Autumn 2022

Talk:3 (22.11.2022)

Title:-d-holomorphic vector bundles 

Speaker:- Ayush Jaiswal

Abstract:- In 1957, Michael Atiyah had developed the theory of holomorphic connection on principle bundles over compact complex manifolds, and gave a criterion (now known as Atiyah-Weil criterion) for the existence of holomorphic connection on holomorphic vector bundles over comapct Riemann surfaces. In 1882, Felix Klein had introduced Klein surface and further analytic theory on Klein surfaces was studied in more depth by Schiffer and Spencer in 1954. Norman Alling and Newcomb Greenleaf studied correspondence between Klein surfaces and real algebraic function fields. In this talk, we will discuss the theory of d holomorphic vector bundle and if time permits we will talk about d-holomorphic connections. 

Talk:1,2 (08.11.2022 & 15.11.2022)

Title:- Euler Gamma Function and its various generalizations. 

Speaker:- Shivajee Gupta

Abstract:-  We will define Euler’s gamma function and its various generalized and related special functions. Also, introduce its important properties like a functional equation, difference equation, reflection formula, etc. We will also look for a result on the generalized Mittag-Leffler functions and technique used in its proof.