Chapter 1. On the Bumpy Fundamental Group Scheme -- Chapter 2. Heat Kernels, Bergman Kernels, and Cusp Forms -- Chapter 3. On a Conjecture of Butler -- Chapter 4. A Survey of Low Dimensional (Quasi) Projective Groups -- Chapter 5. Parabolic Sheaves and Logarithmic Geometry -- Chapter 6. A Survey of Ulrich Bundles -- Chapter 7. Noether-Lefschetz Locus and a Special Case of the Variational Hodge Conjecture: Using Elementary Techniques -- Chapter 8. Tangent Bundle of P2 and Morphism from P2 to Gr(2;C4) -- Chapter 9. Twisting by a Torsor -- Chapter 10. Hitchin Hamiltonians in Genus 2 -- Chapter 11. Smoothness of Moduli Space of Stable Torsion-free Sheaves with Fixed Determinant in Mixed Characteristic -- Chapter 12. Group Compactications and Moduli Spaces -- Chapter 13. The Serre-Swan Theorem for Ringed Spaces -- Chapter 14. An Extension Theorem for Hermitian Line Bundles -- Chapter 15. Elliptic Fibrations on Supersingular K3 Surface with Artin Invariant 1 in Characteristic 3.

This volume is an outcome of the International conference held in Tata Institute of Fundamental Research and the University of Hyderabad. There are fifteen articles in this volume. The main purpose of the articles is to introduce recent and advanced techniques in the area of analytic and algebraic geometry. This volume attempts to give recent developments in the area to target mainly young researchers who are new to this area. Also, some research articles have been added to give examples of how to use these techniques to prove new results.

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