AIS - Algebraic Combinatorics and Spectral Graph Theory(2022)
Speakers and Syllabus
Syllabus: Each speaker is required to deliver minimum 6 lectures (each of 1 hour) or 4 lectures (each of 1.5 hours).
| Name of the Speaker with affiliation | No. of Lectures | Detailed Syllabus |
| Prof R B Bapat, ISI Delhi | 6 | Adjacency matrices of graphs: Eigenvalues of some graphs, Harray’s determinant formula, Sachs coefficient theorem, Inverses of trees, Bounds for the eigenvalues, Wilf’s theorem, Hoffman’s ratio bound, Cvetkovic’s inertia bounds. |
| Dr Rajesh Kannan, IIT Kharagpur | 6 | Laplacian matrices of graphs: Eigenvalues of some graphs, Matrix-Tree theorem. Algebraic connectivity: classification of trees, Monotonicity properties of Fielder vector. Normalized Laplacian: Basic properties, Cheegar’s inequality, Expander mixing lemma. Random walks on graphs: stationary distribution, mixing time. |
| Prof Murali K Srinivasan, IIT Bombay | 6 | Regular graphs, Adjacency algebra of a regular graph, Strongly regular graphs and Friendship theorem. Distance regular graphs, Intersection numbers, Krein parameters, Association Schemes, Bose-Mesner Algebras. |
| Prof R Venkadesh, IISc | 6 | Basic Enumeration: Combinatorial objects counted by numbers like Stirlings numbers of both kinds, q-binomial numbers, Eulerian numbers, Catalan numbers, Bell numbers, Derangements, inclusion-exclusion. |
| Prof Arvind Ayyer, IISc | 6 | Ordinary and Exponential Generating functions, Recurrences and ogfs for combinatorial numbers in Module 1. Exponential formula for egfs and uses in enumerating polynomials (like Eulerian polynomial), Compositional formula for egfs and its permutation version. |
| Prof Krishnan, IIT Bombay | 6 | Symmetric functions, Five bases for the space of degree "d" symmetric functions over \QQ. Change of basis among these, Hall inner product, RSK algorithm, Using SAGE to get acquainted with symmetric functions. |
References:
1. Graphs and Matrices by R.B Bapat
2. Spectra of Graphs by A. E. Brouwer and W. H. Haemers
3. Algebraic Graph Theory by N. Biggs
4. Introduction to the Theory of Graph Spectra – D. Cvetkovic, P. Rowlinson and S. Simic
5. Algebraic Graph Theory – Chris Godsil and Gordon F. Royle
6. Algebraic Combinatorics – Chris Godsil
7. Lecture notes on Association Scheme – Chris Godsil.
8. Spectral Graph Theory - Fan Chung.
9. Expander Graphs and Their Applications – S. Hoory, N. Linial and A. Wigderson
10. Stanley - Enumerative Combinatorics vols 1 and 2
11. Sagan - Combinatorics, the art of counting
12. Wilf – Generatingfunctionology
13. Bona - Introduction to Enumerative Combinatorics
Time Table
Time-Table (with names of speakers and course associates/tutors in abbreviated form)
|
Day |
Date |
Lecture 1 (9.30–11.00) |
Tea (11.05 –11.25) |
Lecture 2 (11.30–1.00) |
Lunch (1.05–2.25) |
Tutorial (2.30–3.30) |
Tea (3.35-3.55) |
Tutorial (4.00-5.00) |
Snacks 5.05-5.30 |
|
|
|
(name of the speaker in abbreviated form) |
|
(name of the speaker in abbreviated form) |
|
(name of the speaker + tutors in abbreviated form) |
|
(name of the speaker + tutors in abbreviated form) |
|
|
Mon |
30.05.22 |
RK |
|
NN |
|
RK/MK/IM |
|
NN/NI/AN |
|
|
Tues |
31.05.22 |
RK |
|
NN |
|
NN/NI/AN |
|
RK/MK/IM |
|
|
Wed |
01.06.22 |
RK |
|
NN |
|
RK/MK/IM |
|
NN/NI/AN |
|
|
Thu |
02.06.22 |
RK |
|
NN |
|
NN/NI/AN |
|
RK/MK/IM |
|
|
Fri |
03.06.22 |
RK |
|
NN |
|
RK/MK/IM |
|
NN/NI/AN |
|
|
Sat |
04.06.22 |
RK |
|
NN |
|
NN/NI/AN |
|
RK/MK/IM |
|
|
SUNDAY : OFF |
|||||||||
|
Mon |
06.06.22 |
AA |
|
MKS |
|
AA/NI/AN |
|
MKS/HK/AS |
|
|
Tues |
07.06.22 |
AA |
|
MKS |
|
MKS/HK/AS |
|
AA/NI/AN |
|
|
Wed |
08.06.22 |
AA |
|
MKS |
|
AA/NI/AN |
|
MKS/HK/AS |
|
|
Thu |
09.06.22 |
AA |
|
MKS |
|
MKS/HK/AS |
|
AA/NI/AN |
|
|
Fri |
10.06.22 |
AA |
|
MKS |
|
AA/NI/AN |
|
MKS/HK/AS |
|
|
Sat |
11.06.22 |
AA |
|
MKS |
|
MKS/HK/AS |
|
AA/NI/AN |
|
|
SUNDAY : OFF |
|||||||||
|
Mon |
13.06.22 |
SS |
|
RBB |
|
SS/HK/MK |
|
RBB/AS/IM |
|
|
Tues |
14.06.22 |
SS |
|
RBB |
|
RBB/AS/IM |
|
SS/HK/MK |
|
|
Wed |
15.06.22 |
SS |
|
RBB |
|
SS/HK/MK |
|
RBB/AS/IM |
|
|
Thu |
16.06.22 |
SS |
|
RBB |
|
RBB/AS/IM |
|
SS/HK/MK |
|
|
Fri |
17.06.22 |
SS |
|
RBB |
|
SS/HK/MK |
|
RBB/AS/IM |
|
|
Sat |
18.06.22 |
SS |
|
RBB |
|
RBB/AS/IM |
|
SS/HK/MK |
|
Tutorial Assistants:
|
S. No. |
Name |
Affiliation |
|
1 |
Dr Hiranya Kishore Dey (IISC) |
HK |
|
2 |
Dr Aniruddha Samanta (ISI Bangalore) |
AS |
|
3 |
Mr Iswar Mahato (IIT Kharagpur) |
IM |
|
4 |
Dr Mukesh Kumar (IIT Kanpur) |
MK |
|
5 |
Ms Nishu (IISC) |
NI |
|
6 |
Ms Anita (IISC) |
AN |
Full forms for the abbreviations of speakers and tutors:
- RBB - Prof R B Bapat
- SS - Prof Sivaramakrishnan Sivasubramanian
- AA - Prof Arvind Ayyer
- MKS - Prof Murali K Srinivasan
- NN – Prof N Narayanan
- RK – Dr Rajesh Kannan