AIS - Topics in Commutative Algebra and Algebraic Geometry (2026)
Venue: IIT, Palakkad
Dates: 8 Jun 2026 to 27 Jun 2026
Convener(s)
| Name: | Prof. Jugal K Verma | Prof. Krishna Hanumanthu | Dr. Parangama Sarkar |
| Mailing Address: | Visiting Professor, Department of Mathematics, Indian Institute of Technology Gandhinagar Palaj, Gujarat-382055 |
Professor, Department of Mathematics, Chennai Mathematical Institute H1, SIPCOT IT Park, Siruseri, Kelambakkam Chennai-603103 |
Assistant Professor, Department of Mathematics, Indian Institute of Technology Palakkad Kanjikode, Palakkad Kerala - 678623 |
| Email: | jugal.verma at iitgn.ac.in | krishna at cmi.ac.in | parangama at iitpkd.ac.in |
The aim of this AIS (Advanced Instructional School) is to introduce participants to powerful tools at the interface of Commutative Algebra and Algebraic Geometry. This school will emphasize how geometric ideas, such as schemes, coherent sheaves, and cohomology, together with homological methods in Commutative Algebra, lead to fundamental results in Commutative Algebra. To ensure that the school is accessible to PhD students whose research interests broadly lie in Commutative Algebra, the first week will be devoted to reviewing foundational topics, including mapping cones, spectral sequences, injective resolutions, and scheme theory. The second week will include Matlis Duality, Gorenstein rings, divisors and cohomology. The final week will focus on advanced topics, including Local cohomology, Local duality theorems, Vanishing theorems (Kodaira-Akizuki-Nakano, Grauert-Riemenschneider) and Formal duality.