## Annual report

The PhD students of our program in Mathematic have an intense research activity on a large spectrum of themes which range from more abstract mathematical questions to topics in applied mathematics.

Most of the topics treated by our students (and the results obtained) are of great interest for international mathematical community.

Some

**Key Words**to have an idea of the variety of topics studied by the students last year:

Biological Evolution, Mutation Processes, Simulations, Replicator Dynamics

Topological Insulators, Wannier Functions, Schroedinger operators with magnetic field

Analysis and simulations of: theory of travelling waves and applications to biomedicine and geophysics

Nonlinear PDE with non regular coefficients, Lorentz regularity

Elliptic boundary valued problems

Feynman-Kac formula, PDEs on networks

Harmonic analysis, Functional analysis and Volterra equations.

Percolation, conductivity in disordered systems at low temperatures

Quantum field theory, quantum electrodynamics, semiclassical analysis

Quantum vertex algebra, quantum group, R-matrix

Anyons, Schrodinger Operators, Self-Adjoint Extensions, Spectral Theory, Von-Neuman Theory, quadratic Forms

3-manifolds, minimal entropy, growth

Variational poisson cohomology, W-algebras

Pre-Lie Algebras, deformation theory

W-algebras, Vertex Algebras

Numbers theory, Weber Class Number One Problem, Class Field Theory

Operator algebras, conformal field theory, representation theory

Liquid crystals, harmonic maps, calculus of variations, geometric analysis

Irregular manifolds, abelian manifolds

Differential Geometry

Logic, Desctiptive Set Theory, Game Theory

Gromov hyperbolic, Tits alternative, doubling, entropy, group of isometries

**Some more data**on the activity of the students during 2023

Number of partecipation to schools or conferences:

**77**

Number of talks or posters at conferences:

**13**

Seminars at other Institutions:

**23**

Days spent abroad:

**849**

Number of publications/preprints of the current students:

**21**

For more details please visit the pages of the students

For more details please visit the pages of the students

__here.__