Algebra Workshop:
This workshop is mainly intended for third-year students, but everyone is welcome to join. The focus this semester is on linear algebra, with sessions held every two weeks. Each meeting is built around a set of problems on topics such as linear maps, determinants, eigenvalues, diagonalization, the Cayley–Hamilton theorem, the Dunford–Jordan decomposition, bilinear algebra, and tensor products.
The sessions last about two and a half hours and are run by the students themselves, who present and discuss the exercises. A tutor will be there each time to guide the discussion and help when needed.
Analysis Workshop:
This workshop is designed as an introduction to some of the most important concepts and theorems in Functional Analysis, with a balance between theory, examples, and problem-solving sessions. It is aimed at students who already have some background in real/complex analysis and linear algebra, and who wish to deepen their understanding of modern analysis and its applications.
The workshop is structured to build progressively from the foundations of Banach and Hilbert spaces to powerful results such as the Hahn–Banach theorem, the Banach–Steinhaus theorem, and an introduction to spectral theory. By the end, participants are expected to have a solid basis for advanced courses and research in analysis and PDEs.
Content Overview:
Part I. Fundamentals about Banach Spaces:
- Introduction & Setup (1 session)
- Weak Topology, Reflexive and Separable Spaces (2 sessions),
- Lebesgue Spaces (1 session – Problem-discussion format),
Part II. Fundamental Theorems and Introduction to Hilbert Spaces
- Fundamental Theorems on Banach Spaces (2 sessions + Problem-discussion),
- Hilbert Spaces (1 session),
Part III. Introduction to Spectral Theory (3 sessions),
Bonus. Exercises Sessions (1-2 session)
