Annual Foundational School-II (part of the ATM schools of NCM),
IISER Thiruvananthapuram, May 10th to June 06th, 2015
Organizers:
Sachindranath Jayaraman (IISER, Thiruvananthapuram),
K. N. Raghavan (IMSc),
Viji Z. Thomas (IISER, Thiruvananthapuram)
Group photo
Advice to
participants:
-
Keep up with updates to this page and
follow instructions posted here.
- Check out the websites of earlier AFS-II schools. In
particular, try this link for
details of the AFS-II held in Almora in May, 2014.
-
You must prepare yourselves carefully in order to gain effectively from the school.
- Solving
problems: This is extremely important---it is perhaps the most
important component of learning mathematics---but there may not be enough time
during the school itself to work out in detail sufficiently many
problems. Therefore, go through, well in advance, the material on the syllabus (as
in any of the standard sources) and give the exercises
listed below a try.
Syllabus: Click
here for the pdf file of the syllabi
for all levels of the AFS: I, II, and III. Particularly relevant for us are
sections 2.1 (ring theory or RT), 2.2 (functional analysis or FA), and 2.3
(differential topology or DT), for these are the ones to be covered in AFS-II.
Each section has four subsections or "modules".
Notation:
For subsections or modules, this is fixed as follows: DT-III refers to the third module of
differential topology, etc. On the timetable, FA10 stands for the tenth lecture
of section FA, etc. Assuming that the modules are covered one after
another in succession (which may not be the case!) and that there are
four lectures per module, FA10 would be the second lecture of the
FA-III module.
Resource persons (in chronological order of appearance):
- Ring theory:
Viji Z. Thomas (IISER, Thiruvananthapuram), K. N. Raghavan (IMSc)
- Functional Analysis: Siddhartha Bhattacharya (TIFR, Mumbai), Manjunath Krishnapur (IISc), Partha Sarathi Chakraborty (IMSc)
- Differential topology: Tejas Kalelkar (IISER, Pune), Samik Basu (RKMVU)
Main Reference for Differential
Topology: Differential Topology by Victor Guillemin and
Alan Pollack, Chapters 1, 2, 3.
Note on references for RT-II and RT-III:
The following
texts are suggested as additional references:
-
M. F. Atiyah and I. G. Macdonald: Introduction to Commutative Algebra, 1969.
-
Daniel Bump: Algebraic Geometry
Exercises for RT-II and RT-III:
from the book of Atiyah and Macdonald mentioned above:
Chapter 1 : 1-12, 14
Chapter 2 : 1-13
Chapter 3 : 1, 2, 5, 6, 7, 9, 12, 13, 14, 17
Chapter 4 : 2, 4, 5, 7, 8, 14, 15, 16
Chapter 5 : 2-7, 11-14
Chapter 7 : 2, 5, 6, 8, 10, 11, 15
Notes (click on the appropriate links):
- Differential topology notes by Professor Amiya Mukherjee (from AFS-II, Almora, May 2014):
part 1,
part 2,
part 3,
part 4,
tutorial problems
- Manjunath Krishnapur: Exercise sets (three of them)
- Samik Basu: Exercise sets 1 and 2,
Exercise sets 3 and 4,
Exercise set 5
- Samik Basu: Slides
of lecture on "The Belt Trick"
- K. N. Raghavan: Integral extensions (includes exercises),
Simple and semisimple finite
dimensional algebras (includes exercises)
- Partha Sarathi Chakraborty: Prerequisites,
Notes including exercises
