The workshop will be targeted primarily at PhD students with a background in Riemannian geometry. The aim will be to introduce themes of current research and advanced topics usually not covered in coursework. Students and young faculty attending the workshop should be able to return to their home institutions after the workshop and be equipped to delve deeper into the research themes covered. We shall deal with 4 selfcontained themes: Complex differential geometry, geodesic flow on negatively curved manifolds, YangMills theory and the hprinciple.
Young faculty and postdocs in related areas, wishing to broaden their area of interest are also encouraged to apply.
Syllabus to be covered in terms of modules of 6 lectures each :
Name of the Speakers with affiliation. 
No. of Lectures 
Detailed Syllabus 
Subhojoy Gupta, Vamsi Pingali and Harish Seshadri/Gautam Bharali (all from IISc Bangalore)

12 
Complex Differential Geometry Basics of Riemann surfaces, holomorphic differentials and harmonic forms, Riemann bilinear relations, the period map, Siegel upper half space, Teichmuller space, quasiconformal maps, Bers embedding, Bers Simultaneous Uniformization, Quasifuchsian groups, complex FenchelNielsen coordinates and the relation to the complex symplectic structure, etc. Complex manifolds, holomorphic vector bundles, Kahler manifolds, dbar equation, Kodaira embedding, Kodaira vanishing, algebraic geometry from a differential perspective. 
Kingshook Biswas RKM Vivekananda U. 
4 
Geodesic Flow: Hyperbolic manifolds, geodesic flow, ergoicity, geodesic conjugacy 
Dishant Pancholi IMSc Chennai 
4 
hprinciple Introduction to Gromov’s hprinciple, leading to Smale's inversion of the sphere theorem 
Sushmita Venugopalan IMSc Chennai 
4 
YangMills theory The YangMills functional, critical points, SD and ASD connetions, Moduli

Tentative timetable :
Day 
Date 
Lecture 1 (9.30–11.00) 
Tea (11.05–11.25) 
Lecture 2 (11.30–1.00) 
Lunch (1.00–2.00) 
Lecture 3 (2.00–3.30) 
Tea (3.353.55) 
Lecture 4 (4.005.30) 
Snacks 5.355.45 


(name of the speaker) 

(name of the speaker) 

(name of the speaker) 

(Name of the speaker) 

Mon 
24.07.2017 
V. Pingali 
S. Gupta 
K. Biswas 
S. Venugopalan 

Tues 
25.07.2017 
V. Pingali 
S. Gupta 
D. Pancholi 
K. Biswas 

Wed 
26.07.2017 
H. Seshadri 
S. Gupta 
S. Venugopalan 
D. Pancholi 

Thu 
27.07.2017 
V. Pingali 
H. Seshadri 
K. Biswas 
S. Venugopalan 

Fri 
28.07.2017 
V. Pingali 
H. Seshadri 
D. Pancholi 
K. Biswas 

Sat 
29.07.2017 
H. Seshadri 
S. Gupta 
S. Venugopalan 
D. Pancholi 