Introduces recent and advanced techniques in the area of analytic and algebraic geometry Includes research articles to demonstrate the usage of these techniques to prove new results Supports further research through a comprehensive bibliography for each chapter

Autorentext
ANILATMAJA ARYASOMAYAJULA is assistant professor at the Indian Institute of Science Education and Research (IISER), Tirupati, India. He did his PhD from the Humboldt University, Berlin. A DST inspire fellow, his areas of interest are automorphic forms, Hilbert modular forms, Arakelov theory and Diophantine geometry.

INDRANIL BISWAS is professor of mathematics at the Tata Institute of Fundamental Research (TIFR), Mumbai, India. He works in algebraic geometry, differential geometry, several complex variables and analytic space, and deformation quantization. He has more than 400 publications to his credit with many collaborators across the world. In 2006, the Government of India awarded him the Shanti Swarup Bhatnagar Prize in Mathematical Sciences for his contributions to algebraic geometry, more precisely moduli problems of vector bundles. He is a fellow of Indian Academy of Sciences and Indian National Science Academy (INSA).

ARCHANA S. MORYE is a faculty in the University of Hyderabad, India. She did her PhD from Harish-Chandra Research Institute, Allahabad, India. Her research area is algebraic geometry, more specifically in vector bundles.

A.J. PARAMESWARAN is professor of mathematics at the Tata Institute of Fundamental Research (TIFR), Mumbai, India. He was the director of Kerala School of Mathematics, Kozhikode, India, for a short period of time. He works in algebraic geometry, several complex variables and analytic space. He is a fellow of Indian Academy of Sciences.

Klappentext
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.

Inhalt
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.