Ph.D. research topics in Mathematics List of possible research topics in Pure and Applied Mathematics Algebra and Geometry Paolo BRAVI Lie theory Alberto DE SOLE Lie Algebras, representation theory Simone DIVERIO Complex-analytic, differential and algebraic geometry Domenico FIORENZA Topological quantum field theories Marco MANETTI Lie and homotopy methods in deformation theory Gabriele MONDELLO Riemann surfaces, differential and algebraic geometry Andrea SAMBUSETTI Riemannian geometry, geometric group theory Analysis Isabeau BIRINDELLI Partial differential equations Piero D'ANCONA Partial differential equations, Harmonic analysis Andrea DAVINI Hamilton-Jacobi equations and weak KAM Theory Luca FANELLI Spectral theory & Dispersive PDE's Adriana GARRONI Variational methods, applications to material science Fabiana LEONI Nonlinear PDEs Corrado MASCIA Biomathematics, differential equations, dynamical systems Claudia PINZARI Operator algebras, Noncommutative geometry Marcello PONSIGLIONE Calculus of Variations Emanuele SPADARO Calculus of Variations, Geometric Measure Theory, PDEs Mathematical physics, Numerical analysis and Probability Paolo BUTTÀ Mathematical physics Camillo CAMMAROTA Nonstationary stochastic processes, data analysis Elisabetta CARLINI Numerical Analysis of Partial Differential Equations Guido CAVALLARO Mathematical physics, Kinetic theory, Fluid mechanics Michele CORREGGI Mathematical physics Alessandra FAGGIONATO Probability, Mathematical physics Maurizio FALCONE Numerical Analysis, Mathematical modeling Maria LOPEZ FERNANDEZ Numerical analysis Silvia NOSCHESE Numerical Linear Algebra Gianluca PANATI Mathematical Quantum Theory