Title | Requirements | Professor/s |
Stochastic partial differential equations and quantum field theory | Stochastic calculus and analytical skills | Albeverio S. |
Stochastic methods in quantum mechanics | Stochastic calculus and analytical skills | Albeverio
S. Ugolini S. |
Invariance properties in stochastic dynamics | Stochastic calculus and analytical skills | Albeverio
S. Ugolini S. |
p-adic modular forms and L-functions, algebraic cycles, motives
and their realizations | Theory of schemes, number theory and homological algebra | Andreatta F. |
Non linear Dynamics | Elementary techniques of dynamic systems | Bambusi D. |
KAM and normal form theory for PDEs | Basic elements of Hamiltonian systems | Bambusi D. |
Inverse problems | Real analysis, functional analysis | Bonetti
E. Cavaterra C. |
Evolution systems of PDE | Real analysis, functional analysis | Bonetti
E. Cavaterra C. |
Mathematical models for applications | Real analysis, functional analysis | Bonetti
E. Cavaterra C. |
Ambiguity modelling in mathematical finance | Functional analysis, measure theory, stochastic calculus | Burzoni
M. Maggis M. |
Space-time stochastic processes, Stochastic geometry and statistical shape analysis: point processes, random sets, random measures | Measure theory; Probability and Mathematical Statistics | Cavaterra
C. Micheletti A. |
Biomathematics and Biostatistics | Probability, Mathematical Statistics. Partial differential equations, analytical and numerical aspects. Differential Modelling. | Cavaterra
C. Micheletti A. |
Geometric properties of solutions to partial differential equation | Knowledge of the basics of analysis and geometry, with emphasis in partial differential equations and basics of functional analysis. | Ciraolo G. |
Financial Mathematics | Functional analysis, probability and stochastic processes | Frittelli M. |
Martingale Optimal Transport and Financial mathematics | Functional analysis, convex analysis, measure theory, stochastic calculus | Frittelli M. |
Stochastic optimal control | Stochastic processes. Stochastic calculus | Fuhrman M. |
Stochastic differential equations. | Stochastic Calculus | Fuhrman M. |
Mathematical logic, algebraic logic, duality theory, model-checking and decision procedures. | Good general mathematical background | Ghilardi
S. Marra V. |
Isogeometric Analysis and Virtual Element Method; Numerical methods for partial differential equations; Biomathematics | Numerical Methods for PDEs | Lovadina
C. Scacchi S. |
Numerical Galerkin methods for partial differential equations | Theory and practice of finite element methods, numerical linear algebra | Lovadina
C. Veeser A. |
Categorical algebra | Basic knowledge of Category Theory, Universal and Homological Algebra | Mantovani
S. Montoli A. |
Differential Geometry and Global Analysis | Riemannian Geometry and PDE’s | Mastrolia
P. Rigoli M. |
Mathematical Physics for quantum and classical statistical mechanics and quantum field theory | Knowledge of mathematical physics, analytical skills | Mastropietro V. |
Group Theory and Representation Theory | Basics in Algebra and Group Theory | Pacifici E. |
Finite dimensional Hamiltonian dynamics: from nonlinear chains to celestial mechanics | Knowledge of mathematical physics and basic elements of Hamiltonian dynamical systems | Paleari S. Penati T. Sansottera M. |
Mathematical Methods in Quantum Mechanics and in General Relativity; Evolution equations (especially, in fluid dynamics) | Basic knowledge of functional analysis and quantum mechanics; Basic knowledge of differential geometry and general relativity | Pizzocchero L. |
Epistemology of Mathematics | Good knowledge of geometry, analysis,…and of the philosophical aspects of the theory of knowledge | Rigoli M. |
Inverse problems for partial differential equations | Basic knowledge of Real and Functional Analysis | Rondi L. |
Variational methods for imaging and for shape optimization | Basic knowledge of Real and Functional Analysis | Rondi L. |
Non linear Analysis, nonlinear partial differential equations | Basic knowledge of Functional analysis, PDEs and Sobolev spaces | Ruf B. |
Algebraic Geometry and Homological Algebra | Slid background in algebraic geometry | Stellari P. |
Non-local Problems and Free boundary problems | Advance skills in mathematical analysis | Valdinoci E. |
Nonlocal minimal surfaces | Knowledge of the basics of analysis and geometry. Geometric intuition and knowledge of partial differential equations | Valdinoci E. |
Phase coexistence problems | Knowledge of the basics of analysis and mathematical physics, with emphasis in partial differential equations. | Valdinoci E. |
Algebraic geometry and Hodge theory, Moduli spaces of curves and Geometry of Calabi-Yau varieties | Basic knowledge of algebraic and complex geometry | van Geemen L. |
Foundations of adaptive methods for the solution of differential equations | Sound knowledge of Galerkin methods with conforming and nonconforming spaces, basic knowledge of nonlinear approximation | Veeser A. |
Functional analysis and infinite-dimensional convexity | Real analysis, Elements of Functional analysis | Vesely L. |