This four-lecture series explores when power series represent rational functions, bridging analysis and arithmetic. The course covers key applications in p-adic analysis, transcendence theory, and zeta functions. These lectures are suitable for graduate and advanced undergraduate students, and all others interested in number theory.

The school programme offers a mathematically focused introduction to contemporary quantum information and matter theory. It bridges deep mathematical structures with practical applications, equipping participants for cutting-edge quantum research. Tailored for advanced math and physics students.

Aiming at undergraduate and graduate students, this school provides a foundational look at group actions on varieties and on abelian varieties. Participants will study algebraic torus actions, quotients, and the complex and arithmetic aspects of abelian varieties. The prerequisites are: commutative algebra, commutative algebra, differential geometry, and introductory algebraic geometry.