Annual Foundation Schools
380 - AFS- I 2021
Dates: 29 Nov 2021 to 8 Jan 2022
Venue: Department of Mathematics,
Savitribai Phule Pune University, Pune
Organizers
Prof. S. A. Katre, Prof. Vinayak Joshi, Dr. Ganesh Kadu
Lecture 1: 29-November-2021
Lecture Title: Algebra
Name of speaker with affiliation : Prof. Dilip Patil (formerly IISc, Bangalore)
In this lecture we discuss the group action and see the correspondence between a group action and the action homomorphism. Later we discuss some examples of group actions, namely, the left regular action and the conjugation operation.
Lecture 1 and 2: 30-November-2021
Lecture Title: Complex Analysis
Name of speaker with affiliation : Hemant Bhate (Prof. Emeritus, S. P. Pune University)
Lecture 2: 30-November-2021
Lecture Title: Algebra
Name of speaker with affiliation : Prof. Dilip Patil (formerly IISc, Bangalore)
In this lecture we discuss the orbit- stabilizer theorem and the class equation of a group action on a set. Later on we will define some special kind of group actions, namely, transitive group action, simply transitive group action, free action and faithful action. Finally, we concentrate on the conjugation group action of a group on itself and explore the class equation in this case.
Lecture 1: 01-December-2021
Lecture Title: Topology
Name of speaker with affiliation :Nitin Nitsure (formerly TIFR, Mumbai)
Review of some set theory. Empty set, ordered pairs, maps, construction of natural numbers as sets, binary products and coproducts, products and coproducts of families of sets, initial and terminal sets, universal properties, the notion of being unique up to nique isomorphism.
Lecture 3: 01-December-2021
Lecture Title: Algebra
Name of speaker with affiliation : Prof. Dilip Patil (formerly IISc, Bangalore)
In this lecture we discuss the class equation for p-groups. Further we see the Cauchy's theorem. We will also see that every group action give rise to a faithful action of another group on the same set. Further we explore an example of a group action of symmetric group of a set on the power set of the same set and see the orbits and isotropy subgroups.
Lecture 2: 02-December-2021
Lecture Title: Topology
Name of speaker with affiliation :Nitin Nitsure (formerly TIFR, Mumbai)
Introduction to some basic notions of categories via examples of Sets, Groups, Commutative Rings and various categories of Metric Spaces. Initial and terminal objects, products, coproducts, universal properties, uniqueness up to unique isomorphism.
Lecture 3: 02-December-2021
Lecture Title: Complex Analysis
Name of speaker with affiliation : Hemant Bhate (Prof. Emeritus, S. P. Pune University)
Lecture 3: 03-December-2021
Lecture Title: Topology
Name of speaker with affiliation :Nitin Nitsure (formerly TIFR, Mumbai)
Lecture 4: 03-December-2021
Lecture Title: Algebra
Name of speaker with affiliation :Prof. Dilip Patil (formerly IISc, Bangalore)
Lecture 4: 04-December-2021
Lecture Title: Topology
Name of speaker with affiliation :Nitin Nitsure (formerly TIFR, Mumbai)
Lecture 4: 04-December-2021
Lecture Title: Complex Analysis
Name of speaker with affiliation : Hemant Bhate (Prof. Emeritus, S. P. Pune University)
Lecture 5: 06-December-2021
Lecture Title: Complex Analysis
Name of speaker with affiliation : Hemant Bhate (Prof. Emeritus, S. P. Pune University)
Lecture 5: 06-December-2021
Lecture Title: Algebra
Name of speaker with affiliation :Prof. Dilip Patil (formerly IISc, Bangalore)
Lecture 6: 07-December-2021
Lecture Title: Complex Analysis
Name of speaker with affiliation : Hemant Bhate (Prof. Emeritus, S. P. Pune University)
Lecture 6: 07-December-2021
Lecture Title: Algebra
Name of speaker with affiliation :Prof. Dilip Patil (formerly IISc, Bangalore)
Lecture 5: 08-December-2021
Lecture Title: Topology
Name of speaker with affiliation :Nitin Nitsure (formerly TIFR, Mumbai)
Lecture 7: 08-December-2021
Lecture Title: Algebra
Name of speaker with affiliation :Prof. Dilip Patil (formerly IISc, Bangalore)
Lecture 6: 09-December-2021
Lecture Title: Topology
Name of speaker with affiliation :Nitin Nitsure (formerly TIFR, Mumbai)
Lecture 7: 09-December-2021
Lecture Title: Complex Analysis
Name of speaker with affiliation : Hemant Bhate (Prof. Emeritus, S. P. Pune University)
Lecture 7: 10-December-2021
Lecture Title: Topology
Name of speaker with affiliation :Nitin Nitsure (formerly TIFR, Mumbai)
Lecture 8: 10-December-2021
Lecture Title: Algebra
Name of speaker with affiliation :Prof. Dilip Patil (formerly IISc, Bangalore)
Lecture 8: 11-December-2021
Lecture Title: Topology
Name of speaker with affiliation :Nitin Nitsure (formerly TIFR, Mumbai)
Lecture 8: 11-December-2021
Lecture Title: Complex Analysis
Name of speaker with affiliation : Hemant Bhate (Prof. Emeritus, S. P. Pune University)
Lecture 9: 11-December-2021
Lecture Title: Complex Analysis
Name of speaker with affiliation : Hemant Bhate (Prof. Emeritus, S. P. Pune University)
Lecture 9: 13-December-2021
Lecture Title: Algebra
Name of speaker with affiliation :Prof. Dilip Patil (formerly IISc, Bangalore)
Lecture 10: 14-December-2021
Lecture Title: Complex Analysis
Name of speaker with affiliation : Hemant Bhate (Prof. Emeritus, S. P. Pune University)
Lecture 10: 14-December-2021
Lecture Title: Algebra
Name of speaker with affiliation :Prof. Dilip Patil (formerly IISc, Bangalore)
Lecture 9: 15-December-2021
Lecture Title: Topology
Name of speaker with affiliation :Nitin Nitsure (formerly TIFR, Mumbai)
Lecture 11: 15-December-2021
Lecture Title: Algebra
Name of speaker with affiliation :Prof. Dilip Patil (formerly IISc, Bangalore)
Lecture 10: 16-December-2021
Lecture Title: Topology
Name of speaker with affiliation :Nitin Nitsure (formerly TIFR, Mumbai)
Lecture 11: 16-December-2021
Lecture Title: Complex Analysis
Name of speaker with affiliation : Hemant Bhate (Prof. Emeritus, S. P. Pune University)
Lecture 11: 17-December-2021
Lecture Title: Topology
Name of speaker with affiliation :Nitin Nitsure (formerly TIFR, Mumbai)
Lecture 12: 17-December-2021
Lecture Title: Algebra
Name of speaker with affiliation :Prof. Dilip Patil (formerly IISc, Bangalore)
Lecture 12: 18-December-2021
Lecture Title: Topology
Name of speaker with affiliation :Nitin Nitsure (formerly TIFR, Mumbai)
Lecture 12 and 13: 18-December-2021
Lecture Title: Complex Analysis
Name of speaker with affiliation : Hemant Bhate (Prof. Emeritus, S. P. Pune University)
Lecture 13: 20-December-2021
Lecture Title: Topology
Name of speaker with affiliation :Nitin Nitsure (formerly TIFR, Mumbai)
Lecture 13: 20-December-2021
Lecture Title: Algebra
Name of speaker with affiliation :Prof. Dilip Patil (formerly IISc, Bangalore)
Lecture 14: 20-December-2021
Lecture Title: Complex Analysis
Name of speaker with affiliation : Hemant Bhate (Prof. Emeritus, S. P. Pune University)
Lecture 14: 21-December-2021
Lecture Title: Topology
Name of speaker with affiliation :Nitin Nitsure (formerly TIFR, Mumbai)
Lecture 15: 21-December-2021
Lecture Title: Complex Analysis
Name of speaker with affiliation : Hemant Bhate (Prof. Emeritus, S. P. Pune University)
Lecture 15: 22-December-2021
Lecture Title: Topology
Name of speaker with affiliation :Nitin Nitsure (formerly TIFR, Mumbai)
Lecture 14: 22-December-2021
Lecture Title: Algebra
Name of speaker with affiliation :Prof. Dilip Patil (formerly IISc, Bangalore)
Lecture 16: 23-December-2021
Lecture Title: Topology
Name of speaker with affiliation :Nitin Nitsure (formerly TIFR, Mumbai)
Lecture 15: 23-December-2021
Lecture Title: Algebra
Name of speaker with affiliation :Prof. Dilip Patil (formerly IISc, Bangalore)
Lecture 16: 25-December-2021
Lecture Title: Complex Analysis
Name of speaker with affiliation : Hemant Bhate (Prof. Emeritus, S. P. Pune University)
Lecture 16: 25-December-2021
Lecture Title: Algebra
Name of speaker with affiliation :Prof. Dilip Patil (formerly IISc, Bangalore)
Lecture 17: 27-December-2021
Lecture Title: Complex Analysis
Name of speaker with affiliation : Hemant Bhate (Prof. Emeritus, S. P. Pune University)
Lecture 17: 27-December-2021
Lecture Title: Algebra
Name of speaker with affiliation :Prof. Dilip Patil (formerly IISc, Bangalore)
Lecture 18: 28-December-2021
Lecture Title: Complex Analysis
Name of speaker with affiliation : Hemant Bhate (Prof. Emeritus, S. P. Pune University)
Lecture 18: 28-December-2021
Lecture Title: Algebra
Name of speaker with affiliation :Prof. Dilip Patil (formerly IISc, Bangalore)
Lecture 17: 29-December-2021
Lecture Title: Topology
Name of speaker with affiliation :Nitin Nitsure (formerly TIFR, Mumbai)
Lecture 19: 29-December-2021
Lecture Title: Algebra
Name of speaker with affiliation :Prof. Dilip Patil (formerly IISc, Bangalore)
Lecture 18: 30-December-2021
Lecture Title: Topology
Name of speaker with affiliation :Nitin Nitsure (formerly TIFR, Mumbai)
Lecture 19: 30-December-2021
Lecture Title: Complex Analysis
Name of speaker with affiliation : Hemant Bhate (Prof. Emeritus, S. P. Pune University)
Lecture 19: 31-December-2021
Lecture Title: Topology
Name of speaker with affiliation :Nitin Nitsure (formerly TIFR, Mumbai)
Lecture 20: 31-December-2021
Lecture Title: Algebra
Name of speaker with affiliation :Prof. Dilip Patil (formerly IISc, Bangalore)
Lecture 20: 01-January-2021
Lecture Title: Topology
Name of speaker with affiliation :Nitin Nitsure (formerly TIFR, Mumbai)
Lecture 20: 01-January-2021
Lecture Title: Complex Analysis
Name of speaker with affiliation : Hemant Bhate (Prof. Emeritus, S. P. Pune University)
Lecture 21: 03-January-2021
Lecture Title: Complex Analysis
Name of speaker with affiliation : Hemant Bhate (Prof. Emeritus, S. P. Pune University)
Lecture 21: 03-January-2021
Lecture Title: Algebra
Name of speaker with affiliation :Prof. Dilip Patil (formerly IISc, Bangalore)
Lecture 22: 04-January-2021
Lecture Title: Complex Analysis
Name of speaker with affiliation : Hemant Bhate (Prof. Emeritus, S. P. Pune University)
Lecture 21: 04-January-2021
Lecture Title: Topology
Name of speaker with affiliation :Nitin Nitsure (formerly TIFR, Mumbai)
Lecture 22: 05-January-2021
Lecture Title: Topology
Name of speaker with affiliation :Nitin Nitsure (formerly TIFR, Mumbai)
Lecture 22: 05-January-2021
Lecture Title: Algebra
Name of speaker with affiliation :Prof. Dilip Patil (formerly IISc, Bangalore)
Lecture 23: 06-January-2021
Lecture Title: Topology
Name of speaker with affiliation :Nitin Nitsure (formerly TIFR, Mumbai)
Lecture 23: 06-January-2021
Lecture Title: Complex Analysis
Name of speaker with affiliation : Hemant Bhate (Prof. Emeritus, S. P. Pune University)
Lecture 24: 07-January-2021
Lecture Title: Topology
Name of speaker with affiliation :Nitin Nitsure (formerly TIFR, Mumbai)
Lecture 23: 07-January-2021
Lecture Title: Algebra
Name of speaker with affiliation :Prof. Dilip Patil (formerly IISc, Bangalore)
Lecture 24: 08-January-2021
Lecture Title: Algebra
Name of speaker with affiliation :Prof. Dilip Patil (formerly IISc, Bangalore)
Lecture 24: 08-January-2021
Lecture Title: Complex Analysis
Name of speaker with affiliation : Hemant Bhate (Prof. Emeritus, S. P. Pune University)