AFS-III - Annual Foundation School - III (2024) IIST Tvm

Speakers and Syllabus

 Field and Galois Theory
We will cover most of the material found in Chapters 15 and 16 found in Michael Artin’s Algebra, Pearson,1991.

  • Speakers: AA Ambily (CUSAT, Cochin) for Module 1, Prosenjit Das (IIST) for Module 2, Viji Z Thomas(IISER TVM) for Module 3, K N Raghavan (IMSc) for Module 4.
  • Course Associates: Prosenjit Das (Faculty, IIST), AA Ambily (Faculty, CUSAT, Cochin) and Gayathry Pradeep(PhD student, CUSAT); two CAs at a time.

References

  • M. Artin:Algebra, 2nd Edition, Prentice Hall of India, 2011.
  • S. Lang: Algebra, Revised 3rd Edition, Springer.
  • N. Jacobson: Basic Algebra, Vol.1 and Vol.2, Dover, 2011.

 

Functional Analysis
We will cover most of the material found in Chapters 8,9, 10 and 11 of Simmons book Introduction to Topology and Modern Analysis.

  • Speakers: Jaydeb Sarkar (ISI, Bangalore) for Module 1, Sakthivel Kumarswamy (IIST) for Module 2,Samya Kumar Ray (IISER TVM) for Module 3, Ramiz Reja (IISER TVM) for Module 4.
  • Course Associates: Kalpana Rawat (PhD student, IIST), Sneha B (Post-Doc, ISI Bangalore) and Ashish Kujur (PhD student, IISER Trivandrum); two CAs at a time.

References

  • G. F. Simmons: Introduction to Topology and Modern Analysis,
  • John B. Conway: A course in Functional Analysis;
  • Elias Stein and Rami Shakarchi: Functional Analysis: Introduction to further topics in analysis

Topology III
We will cover most of the material found in Chapters 9 and 13 of Munkres’s Topology book and Chapters 3 and 4 of Spanier’s book.

  • Speakers: Arpan Kabiraj (IIT Palakkad) for Module 1, Tejas Kalelkar (IISER Pune) for Module 2,Sandeep Varma (TIFR Bombay) for Module 3, A. J. Parameswaran (TIFR Bombay) for Module 4.
  • Course Associates: Deblina Das (PhD Student, IIT Palakkad), Koushik Brahma (Post-Doc, CMI) and Subhankar Sau (Post-Doc, ISI Kolkata) ; two CAs at a time.

References

  • E. H. Spanier: Algebraic Topology, Springer.
  • M. J. Greenberg and J. R. Harper: Algebraic Topology: A first course.
  • J. R. Munkres: Topology, A First Course, Prentice-Hall of India, New Delhi, 1987.

Time Table

 Week 1

Date 9.30 − 11.00 11.00 − 11.30 11.30 − 1.00 1.00 − 2.30 2.30 − 3.30 3.30 − 4.00 4.00 − 5.00
17 Jun GT-L1 T FA-L1 L GT-T1 T FA-T1
18 Jun T-L1 T GT-L2 L T-T1 T GT-T2
19 Jun FA-L2 T T-L2 L FA-T2 T T-T2
20 Jun GT-L3 T FA-L3 L GT-T3 T FA-T3
21 Jun T-L3 T GT-L4 L T-T3 T GT-T4
22 Jun FA-L4 T T-L4 L FA-T4 T T-T4

 Week 2

Date 9.30 − 11.00 11.00 − 11.30 11.30 − 1.00 1.00 − 2.30 2.30 − 3.30 3.30 − 4.00 4.00 − 5.00
24 Jun GT-L5 T FA-L5 L GT-T5 T FA-T5
25 Jun AT-L5 T GT-L6 L AT-T5 T GT-T6
26 Jun FA-L6 T AT-L6 L FA-T6 T AT-T6
27 Jun GT-L7 T FA-L7 L GT-T7 T FA-T7
28 Jun AT-L7 T GT-L8 L AT-T7 T GT-T8
29 Jun FA-L8 T AT-L8 L FA-T8 T T-T8

Week 3

Date 9.30 − 11.00 11.00 − 11.30 11.30 − 1.00 1.00 − 2.30 2.30 − 3.30 3.30−4.00 4.00 − 5.00
1 Jul GT-L9 T FA-L9 L GT-T9 T FA-T9
2 Jul AT-L9 T GT-L10 L T-T9 T GT-T10
3 Jul FA-L10 T AT-L10 L FA-T10 T T-T10
4 Jul GT-L11 T FA-L11 L GT-T11 T FA-T11
5 Jul AT-L11 T GT-L12 L T-T11 T GT-T12
6 Jul FA-L12 T AT-L12 L FA-T12 T T-T12

 Week 4

Date 9.30 − 11.00 11.00 − 11.30 11.30 − 1.00 1.00 − 2.30 2.30 − 3.30 3.30 − 4.00 4.00 − 5.00
8 Jul GT-L13 T FA-L13 L GT-T13 T FA-T13
9 Jul AT-L13 T GT-L14 L T-T13 T GT-T14
10 Jul FA-L14 T AT-L14 L FA-T14 T T-T14
11 Jul GT-L15 T FA-L15 L GT-T15 T FA-T15
12 Jul AT-L15 T GT-L16 L T-T15 T GT-T16
13 Jul FA-L16 T AT-L16 L FA-T16 T T-T16

 

• GT-Ln : nth lecture in Galois Theory
• GT-Tn: nth tutorial in Galois Theory
• FA-Ln : nth lecture in Functional Analysis
• FA-Tn: nth tutorial in Functional Analysis
• AT-Ln : nth lecture in Algebraic Topology
• AT-Tn: nth tutorial in Algebraic Topology
• T : Tea
• L : Lunch
• Galois Theory Tutorials : GT-T1 – GT-T4: Speaker + Prosenjit Das and Gayathry Pradeep GT-T5 – GT-T8: Speaker + AA Ambily and Gayathry Pradeep GT-T9 – GT-T12: Speaker + Prosenjit Das and Gayathry Pradeep GT-T13 – GT-T16: Speaker + Prosenjit Das and Gayathry Pradeep
• Functional Analysis Tutorials: FA-T1 – FA-T4: Speaker + Kalpana Rawat and Sneha B FA-T5 – FA-T8: Speaker + Kalpana Rawat and Sneha B FA-T9 – FA-T12: Speaker + Kalpana Rawat and Ashish Kujur FA-T13 – FA-T16: Speaker+ Kalpana Rawat and Ashish Kujur
• Algebraic Topology Tutorials: AT-T1 – AT-T4: Speaker + Deblina Das and Subhankar Sau AT-T5 – AT-T8: Speaker + Deblina Das and Subhankar Sau AT-T9 – AT-T12: Speaker + Deblina Das and Koushik Brahma AT-T13 – AT-T16: Speaker + Deblina Das and Koushik Brahma
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