Teaching
Undergraduate level
- Universidad Complutense de Madrid:
2022/23 Differential Geometry of curves and surfaces, 3rd and 4th year students, Mathematics and Physics degree and Computer engineering degree.
2022/23 Physics with applications to Economy, 2nd year students, Economy and Mathematics degree.
2019/22 History of Mathematics, 3rd and 4th year students, Mathematics degree.
2019/22 Differential Geometry with applications,, 3rd year students, Mathematics Engineering degree.
2019/22 Elements of Mathematics, 1st year students, several degrees.
- University of Plymouth:
2017/19 Real and Complex Analysis, 2nd year students.
2016/19 Optimisation, Graphs and Networks, 3rd year students.
2016/19 Data Mining and Algorithms, foundation year students.
- University of Oxford:
2016/17 Algebraic Topology C3.1, intercollegiate tutorials, 3rd year, MSc. and PhD. students.
- Universidad Autónoma de Madrid:
2012/14 Topology and Geometry, 4th year students.
2011/12 Curves and Surfaces Geometry, problem sessions, 2nd year students.
2010/11 Linear Algebra and Geometry, problem sessions, 1st year students.
MSc. and PhD. level
- University of Oxford:
2016/17 Algebraic Topology C3.1, intercollegiate tutorials, 3rd year, MSc. and PhD. students.
- Instituto de Ciencias Matemáticas (ICMAT):
2013 Algebraic Geometry with Analytic Techniques, JAE School of Mathematics (10h).
2012 Complex Geometry and Gauge Theories (with a short introduction to the Hodge conjecture), JAE School of Mathematics (10h).
2011/12 Algebraic Topology, Master and PhD. Students in Physics and Mathematics (30h).
2011 Introduction to Morse Theory, JAE School of Mathematics (10h).
Students supervision
PhD. Theses advised/ing
- MSc. Alberto Lopez Moral (co-advised with Prof. Enrique Arrondo) (started 2020)
- Dr. José Angel González Prieto "Topological Quantum Field Theories for Character Varieties" (co-advised with Prof. Vicente Muñoz Velázquez) (2018)
MSc. Theses supervised/ing
- Mr. Santiago Pareja Pérez, " Introducción a las teorías topológicas de campos cúanticos y algunas aplicaciones" (co-advised with Prof. Ángel González-Prieto), Universidad Complutense de Madrid (started 2023)
- MSc. Victor Vela Cuena, "Representaciones del grupo fundamental orbifold y fibrados parabólicos", Universidad Complutense de Madrid (2022).
- MSc. Samuel Ranz, "Geometric invariant theory and symplectic quotients", Universidad Autónoma de Madrid (2016).
- Dr. José Angel González Prieto, "Deligne-Hodge polynomials of character varieties of doubly periodic instantons", (co-advised with Prof. Vicente Muñoz Velázquez), Universidad Autónoma de Madrid (2015).
BSc. Theses supervised/ing
- Mr. Sergio Alvira del Olmo, "Fibrados vectoriales en física y geometría", (started 2023).
- Mr. Jaime Jacobo Romo González, "El problema isoperimétrico y las curvas de Bezier", (started 2023).
- Ms. Elisa Ramírez García, "El péndulo", (started 2022).
- Ms. Claudia Sanchez Martín, "La transformación de Tschirnhaus", Universidad Complutense de Madrid (started 2022).
- Ms. Laura Herrero García, "Herramientas geométricas para la música", Universidad Complutense de Madrid (2023).
- Mr. Javier Sempere Hernández, "Aproximación de puntos vía curvas de Bezier generalizadas", (2023).
- Ms. Lucía Municio Padilla, "Las 27 líneas de una superficie cúbica", (co-supervised with Prof. Ángel González Prieto), Universidad Complutense de Madrid (2023)
- Ms. Beatriz del Pozo Martín, "Curvas elípticas: automorfismos y teorema de Hurwitz", Universidad Complutense de Madrid (2023).
- Ms. Aura Jiménez Rodríguez, "Domingo de Soto y el nacimiento de la mecánica clásica", Universidad Complutense de Madrid (2022).
- Mr. Marcos Truchuelo Rodríguez, "Una aproximación algebraico geométrica a la optimización no lineal", Universidad Complutense de Madrid (2022).
- Mr. Arturo Anadón González, "Singularidades de la teoría general de la relatividad", Universidad Complutense de Madrid (2021).
- Ms. Andrea Blanco Delgado, "Curvas de Bezier complejas aplicadas a la geometría de ciertos polígonos", Universidad Complutense de Madrid (2021).
- Mr. Raúl Peral Muela, "Demostraciones Geométricas Automáticas", Universidad Complutense de Madrid (2020).
- Dr. Ángel González Prieto, "El teorema del h-cobordismo", Universidad Autónoma de Madrid (2014).
- Dr. Iván E. Rasskin Friederichs, "Curvatura total de curvas convexas y nudos: Teoremas de Fenchel y Milnor", Universidad Autónoma de Madrid (2013).
- MSc. Victoria Eugenia Arribas Guerrero, "Grupos de Lie. Espacios homogéneos", Universidad Autónoma de Madrid (2013).
BSc. Theses directly assessed
- Mr. Edward Evans, "Algebraic Number Theory and Fermat’s last Theorem", (advisor Prof. Daniel Robertz) University of Plymouth (2018).
- Mr. Daniel Holden, "The surreal numbers and combinatorial games", (advisor Prof. Nathan Broomhead) University of Plymouth (2018).