (with M.L Hsieh). Submitted (arXiv).  (Notes based on this work of my talk at Bordeaux).

2) Eisenstein points on the Hilbert cuspidal Eigenvariety (with M. Dimitrov and S.C. Shih), Submitted (arXiv).

(Notes based on this work of my talk at UC Santa Barbara).

3) Eisenstein congruences for GU(2,1) and higher derivatives of Katz p-adic L-functions for CM fields (with M.L Hsieh). Available soon. 

4) Eigenvarieties for non-cuspidal modular forms over certain PEL Shimura varieties (with R. Brasca and G. Rosso). Available soon. 

5) p-adic adjoint L-function on the Hilbert eigenvariety and Higher Coleman Theory. In preparation. 

Publications (Sorted by arXiv submission date): (My most important papers are highlighted in color)

1) Arithmetic of p-irregular modular forms: families and p-adic L-functions, (with C. Williams), Mathematika, 67 (2021), no.4, pp.917-948 (arXiv version).

2) A geometric view on Iwasawa theory (with M. Dimitrov), J. Théor. Nombres Bordx. 33, No. 3, Part 1, 703-731 (2022). pdf. 

3) Geometry of the Eigencurve at CM points and trivial zeros of Katz p-adic L-functions, (with M. Dimitrov), Adv. Math. 384 (2021). (DOI: https://doi.org/10.1016/j.aim.2021.107724). pdf. 

4) On Siegel eigenvarieties at Saito-Kurokawa points, (with T. Berger),  Ann. Inst. Fourier (Grenoble) 72 (2022), no. 3, 901–961. (DOI : 10.5802/aif.3482). pdf. 

5) On the Hilbert eigenvariety at exotic and CM classical weight 1 points, (with S. Deo and F. Fité), Math. Z. (2020). (DOI: https://doi.org/10.1007/s00209-020-02626-1). pdf. 

6) On the failure of Gorensteinness at weight 1 Eisenstein points of the eigencurve, (with M. Dimitrov and A. Pozzi), American Journal of Mathematics 144 (1), 227-‌265, 2022. pdf. 

7) Congruence Formulae for Legendre modular polynomials, (with E. Lecouturier), J. Number Theory 188 (2018), 71-87 (Elsevier) (DOI: https://doi.org/10.1016/j.jnt.2018.01.006). pdf. 

8) On the p-adic periods of the modular curve X(Γ0(p) ∩ Γ(2)), (with E. Lecouturier), Trans. Amer. Math. Soc. 371 (2019), no. 1, 413-429 (DOI: https://doi.org/10.1090/tran/7236). pdf. 

9) Les Variétés de Hecke-Hilbert aux points classiques de poids parallèle 1, J. Théor. Nombres Bordx. 30 (2018), no. 2, 575-607 (Doi: https://doi.org/10.5802/jtnb.1040). pdf. 

10) Ramification of the Eigencurve at classical RM points, Canad. J. Math. 72 (2020), no. 1, 57-88 (DOI: https://doi.org/10.4153/CJM-2018-029-4). pdf. 

Upcoming talks

20/12/2023 University of Luxembourg, Luxembourg, The Luxembourg Number Theory Day 2023. Title: Eigenvarieties for non-cuspidal modular forms over PEL Shimura varieties.

EXPOSITORY NOTES

Eisenstein intersection points on the Hilbert Eigenvariety (Notes of my talk in the seminary of geometry and arithmetic in UC Santa Barbara).

• My Talk in the study group on K3 Surfaces at Sheffield University (Autumn 2019). pdf. 

• Notes of my talk in the seminary of number theory at the University of Copenhagen. pdf.

Thesis (06/2016)

• "Structure locale des Variétés de Hecke aux points classiques de poids 1" , at Université de Lille and under the direction of the professor Mladen Dimitrov. (pdf)