Daniel Barrera Salazar 

I am currently associate professor at Universidad de Santiago de Chile

My CV (updated October 2024)

I am interested in number theory and algebraic geometry. More precisely my research treats p-adic L-functions, p-adic variation and arithmetic applications. 

Papers and preprints

Strong multiplicity-one for Bianchi Eisenestein eigensystems and the the eigenvariety around non-cuspidal points,  (with Luis Santiago Palacios), preprint 2024.

On the 2-Selmer group of Jacobians of hyperelliptic curves,  (with Ariel Pacetti and Gonzalo Tornaría), preprint 2023.

 On p-refined Friedberg-Jacquet integrals and the classical symplectic locus in the GL2n eigenvariety , (with  Andrew. Graham and Chris  Williams), preprint 2023. 

On the GL(2n) eigenvariety: branching laws, Shalika families and p-adic L-functions  , (with  Mladen Dimitrov,  Andrew. Graham, Andrei Jorza and Chris  Williams), preprint 2022. 

On p-adic L-functions for GL(2n) in finite-slope Shalika families , (with  Mladen Dimitrov and Chris  Williams), preprint 2021.

Parabolic eigenvarieties via overconvergent cohomology, (with Chris  Williams), Mathematische Zeitschrift (No.1), 299 (2021), pp.961-995.

Overconvergent cohomology, p-adic L-functions and families for GL(2) over CM fields, (with Chris  Williams), Journal de Théorie des Nombres de Bordeaux (No. 3), 33 (2021), (Iwasawa 2019 special issue), pp.659-701.

On 2-Selmer groups and quadratic twists of elliptic curves  (with Ariel Pacetti, Gonzalo Tornaría),  Mathematical Research Letters (No. 6), 28 (2021), pp. 1633—1659.

Triple product p-adic L-functions for Shimura curves over totally real fields (with Santiago Molina), Ann. Inst. Fourier, to appear.. 

Overconvergent Eichler-Shimura isomorphisms for unitary Shimura curves over totally real fields (with Shan Gao), Israel Journal of Mathematics, 242 (2021), pp. 707--767. 

Families of Bianchi modular symbols: critical base-change p-adic L-functions and p-adic Artin formalism (with Chris  Williams) (with an appendix by Carl Wang-Erickson), Selecta Mathematica (No. 82), 27 (2021), pp. 1-45.

p-adic L-functions for nearly finite flope Hilbert modular forms and the exceptional zero conjecture (with Mladen Dimitrov and Andrei Jorza), Jounal of the European Mathematical Society (No. 10), 24 (2022), pp.  3439--3503.

p-adic L-functions for GL(2) (with Chris  Williams), Canadian Journal of Mathematics (No. 5), 71 (2019), pp. 1019--1059.

Exceptional zeros of p-adic L-functions of Bianchi modular forms (with Chris  Williams), Trans. AMS (No. 1), 372 (2019), pp. 1--34.

Overconvergent cohomology of Hilbert modular varieties and p-adic L-functions , Ann. Inst. Fourier, 68 (2018), pp. 2177--2213.

Overconvergent Eichler-Shimura isomorphisms for quaternionic modular forms over Q (with Shan Gao), Int. Journal of Number Theory (No. 10), 13 (2017), pp. 2487--2504.

On critical values of L-functions of potentially automorphic motives (with Lucio Guerberoff), Manuscripta Mathematica (3-4), 156 (2017), pp. 341--371.

Research activities  

Arithmetic and p-adic geometry in Chile, summer school and conference (2-13 December 2024). Co-organized with R. Brasca, H. del Castillo, F. Castillo,  A. Iovita, R. Labarca, J. Lang, R. Menares and G. Rosso.

Los problemas del Milenio coorganizado junto a Centro de Alumnos INGEMAT, Héctor del  Castillo y Patricio Cerda. 2024 USACH.

Seminario teoría de Cuerpos de clases explícita coorganizado junto a Ricardo Menares y Patricio Perez. 2024 PUC-USACH

Seminario SANTAS  coorganizado junto a Federico Castillo, Héctor del Castillo y Giancarlo Lucchini. Seminario de Algebra, Teoría de números, y áreas afines organizado en conjunto entre la PUC, la U. de Chile, y la USACH.

Past activities

Jornada de Geometría Aritmética, coorganizado con Sebastián Herrero. 29 Noviembre 2023. 

Seminario Automorfo, coorganizado con Hector del Castillo y Sebastián Herrero.  Octubre 2023 a Enero 2024.  USACH. 

Seminario Puntos de Darmon, coorganizado con Sebastián Herrero, Ricardo Menares y Patricio Perez. Agosto-Diciembre 2023. PUC.

Jornada Promoción Doctorado USACH, 25 Agosto 2023, USACH (participación online posible!). Coorganizador.

Course "Algebra Commutativa" organized with David Grimm . March 2023- August 2023. 

VII Encuentro regional de Teoría de Números, co-organize. Universidad Nacional de Córdoba, Argentina.  17, 18 y 19 de Mayo, 2023. 

Jornada sobre Representaciones Automorfas y Teoría de Números, organized with Hector del Castillo and Cristobal Rivas, 26/01/2023. 

Seminario  Funtorialidad de Langlands y variación p-ádica, organized with Hector del Castillo y Luis Palacios. Marzo 2022-  Enero 2023. 

Mini course about GGP conjectures by Xenia Dimitrakopoulou (Warwick University). 12, 16, 19 January 2023.

Curso "Una introducción a las curvas de Shimura".  Agosto 2022- Enero 2023. 

Mini course An introduction to Proof Assistants by Riccardo Brasca . organized with Hector del Castillo. 26/10, 27/10 and 02/11. 2022

Encuentro Usachino de Teoría de Números y Álgebra  organized with Hector del Castillo. Wednesday May 4, 2022.  USACH.

Seminario Latinoamericano de Teoría de Números LATeN . 

Course "Una introducción a las curvas de Shimura".  March 2022- July 2022. 

Seminario (introductivo) de Representaciones automorfas y Variedades de Shimura, Octubre 2021-January 2022. Detalles visitar el sitio.  

Course "Algebra Commutativa" organized with David Grimm . March 2021- July 2021, 

Course, "Curvas elíptica, períodos y deformación",  End of August 2020- January 2021.  To see the talks and schedule click  aquí.  

Special thematic semester  Cohomology in Arithmetic , CRM, September-December 2020.

Course ,  ``Ceros excepcionales refinados y p-ádicos'' April- August 2020.

Course  ''Topics in Iwasawa theory and Euler Systems", USACH , March- August 2020. (POSTPONED)

Jornada de Teoría de Números y Representaciones, organized with Luis Lomelí. USACH, January 2020.