AIS Mathematical Programming(2016)

Venue:	Central University of Tamilnadu, Thiruvarur
Dates:	July 4 – 23, 2016

Convener(s)

Speakers, Syllabus and Time table

Applicants/Participants

School Convener(s)
Name	Dr. A. Chandrashekaran	Prof. R. B Bapat
Mailing Address	Professor & Head, Department of Mathematics Central University of Tamil Nadu	Indian Statistical Institute Delhi

Speakers and Syllabus

Name of the Speaker with affiliation	Detailed Syllabus
Prof. R. B. Bapat, Indian Statistical Institute Delhi [RBB]	Fixed point theorems and computation of fixed points, Sperner's lemma, graph theoretic proof, constructive proof. Brouwer's fixed point theorem, proof using Sperner's lemma, applications. No retraction theorem, hairy ball theorem, Kronecker index theorem. Continuous mappings of a circle, homotopy and degree of a mapping. Tucker's lemma, Borsuk-Ulam theorem.
Dr. A. Chandrashekaran,Central University of Tamil Nadu, Thiiruvarur [ACS] Prof. K. C. Sivakumar ,Indian Institute of Technology Madras, Chennai [KCS]	Convex sets and convex functions, separation theorem, theorems of alternatives(Farkas lemma and Gordans theorem). Necessary and sufficient conditions for local and global optimality of a feasible point, WeierstrassTheorem. Fritz John optimality conditions and KKT optimality conditions. Lagrangian duality; strong and weak duality theorems. Algorithm for convex programs.
Dr. I. Jeyaraman, National Institute of Technology, Suratka l[IJ]	Complementarity problems: Problem Description, Source Problems, Examples, Existence and Uniqueness of solutions, Matrix classes: Positive definite, $P$, $Q$, $P_0$, sufficient, nondegenerate and semimonotone. Generalizations.
Prof. G. S. R. Murthy, Indian Statistical Institute Hyderabad [GSR]	Introduction to Semidefinite Programming Problem (SDP) with a historical perspective; some applications of SDP; how Linear Programming and Quadratic Programming Problems are special cases of SDP; some properties of SDP such as convexity; brief discussion on algorithms for solving SDPs. Case studies in operations research.
Prof. T. Parthasarathy, Indian Statistical Institute Chennai [TP]	Introduction to zerosum two person matrix games with some examples. Statement of Von Neumann's minimax theorem. Formulation of the game problem as a linear programming problem thereby giving an algoritm to find optimal strategies for matrix games through simplex method due to Dantzig. Statement of Nash theorem on bimatrix games and its LCP formulation. Stochastic games.
Prof. Sharad S Sane,Indian Institute of Technology, Mumbai [SS]	Theory of network flows, augmenting paths and Ford-Fulkerson algorithm and its scaling improvement, Edmonds-Karp polynomial time algorithm, Some applications: weighted bipartite matching problem, demand-supply network, airline scheduling, image segmentation and baseball elimination. Independence number determination and some idea of NP-complete problems including SAT and 3-SAT

Time Table

Day	Date	Lecture 1 (9.30–11.00)	Tea (11.00–11.30)	Lecturer 2 (11.30–1.00)	Lunch (1.00–2.30)	Tutorial (2.30–3.30)	Tea (3.30-4.00)	Tutorial (4.00-5.00)	Snacks 5.00-5.30
		(name of the speaker		(name of the speaker		(name of the speaker/tutor		(name of the speaker/tutor
Mon	04.07.2016	RBB		SS		RBB		SS
Tues	05.07.2016	SS		RBB		SS		RBB
Wed	06.07.2016	RBB		SS		RBB		SS
Thu	07.07.2016	SS		RBB		SS		RBB
Fri	08.07.2016	RBB		SS		RBB		SS
Sat	09.07.2016	SS		RBB		SS		RBB
SUNDAY
Mon	11.07.2016	TP		GSR		TP		GSR
Tues	12.07.2016	GSR		TP		GSR		TP
Wed	13.07.2016	TP		GSR		TP		GSR
Thu	14.07.2016	GSR		TP		GSR		TP
Fri	15.07.2016	TP		GSR		TP		GSR
Sat	16.07.2016	GSR		TP		GSR		TP
SUNDAY
Mon	18.07.2016	IJ		ACS		IJ		ACS
Tues	19.07.2016	ACS		IJ		ACS		IJ
Wed	20.07.2016	IJ		ACS		IJ		ACS
Thu	21.07.2016	KCS		IJ		KCS		IJ
Fri	22.07.2016	KCS		IJ		KCS		IJ
Sat	23.07.2016	KCS		IJ		KCS		ACS

Tutors

1. Dr. Mukesh Kumar Nagar, IIT Bombay (1^st and 2^nd weeks)

2. Dr. A. Chandrashekaran, Central University of Tamil Nadu, Thiruvarur (All three weeks)

3. Dr. I. Jeyaraman, NIT Surathkal (3^rd Week)

Actual Participants

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. Degree Date
1	5216	Ms Poonam Kesarwani	Female	IIT Kanpur	PhD	Msc, Iit Kanpur	2012
2	5532	Ms Tanushree Pandit	Female	Indian Institute Of Technology Kanpur	PhD Student	Iit Kanpur	2013
3	5547	Mr Geno Kadwin J	Male	Bharathidasan University	PhD	Bharathidasan University	2011
4	5674	Mr Kanagaraj K	Male	National Institute Of Technology	phD student	Bharathidasan University	2011
5	5923	Mr. Chaitanya G K	Male	NIT Karnataka	PhD Student	Mangalore University	2014
6	5972	Ms. Taruni Sridhar	Female	Central University Of Tamilnadu	Student	Pondicherry University	2015
7	6037	Mr Prashant Jha	Male	IIT Kanpur	PhD	IIT Kanpur	2013
8	6120	Ms Divyabharathi G	Female	Central University Of Tamilnadu, Thiruvarur.	PhD	Central University Of Tamilnadu	2015
9	6122	Mr Gokulraj S	Male	Central University Of Tamilnadu	PhD Student	Pondicherry University	2015
10	6145	Mr. Imran Khan	Male	Rukmini Devi Institute Of Advanced Studies	Asst. Prof.	Aligarh Muslim University	2001
11	6241	Mrs Dhivya Pari Rajmohan	Female	Bharathidasan University	PhD Student	Bharathidasan University	2012	10/1/2013
12	6331	Ms Thenmozhi Shunmugam	Female	Bharathidasan University	PhD	Bharathidasan University	2007	1/1/2015
13	6349	Ms Jamal Fathima	Female	Manonmaniam Sundaranar University	Ph.D	Manonmaniam Sundaranar University	2010
14	6509	Ms. Jigyasa Gaurav	Female	Indian Institute Of Science, Bangalore	Master of Science	Indian Institute Of Science, Bangalore	Awaiting Result
15	-	Mr. Vatsalkumar Nandkishor Mer	Male	IISER, Thiruvananthapuram
16	-	Ms. Ramya Selvaraj	Female	NIT, Tiruchirapalli

How to reach

CUTN is located at about eight kilometres from Thiruvarur town. The following is some information on getting to Thiruvarur and to CUTN from Thiruvarur.

Reaching Thiruvarur:

By Air: The nearest airport to Thiruvarur is Tiruchirapalli International Airport. Its about 120 kms from Thiruvarur. Frequent buses and few passenger trains are available from Tiruchirapalli.
By Train: There are direct trains from Chennai Egmore, Ernakulam, Goa and Tiruchendur to Thriruvarur. Those who travel from Bangalore may get down at Thanjavur. From Thanjavur there are passenger trains and frequent buses to Thiruvarur.

Reaching CUTN from Thiruvarur:

Thiruvarur bus stand and railway station are close by(five minutes walk). One can hire an auto at an approximate cost of Rs. 250 from Thiruvarur to reach CUTN. Otherwise there are CUTN bus service from Kangalancheri to university campus in the morning(between 8Am to 10AM) and evening(between 4:30PM and 5:30PM). Kangalancheri is en route to Mayiladuthurai from Thiruvarur at about 6kms.