Lecturers:

• Dimitris Makris (Université de Bourgogne) : An Introduction to Integrable Systems and Their Applications in Topological Quantum Field Theories 
  Integrable systems form a special class of evolutionary differential equations characterized by their remarkable mathematical properties and relevance to numerous physical problems. Depending on the context, various approaches and tools are employed to study these systems. The lectures aim to explore key examples, such as the Toda lattice and the Korteweg–de Vries (KdV) equation, and illustrate fundamental aspects of the theory of integrable systems. Topics will include the Lax representation of evolutionary equations and the bihamiltonian framework for integrability. If time permits, we will also provide an overview of the applications of bihamiltonian integrable hierarchies to two-dimensional topological quantum field theories, following the seminal work of Witten, Dubrovin- Zhang, and others.
  
  

• Rafailia Tsiavou (Aristotle University of Thessaloniki) : A bounded introduction to Seiberg-Witten equations on Hermitian symmetric spaces
  Seiberg-Witten equations, originally stated on a 4-dimensional manifold M, involve the kernel of a Dirac-type operator and a monopole condition on the curvature of the line bundle of the spin^c-structure of M. We will define each one of these components, discuss the importance of dimension 4 and, time permitting, examine the equations on Hermitian symmetric spaces.

Talk 1. Definition and basic structure.  Definition of the Spin structure the Clifford multiplication and Dirac operators.  Talk 2. The emergence of Seiberg-Witten equations.  Complex Spin structures and their corresponding line bundle. The energy functional of Seiberg and Witten and a rough idea behind their invariants. Talk 3. Towards Seiberg-Witten equations on Hermitian symmetric spaces.  The Geometry of Hermitian symmetric spaces, G-equivariant Spin structures and Wang's Theorem on G-equivariant connections.

Speakers:

• Ilias Ermeidis (Georg-August-Universität Göttingen) : Deformation theory of Lie ideals

Lie ideals are one of the cornerstone notions in Lie theory and the representation theory of Lie algebras. In this talk, we address the deformation theory of an ideal within a Lie algebra. We explicitly present the differential graded Lie algebra associated with each Lie ideal that controls its deformation problem. Furthermore, we establish rigidity and stability results for Lie ideals, as well as provide obstruction criteria for extending infinitesimal deformations to formal ones. Time permitting, we will also discuss how the aforementioned theory can be generalized to the context of Lie algebroids. This talk is based on joint work(s) with Madeleine Jotz.

• Anastasios Fotiadis (Université Claude Bernard - Lyon 1) : Universal central extensions of Lie algebras of vector fields
  Central extensions of Lie algebras play a fundamental role in mathematics and physics, appearing in areas such as geometric quantization, projective representations of Lie groups, and conformal field theory. A key result in this context is that central extensions are classified by the second Lie algebra cohomology with trivial coefficients. In this talk, we will review previous work dealing with central extensions of Hamiltonian and divergence-free vector fields, and focus on the case of contact vector fields where we will prove that the Lie algebra of contact vector fields is centrally closed.
  
  

• Grigoris Kittas (Aristotle University of Thessaloniki) : Dorfmann connections on dg-manifolds
  In this talk we will give a brief introduction of the notion of Courant Algebroid and linear connections. We will give the definition of a predual vector bundle and the non - linear connections arising from them which are called Dorfmann connections. The next step is to show how the torsion and basic curvature of Courant algebroid can be related to the dg manifold side. The question is how can be described the graded picture of  a Dorfmann connection on a pair of Courant algebroid and predual vector bundle? We will show the first steps that we have done in this direction and what problems arise.
  
  

• Anastasios Slaftsos (Università degli Studi di Padova) : t-structures in Q-shaped derived categories
  The concept of the Q-shaped derived category was introduced in 2022 by H. Holm and P. Jørgensen and it generalises the notion of the usual derived category. When one works with the standard derived category, t-structures provide an important tool in the study of the representation theory of algebras. For this purpose, we construct certain t-structures in the more general setting of the Q-shaped derived category, using combinatorial techniques on the underlying quiver. Time permitted, we will show case our results in the context of certain examples. This talk is based on a work in progress.