Algebraic Combinatorics and Spectral Graph Theory(2022)

Convener(s)


Name:	Prof. Sivaramakrishnan Sivasubramanian	Dr. M. Rajesh Kannan	Mr. R. Gurusamy
Mailing Address:	Professor, Department of Mathematics, Indian Institute of Technology, Bombay, Powai, Mumbai, Maharashtra - 400076	Assistant Professor, Department of Mathematics, Indian Institute of Technology, Kharagpur, West Bengal – 721302	Assistant Professor (Sr.G), Department of Mathematics, Mepco Schlenk Engineering College, Sivakasi, Tamil Nadu - 626005
Email:	krishnan at math.iitb.ac.in	rajeshkannan at maths.iitkgp.ernet.in	rgurusamy at mepcoeng.ac.in

The main objective of this AIS is to introduce the basics of spectral graph theory and algebraic combinatorics.

Dates:

Monday, May 30, 2022 - 09:00 to Saturday, June 18, 2022 - 18:00

Venue:

Mepco Schlenk Engineering College

Venue Address:

Department of Mathematics, Mepco Schlenk Engineering College,
Sivakasi 626005, Tamil Nadu.

Venue State:

Karnataka

Venue City:

Offline Mode

PIN:

560065

Chrono Order:

392

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

Selected Applicants:

Sr.	SID	Full Name	Gender	Affiliation	Position in College/ University	University/ Institute M.Sc./M.A.	Year of Passing M.Sc./ M.A	Ph.D. Deg Date
1	39201	Ms Raina Mary Thomas	Female	Savitribai Phule Pune University	MSc Student till 2020	Savitribai Phule Pune University	2020
2	39229	Mr. Hitesh Wankhede	Male	NA	NA	IISER Pune	2021
3	39247	Mr. Rajiv Mishra	Male	IISER Kolkata	PhD	Indian Institute of Technology Bhubaneswar	2020
4	39276	Mr. Joyentanuj Das	Male	IISER Trivandrum	PhD student	IISER TVM	2018
5	39284	Mrs. Najiya V K	Female	NIT, Calicut	PhD Student	Cochin University of Science and Technology	2018
6	39285	Ms Haritha T	Female	NIT, Calicut	PhD	M.Sc.	2018
7	39287	Mr Priti Prasanna Mondal	Male	SRM University-AP	PhD	IIT Bhubaneswar	2016
8	39323	Mr. Balamoorthy S	Male	Central University of Tamilnadu	PhD	Ayya Nadar Janaki Ammal College	2017
9	39354	Mr. Debabrota Mondal	Male	Indian Institute of Technology Bhubaneswar	PhD	IIT Bhubaneswar	2020
10	39445	Ms Kadali Kranthi Priya	Female	IIT madras	PhD	Pondicherry central university	2019
11	39512	Ms. Kavita Samant	Female	Shiv Nadar University	Ph.D. Scholar	University Of Delhi	2018
12	39566	Mr Santanu Mandal	Male	NIT Rourkela	PhD Scholar	Vidyasagar University	2014
13	39612	Ms. Jharna Kalita	Female	Tezpur University	PhD Student	North Eastern Hill University	2020
14	39697	Ms Sucharita Biswas	Female	Presidency University	PhD Scholar	Presidency University	2019
15	39614	Ms. Sonali Sharma	Female	MNIT Jaipur	PhD Student	Department of Mathematics, University of Rajasthan, Jaipur	2017
16	39707	Mr. Milton Saha	Male	Savitribai Phule Pune University	PhD	Savitribai Phule Pune University	2020
17	39732	Mr. Mohamed Harith	Male	IIT Madras	PhD	IIT Bombay	2020
18	39733	Ms Hepsi D	Female	Ramanujan Institute for Advanced Study in Mathematics	PhD	Ramanujan Institute for Advanced Study in Mathematics	2019
19	39829	Ms. Priyanka Vishwakarma	Female	Birla Institute of Technology and Science, Pilani Hyderabad Campus.	Ph.D.	Devi Ahilya University, Indore.	2018
20	39831	Mr. Khalid Akthar M	Male	Ramanujan Institute for Advanced Study in Mathematics, University of Madras	Ph.D.	Ramanujan Institute for Advanced Study in Mathematics, University of Madras	2020
21	39842	Ms. Kusum Saheblal Rajbhar	Female	university of Mumbai	Ph.D student	university of mumbai	2015
22	39853	Mr. Thamizhmaran Ramalingam	Male	Thiruvalluvar University, Serkkadu.	Ph.D Research Scholar, Dept. of Mathematics.	Thiruvalluvar University	2021
23	39899	Ms Caroline Vincy	Female	Vellore Institute of Technology Chennai	Research Scholar	Stella Maris College	2019
24	39906	Mr. Aqib Khan	Male	Indian Institute of Technology	PhD student	I.I.T. Bhubaneswar	2015
25	39929	Mr. Krishnendu Paul	Male	Ramakrishna Mission Vivekananda Educational and Research Institute (RKMVERI)	PhD Student	University of Calcutta	2015
26	40089	Dr. Sairam Kaliraj Anbareeswaran	Male	IIT Ropar	Assistant Professor		2007	18/07/2014
27	40173	Dr. Shameek Paul	Male	Ramakrishna Mission Vivekananda Educational and Research Institute	Assistant Professor	Mumbai University	2005	19/01/2012
28	40253	Ms. Komal Kumari	Female	Indian institute of technology, Kharagpur	PhD	Central University of Rajasthan	2021
29	40306	Dr. Projesh Nath Choudhury	Male	Indian Institute of Science	Postdoctoral Fellow	Indian Institute of Technology Guwahati	2013	14/05/2018
30	40338	Mr. Punit Kumar Yadav	Male	Malaviya National institute of technology	Phd	University of Rajasthan	2015
Wait-listed candidates
1	40264	Ms. Deblina Dey	Female	IIT Madras	PhD	RKMVERI	2020
2	40208	Ms. Divya Bankapur	Female	CHRIST (Deemed to be University)	Ph.D student	CHRIST (Deemed to be University) M.Sc.	2021
3	40216	Mr. Mohan Ramu	Male	Christ University	PhD	St. Joseph's College (Autonomous)	2018
4	40079	Mr. Veerendra Kumar	Male	Indian Institute of Technology (IIT-BHU)	PhD Student	Central University of South Bihar, Gaya	2018
5	39238	Dr. N. Annamalai	Male	Central University of Tamil Nadu	Guest Faculty	Bharathidasan University/ M.Sc	2011	26/02/2019
6	39731	Ms. Jeromi Jovita J	Female	J. J. College of Arts and Science(A), Pudukkottai	PhD	M.Sc	2020
7	39821	Ms. Somasundari K	Female	The Madurai Diraviyam Thayumanavar Hindu College	Research Scholar	The Madurai Diraviyam Thayumanavar Hindu College	2018	20/12/2018
8	39793	Ms. Senbaga Priya K	Female	SRI KRISHNA ARTS AND SCIENCE COLEGE, KUNIAMUTHUR, COIMBATORE	PhD student	SRI KRISHNA ARTS AND SCIENCE COLLEGE, M.Sc.	2021
9	39466	Dr Vijayaragavan Masilamani	Male	Veltech Multitech Engineering College	Assistant Professor	Madras Christian College	2010	13/02/2017
10	39603	Dr Nalliah M	Male	Vellore Institute of Technology	Assistant Professor	Sri.S. Ramasamy Naidu Memorial College, Sattur	2004	27/08/2014
11	39834	Dr. Sattanathan M	Male	Sri Paramakalyani College	Assistant Professor	St.Joseph's College, Trichy	2007	08/03/2012

How to Reach:

TBA

School Short Name:

acsgt

Last Date Application:

Friday, April 15, 2022

School Type:

AIS