After a student has completed courses of level M2 worth 48 credits, he or she must complete their Master's thesis, worth 12 credits.
Master's thesis work can be done under the supervision of one or several tutors working on an advanced topic related to the student's specialization. Each thesis will be defended in a public act, after which a comittee will assign a grade. The following staff members of our department and of the nearby ICMAT Institute offer the following topics for students interested in writing a Master's Thesis:
- Julia Novo: Numerical methods for PDEs
- Marco Zambón: Symplectic and Poisson geometry, foliations, Lie algebras
- Eugenio Hernandez: Fourier analysis, Wavelets and signal processing, Non-linear approximation on function spaces, Systems for function and signal reproduction.
- Marina Logares: h-cobordism
- Kurusch Ebrahimi-Fard: Multiple Zeta Values and Hopf algebras
- Maria-Angeles Zurro Moro: Geometry of Analytic Spaces. Differential Galois theory.
- Cédric M. Campos: spRK and affine methods
- Diego Córdoba Gazolaz: Fluids dynamics
- Ana Vargas: Harmonic Analysis and Dispersive Equations
- Luis Guijarro: Ricci flow, pinching sets and the differentiable sphere theorem.
- Andrei Jaikin: Group Theory and its applications to other parts of Mathematics.
- María Barbero Liñán: Hybrid Geometric Control Systems.
- Dragan Vukotic: Integrability of derivatives of conformal mappings and related topics. Classical operators in analytic function spaces.
- Antonio Cuevas: Medial axis of a set and associated concepts, statistical aspects; Statistics on Manifolds; Probability in infinite dimensional spaces: applications to statistics with functional data.
- Orlando Villamayor: Algebraic Geometry; Commutative Algebra; Homological Algebra.
- Gabino González: Riemann surfaces and dessins d'enfants.
- Adolfo Quirós: Arithmetic algebraic geometry. Criptography.
- Ana Bravo: An introduction to arc spaces.
Alternatively, a student can contact a faculty member which will become his or her tutor, and choose the topic of the Thesis. We list the titles of the Thesis that were defended during the academic years 2010/11 and 2011/12:
2010/11
- Morfismos de esquemas proyectivos
- Las conjeturas de Weil
- Esquemas proyectivos y blow-ups de ideales
- Espacios Lp no conmutativos y Teoría de Calderón-Zygmund con medidas no doblantes
- Una aplicación de la teoría de modelos a grupos algebraicos reales
- Teoría de Morse: geodésicas y topología
- El Teorema de Belyi
- Métodos variacionales y aplicaciones numéricas
- Operadores del análisis armónico descritos con ayuda de la teoría de semigrupos
- Modelos de las ecuaciones de Navier-Stokes axisimétricas
- Espacios BMO
- Los teoremas de la esfera: de Berger-Klingerberg a Hamilton
- Sumando primos: ¿hay tres sin dos?
- Las ecuaciones de Euler: soluciones axisimétricas, helicoidales y de vorticidad
2011/12
- Higher-Order Euler-Poincaré Equations and their Applications to Optimal Control
- Soluciones débiles de la ecuación de Euler e integración convexa
- Sobolev Theorems in Group Von Neumann Algebras
- Combinatoria y topología de complejos simpliciales “con pocos vértices”
- Klein surfaces and Real vector bundles
- Propiedades euclídeas de cuerpos cuadráticos y ciclotómicos
- Trivialización de gérmenes de aplicaciones analíticas para la resolución de singularidades
- Criptografía post-cuántica
- Equilibrio en estrategias puras para el problema de localización en el modelo lineal con función de coste de transporte cóncava. Una variante del modelo de Hotelling
- Una martingala de Feller