Arithmetic Geometry, Number Theory, Definability and Decidability in Number Theory

Students

• Javier Reyes Bastidas. "Sucesiones de potencias que anulan ciertos operadores de diferencia." Undergraduate. 2019.
• Fernanda Cares Cuevas, "Isogenias de curvas elípticas y su relación con representaciones de Galois." Undergraduate. 2019.
• Pedro Mendoza Roca, "Arithmetic progressions of integral points on congruent elliptic curves of rank two." M.Sc. 2019.
• Pedro Contreras Peña, "Cota de Hurwitz para automorfismos sobre superficies de Riemann." Undergraduate. 2018.

Teaching

• MPG3200 (Graduate Algebra I). First semester 2020.
• MAT1620 (Calculus II). First semester 2020.
• MAT1306 (Introduction to Geometry). Second semester 2019.
• MAT2405 (Foundations of Mathematics). First semester 2019.
• MAT2205 (Abstract Algebra I). Second semester 2018.
• MAT2335 (Introduction to Algebraic Geometry). First semester 2018.
• MAT1620 (Calculus II). Second semester 2017.

Organization:

• Director of the Female Math Olympiad Training of the Chilean Mathematical Society. March 2018-present.
• Organizer and founder (with Constanza del Campo y Fernanda Cares) of the series of mathematical talks "Club de Matemática" at Pontificia Universidad Católica de Chile. September 2017-present.
• Scientific committee for the "8th Jornadas de Teoría de Números", to be held in Vilanova i la Geltrú, Spain. 2019.
• Organizing committee for the Latin American School of Algebraic Geometry and Applications (ELGA IV), to be held in Talca, Chile. December 2-13, 2019.
• Organizer and founder (with Hector Pasten) of "Seminario de Teoría de Números" at Pontificia Universidad Católica de Chile. March 2018-present.
• Organizer and founder (with David Grimm and Giancarlo Lucchini) of "Santiago Number Theory and Algebra Seminar (SaNTAS)". January 2018-present.
• Organizing committee for the thematic session "Geometría Algebraica y Aritmética" at LXXXVI Encuentro Anual de la Sociedad de Matemática de Chile. Talca, Chile. November 2-4, 2017.

Academic visits:

• Institut de Mathématiques de Jussieu-Paris Rive Gauche, France. February 16-March 3, 2019. Invited by Loïc Merel.
• Department of Mathematics, Utrecht University, The Netherlands. February 2-16, 2019. Invited by Damaris Schindler.
• Department of Mathematics, Harvard University, USA. February 1-26, 2018. Invited by Hector Pasten.
• Institut de Mathématiques de Bordeaux, Université de Bordeaux, France. December 6-15, 2017. Invited by Yuri Bilu.
• Departament de Matemàtiques, Universitat Autònoma de Barcelona, Spain. June 19-25, 2017. Invited by Xavier Xarles.
• Mathematical Institute, University of Oxford, England. October 31- November 04, 2016. Invited by Jochen Koenigsmann.
• Departament de Matemàtiques, Universitat Autònoma de Barcelona, Spain. October 15-22, 2016. Invited by Xavier Xarles.
• Institute of Mathematics, Academia Sinica, Taiwan. May 07-28, 2016. Invited by Julie Tzu-Yueh Wang.

Conference talks:

• Sobre el décimo problema de Hilbert para anillos de enteros. XXXII Jornada de Matemática de la Zona Sur. Punta Arenas, Chile. April 24-26, 2019.
• Ranks of elliptic curves and arithmetic progressions of rational points. Explicit Number Theory. Universidad de Valparaíso. January 7-11, 2019.
• Ranks of elliptic curves and arithmetic progressions of rational points. 15th meeting of the Canadian Number Theory Association (CNTA XV). Université Laval. July 9-13, 2018.
• Mini course: Rangos de curvas elípticas y progresiones aritméticas de puntos racionales. V Encuentro Chileno de Teoría de Números. Universidad de Chile. May 14-16, 2018.
• Rangos de curvas elípticas y progresiones aritméticas de puntos racionales. XXXI Jornada de Matemática de la Zona Sur. Valdivia, Chile. April 25-27, 2017.
• Variations of the truncated Nevanlinna-Cartan's theorem in the context of function fields. Geometry at the Frontier II. Pucón, Chile. November 15-17, 2017.
• Curvas de género bajo en superficies y aplicaciones aritméticas. Subplenary talk at LXXXVI Encuentro Anual de la Sociedad de Matemática de Chile. Talca, Chile. November 2-4, 2017.
• Curves of low genus and applications to Diophantine problems. Talk at the Arithmetic Geometry and Related Topics Special Session of the Mathematical Congress of the Americas MCA 2017. Montreal, Canada. July 24-28, 2017.
• Curves of low genus and arithmetic applications. Plenary talk at Séptimas Jornadas de Teoría de Números. Lleida, Spain. June 26-29, 2017.
• "Curves of low genus on surfaces and some extensions of Büchi's problem." Workshop on Definability and Decidability Problems in Number Theory, Mathematisches Forschungsinstitut Oberwolfach, Germany. October 23-29, 2016.
• "Symmetric differentials and some applications in the arithmetic of function fields." Maine-Québec Number Theory conference, Université Laval, Canada. October 8-9, 2016.
• "Curves of low genus and applications to Diophantine problems." 14th meeting of the Canadian Number Theory Association (CNTA XIV), University of Calgary, Canada. June 20-24, 2016.
• "Curves of low genus and applications." Current trends in Diophantine geometry and transcendence. National Taiwan University, Taiwan. May 23-27, 2016.
• "Powers with constant second differences." Workshop on algebraic varieties. Fields Institute, Canada. November 21-22, 2015.
• "Curves of low genus on surfaces." Workshop on algebraic varieties. Fields Institute, Canada. November 15-16, 2014.
• "Hilbert's 10th Problem for one variable non-Archimedean entire functions." 13th Conference of the Canadian Number Theory Association (CNTA XIII). Ottawa, Canada. June 16-20, 2014.
• "A note on generalized power series in the non-Archimedean context." Satellite Meeting of the First AMS-SOMACHI meeting. Pucón, Chile. December 13-14, 2010.
• "Completación esférica del campo Levi-Civita." Seventh National Conference of Non-Archimedean Analysis. Temuco, Chile. August 5-6, 2010.

Seminar talks:

• "Variaciones del Segundo Teorema Fundamental de Nevanlinna-Cartan para campos de funciones y las Conjeturas de Vojta." Seminario Lógica y Teoría de Números. Universidad de Concepción. August 2019.
• "Extensions of the truncated Nevanlinna-Cartan theorem in the context of function fields." Séminaire de théorie des nombres de l'IMJ-PRG. February 2019.
• "Ranks of elliptic curves and arithmetic progressions of rational points." Utrecht Geometry Center Seminar, Universiteit Utrecht. February 2019.
• "Rangos de curvas elípticas y progresiones aritméticas de puntos racionales." Coloquio de Matemática, Universidad de Chile. Septiembre 2018.
• "Rangos de curvas elípticas y progresiones aritméticas de puntos racionales." Coloquio de Matematica UC, Pontificia Universidad Católica de Chile. Agosto 2018.
• "Variaciones del Segundo Teorema de Nevanlinna-Cartan para cuerpos de funciones." Seminario Aritmética y Geometría en Valparaíso, Instituto de Matemática de la Pontificia Universidad Católica de Valparaíso. Abril 2018.
• "Curves of low genus on surfaces and applications. Number Theory Seminar, University of Georgia. Winter 2018.
• "Arithmetic applications of omega-integral curves." Séminaire de Théorie des Nombres de Bordeaux, Université de Bordeaux. Fall 2017.
• "From arithmetic undecidability to curves on surfaces." Québec-Vermont Number Theory Seminar, McGill University. Winter 2017.
• "Curvas de Género Bajo en Superficies y Aplicaciones Aritméticas." Talk at Pontificia Universidad Católica de Chile. December 2016.
• "Curvas de género bajo y las conjeturas de Mohanty." Talk at Universidad de Concepción. December 2016.
• "Arithmetic applications of w-integral curves in varieties." Joint Number Theory/Logic seminar, University of Oxford. Fall 2016.
• "Curves of low genus and k-th power consecutive values of quadratic polynomials." Seminari Geometria Algebraica, Universitat de Barcelona/Universitat Politècnica de Catalunya/Universitat Autònoma de Barcelona. Fall 2016.
• "Variaciones del Segundo Teorema Fundamental de Nevanlinna-Cartan para cuerpos de funciones." Talk at Universitat Autònoma de Barcelona. Fall 2016.
• "Variations of the truncated Nevanlinna-Cartan's Second Main Theorem for function fields." Number/Representation theory seminar, University of Toronto. Fall 2016.
• "Powers with second differences equal to 2." Arithmetic geometry seminar, Taida Institute for Mathematical Sciences. Summer 2016.
• "Curves of low genus on surfaces and some applications to Diophantine problems." Number/Representation theory seminar, University of Toronto. Fall 2015.
• "Diagonal quotient surfaces and the box variety." GANITA seminar, University of Toronto. Fall 2015.
• "Squares with constant second differences." Calabi-Yau seminar, Queen's University. Winter 2015.
• "Curvas de género bajo en superficies." Talk at Universidad de Concepción. January 2015.
• "Curves of low genus on surfaces." Number theory seminar, Queen's University. Fall 2014.
• "The box variety." Calabi-Yau seminar, Queen's University. Fall 2014.
• "Mazur's Question and moduli spaces." Number theory seminar, Queen's University. Winter 2014.
• "The Bombieri-Lang conjecture." Number theory seminar, Queen's University. Fall 2013.
• "Isogenies and Galois representation of elliptic curves." Number theory seminar, Queen's University. Summer 2013.
• "Powers in arithmetic progression." Graduate seminar, Queen's University. Winter 2013.
• "Elliptic surfaces." Calabi-Yau seminar, Queen's University. Winter 2012.