09:00 to 10:30 
Vikraman Balaji (CMI, India) 
Representations of Fuchsian groups, parahoric group schemes The mini course will be on representations of Fuchsian groups, parahoric group schemes and Parabolic bundles on Riemann Surfaces. The course will introduce parahoric groups and BruhatTits group schemes and torsors and relate them to representations of Fuchsian groups. I will close the course with new developments involving these themes towards the study of torsors on stable curves.



11:00 to 12:30 
Oscar GarcíaPrada (ICMAT, Madrid, Spain) 
Higgs bundles and higher Teichmüller components (Lecture 1) In these lectures, we first briefly review the nonabelian Hodge correspondence between the moduli space of GHiggs bundles over a compact Riemann surface and the moduli space of representations of the fundamental group of the surface in G. We then introduce the Hitchin components, corresponding to the case when G is a split real group, the maximal Toledo components, corresponding to G being a real group of Hermitian type, and certain special components when G=SO(p,q). These are all examples of higher Teichmüller components. As for the classical Teichmüller space (a component of the moduli space for G=PSL(2,R)), such components consist entirely of discrete and faithful representations. We will finish describing a general construction that is believed to produce all the possible Teichmüller components (including some existing for certain exceptional real forms) in terms of sl_2triples and the Cayley transform.



14:00 to 15:00 
Sarbeswar Pal (IISER, Thiruvananthapuram, India) 
Classification of obstructed bundles over a very general sextic surface and MestranoSimpson Conjecture Let $S$ be a very general sextic surface over complex numbers. Let $\mathcal{M}(H, c_2)$ be the moduli space of rank $2$ stable bundles on $S$ with fixed first Chern class $H$ and second Chern class $c_2$. In this talk we will introduce a new approach using AlexanderHirschowitz Theorem to classify the obstructed bundles in $ \mathcal{M}(H, c_2)$. We will apply this classification to proof Mestrano Simpson conjecture on number of irreducible components of $\mathcal{M}(H, 11)$.



16:00 to 17:30 
Carlos Simpson (Nice Sophia Antipolis University, Nice, France) 
InfosysICTS Ramanujan lectures: Exploring Moduli: basic constructions and examples (Lecture 1) The objective of this lecture series is to discuss the techniques and results that can be used to explore the classification of objects such as vector bundles in algebraic geometry and beyond. In the first lecture, we'll discuss some basic examples and constructions with a view towards some of the main topics to come.


