Annual Foundation School - Part II (2012)
|Venue:||Pune University, Pune|
|Dates:||4th Jun - 30th Jun, 2012|
|Convener(s)||Speakers, Syllabus and Time table||Applicants/Participants|
|Name||S. A. Katre||A. R. Shastri||V. V. Joshi|
Centre for Advanced Study in Mathematics,
|102 C, Department of Mathematics,
Indian Institute of Technology Bombay,
Mumbai - 400 076
|Dept. of Mathematics,
Univ. of Pune
2.1. Ring Theory.
(1) Module 1: (6 lectures) Commutative rings, nil radical, Jacobson radical, localization of rings and modules, Noetherian rings, primary decomposition of ideals and modules.
(2) Module 2: (6 lectures) Integral extensions of rings, Going up and going down theorems, ﬁniteness of integral closure, discrete valuation rings, Krull’s normality criterion, Noether normalization lemma,Hilbert’s Nullstellensatz
(3) Module 3 : 6 lectures Semisimple rings, Wedderburn’s Theorem, Rings with chain conditions and Artin’s theorem, Wedderburn’s main theorem,
(4) Module 4 : 6 lectures Semisimplicity and tensor products, SkolemNoether theorem, Wedderburn’s theorem about ﬁnite division rings,Frobenious theorem about division algebras over the reals.
(1) S. Lang, Algebra, 3rd edition, Addison-Wesley, (2) D. S. Dummit and R.
M. Foote, Abstract Algebra, 2nd edition John-Wiley (3) N. Jacobson, Basic
Algebra, Vol. 1 and 2, Dover, 2011. (4) A. W. Knapp, Advanced Algebra,
2.2. Functional Analysis. Chapters refer to the ones in [K].
(1) Module 1 : 6 lectures Normed linear spaces, Continuous linear transformations, application to diﬀerential equations,Hahn-Banach theorems-analytic and geometric versions, vector valued integration
(2) Module 2 : 6 lectures Baire’s theorem and applications: Uniform boundedness principle and application to Fourier series, Open map-
ping and closed graph theorems, annihilators, complemented subspaces, unbounded operators and adjoints
(3) Module 3 : 6 lectures Weak and weak* topologies, Applications to reﬂexive separable spaces, Uniformly convex spaces, Application to calculus of variations
(4) Module 4 : 6 lectures : Chapter 7 of [K] Hilbert spaces, Riesz representation theorem, Lax-Milgram lemma and application to variational inequalities, Orthonormal bases, Applications to Fourier series and examples of special functions like Legendre and Hermite polynomials.
2.3. Algebraic Topology. Numbers in brackets indicate sections from [Sh].
(1) Module 1: 6 lectures: Statement of basic problems in Algebraic Topology: extension problems and lifting problems; homotopy, relative homotopy, deformation, contraction, retracts etc.(1.1),Typical constructions: Adjunction spaces, Mapping cones, Mapping cylinder, Smash-product, reduced cones reduced suspension etc.(1.2,1.3), Categories and Functors. Deﬁnition and examples. Equivalence of functors, adjoint functors, examples.(1.4), Computation of fundamental group of the circle and applications. (3.1,3.2).
(2) Module 2: 6 lectures: Spaces obtained by attaching n-cells. Basic topological properties. Tubular neighbourhood theorem. Examples (2.1), CW-complexes and basic topological properties. Products of CW complexes. (2.1), Homotopy theoretic properties of CW compelxes.(2.1), Abstract Simplicial complexes and geometric realization. (2.2), Barycentric subdivision and Simplicial Approximation theorem.(2.3), Cellular Approximation theorem and applications.(2.4)
(3) Module 3: 6 lectures: Covering Spaces. (4.1), Lifting properties.(4.2), Relation with fundamental group. (4.3) Classiﬁcation (proof of existence may be skipped).(4.4), Computation of Fundamental groups: simpler cases of Van-Kampen theorem. Eﬀect of attaching n-cells.(4.6).
(4) Module 4: 6 lectures: Chain complexes, exact sequences of complexes, snake lemma, four lemma and ﬁve lemma. Homology long exact sequence, Axioms for homology, Construction of Singular chain complex, veriﬁcation of axioms (except homotopy axiom and excisionaxiom), Simplicial and Singular simplicial chain complexes. Statement of equivalence of all these homologies, Computations, Separation theorems, Invariance of Domain. Euler charasteristic.
[H] A Hatcher, Algebraic Topology, Cambridge University Press.
[M] Algebraic Topology, C. R. F. Maunder, Van Nostrand Reinhold Companay. London.
[Sp] E. H. Spanier, Algebraic Topology, Tata McGraw-Hill.
[Sh] A. R. Shastri, Basic Algebraic Topology, http//www.math.iitb.ac.in/ ars
- The selected participants are requested to confirm their participation by 31st March 2012 for booking accommodation.
- Confirmation mail should be sent to sakatre at gmail.com and to "Vinayak Joshi" vinayakjoshi111 at gmail.com
- Travel by 3rd AC Train fare is allowed to the participants.
- The participants are encouraged to bring along books related to topics of AFS-II.
|Sr||SID||Full Name||Gender||Affiliation||State||Position||University /Institute M.Sc./ M.A||Year of Passing M.Sc./ M.A||Ph.D. Deg. Date|
|1||923||Mr. Debashish Sharma||M||National Institute of Technology, Silchar||Assam||PhD scholar||Assam University, MSc Mathematics||2011||-|
|2||941||Mr. Pritam Rooj||M||
Dept. Of Pure Mathematics. Univ. Of Calcutta
|West Bengal||JRF||RAMAKRISHNA MISSION VIDYAMANDIRA , BELURMATH||2010||-|
|3||948||Mr Gopinath Panda||M||Indian Institute of Technology||Odisha||Research Scholar||Utkal University||2008||-|
|4||962||Mrs Nidhi Chaudhary||F||BITS Pilani||Rajasthan||Research Scholar||C C S University||2009||-|
|5||965||Ms Preeti Dubey||F||BITS Pilani||Rajasthan||Research Scholar||CSJMU Kanpur, M.Sc.||2006||-|
|6||975||Mr. Laxmi Kant Mishra||M||Univ.y of Allahabad||Uttar Pradesh||Research Scholar||University of Allahabad||2009||-|
|7||994||Mr. Sumit Kumar Kumar||M||Indian Institute of Science, Bangalore||Karnataka||Student||Depatment Of Mathematics , Indian Institute Of Science , Bangalore||-||-|
|8||996||Mr. Sachin Vitthalrao Sarode||M||Shri Muktanand College||Maharashtra||Assistant Professor||Pune University||2010||-|
|9||1019||Mr. Chiranjit Ray||M||Indian Institute of Technology, Guwahati||Assam||research scholar||Ramakrishna Mission Vidyamandira||2010||-|
|10||1045||Mr. Manish Chhabanrao Agalave||M||Fergusson College, Pune||Maharashtra||Assistant Professor||University of Pune||2006||-|
|11||1050||Mr. Rahul Gupta||M||IIT Delhi||Delhi||Research scholar||IIT Delhi||2011||-|
|12||1056||Mr. Rohit Gupta||M||IIT DELHI||DELHI||RESEARCH SCHOLAR||IIT DELHI||2011||-|
|13||1060||Ms Kumari Saloni||F||IIT Guwahati||Assam||Research Scholar||IIT Guwahati||2010||-|
|14||1066||Mr. Pralhad Mohan Shinde||M||IISER Pune||Maharashtra||Ph.D student||University of Pune (M.Sc)||2011||-|
|15||1070||Ms Dishari Chaudhuri||F||Indian Institute of Technology, Guwahati||Assam||Research Scholar||Indian Institute of Technology, Kharagpur||2010||-|
|16||1072||Ms. Manidipa Pal||F||IISER PUNE||Maharashtra||Research Fellow||IIT BOMBAY / M.Sc.||2011||-|
|17||1073||Mr Palraj J||M||
PSG College Of Arts And Science
|Tamil Nadu||Research Scholar||Sri Ramakrishna Mission Vidyalaya College of Arts & Science, Coimbatore||2009||-|
|18||1079||Mrs. T. Yogalakshmi T.Yogalakshmi||F||
Sri Sarada College For Women
|Tamil Nadu||Research Scholar (student)||University of Madras||2008||-|
|19||1090||Mr Sushil Bhunia||M||IISER PUNE||Maharashtra||Research Scholar||JADAVPUR UNIVERSITY/ M.Sc||2010||-|
|20||1091||Ms. Rana Noor||F||Banaras Hindu University||Uttar Pradesh||Research Scholar||Banaras Hindu University||2010||-|
|21||1102||Ms Vijayalakshmi Palanisamy||F||PSG College Of Arts And Science||Tamilnadu||Research Scholar||PSG College Of Arts And Science||2009||-|
|22||1106||Mr. Abhash Kumar Jha||M||NISER, Bhubaneswar||Orissa||research scholar||Banaras hindu university||2010||-|
|23||1109||Mr Loganathan Seenivasan||M||VHNSN College||Tamilnadu||Assistant Professor||Gandhigram Rural University||2006||-|
|24||1111||Mr. Hitesh Ramesh Raundal||M||IISER, Pune.||Maharashtra||2nd year Ph.D. Student||M.Sc. from University of Hyderabad, Hyderabad.||2010||-|
|25||1114||Ms Gunja Sachdeva||F||
Dayalbagh Educational Institute, Deemed University
|Uttar Pradesh||student||DAYALBAGH EDUCATIONAL INSTITUTE||2011||-|
|26||1119||Mr. Sheo Kumar Singh||M||Banaras Hindu University||Uttar Pradesh||Research Scholar||Banaras Hindu University||2006||-|
|27||1120||Mr. Prabhat Kumar Kushwaha||M||IISER, PUNE||Maharashtra||Research Scholar||
Dept. Of Mathematics, Faculty Of Science, B.H.U. , Varanasi
|28||1136||Mr. Gugan Chandrashekhar Thoppe||M||TIFR||Maharashtra||Research Scholar||-||-||-|
|29||1140||Mrs Visalakshi Vairavan||F||Sri Sarada College for women||Tamil Nadu||student||Sri Sarada College for women (autonomus)||2008||-|
|30||1143||Mr. Sasi Kumar Palanisamy||M||Gobi Arts & Science College, Gobichetti - palayam||Tamil Nadu||Research Scholar||Gandhigram Rural University, Dindigul||2004||-|
|31||1144||Mr. Abdul Nadim Khan||M||
Aligarh Muslim University, Aligarh
|Uttar Pradesh||Research Scholar||M.SC||2009||-|
|32||1162||Mr. Pabitra Debnath||M||St. Xavier's college (Autonomous), Kolkata||West Bengal||Assistant Professor.||I.I.T KANPUR||2004||-|
|33||1171||Mr. Chirag Garg||M||IIT Delhi||New delhi||Research scholar||Punjabi university Patiala||2010||-|
|34||1172||Mr . Yogesh Kumar||M||IIT Delhi||New delhi||Phd. Research Scholar||M.D.U. ROHTAK||2008||-|
|35||1179||Mr D Chellapillai||M||
|Tamil Nadu||Research Scholar||M.Sc Mathematics, Bharathidasan University, Tiruchirappalli, Tamil Nadu||2009||-|
|36||1191||Mr Azeef Muhammed Pa||M||University Of Kerala||Kerala||Research Scholar||University Of Hyderabad, M Sc Mathematics||2011||-|
|37||1194||Mr. Saurabh Chandra Maury||M||University of Allahabad||U.P.||Research scholar||University of Allahabad, Allahabad||2007||-|
|38||1201||Ms. Ishrat Jahan Md.Haroon Ansari||F||M.C.E Society's Abeda Inamdar Sr.College||Maharashtra||Assistant Professor||Department of Mathematics ,University of Pune||2007||-|
|39||1203||Ms. Sonali Vishnu Mandavkar||F||M.C.E.Society's Abeda Inamdar Senior College||Maharashtra||Assistant Professor||M.C.E.Society's Abeda Inamdar Senior College||2008||-|
|40||1204||Mr Dillip Kumar Pradhan||M||
|41||1206||Ms. Nasreen Bano Muslim Shaikh||F||Abeda Inamdar Senior College||Maharashtra||Assisstant Professor||Abeda Inamdar Senior College||2010||-|
|42||1222||Mr. Hardeep Singh Singh||M||JNU, New Delhi||DELHI||Pre. Ph.D.||
Punjabi University, Patiala
|43||1230||Mr. Ramdas Raosaheb Shiketod||M||
School Of Mathematical Sciences,
|Maharashtra||Student||School Of Mathematical Sciences,
SRTM Univ., Vishnupuri,
|44||1232||Ms. Priyanka Mahajan Ambulge||F||
Swami Ramanand Teerath Marathwada University, Nanded
|45||1248||Mr Rajiv Ganthi||M||Gandhigram Rural Institute, Deemded University||Tamil Nadu||Research Scholar||M.sc||2007||-|
| How to reach
University of Pune is on the University Road, and it is about 5 km from the Main Railway Station and Main Bus stand. The nearest Railway Station is Shivajinagar Railway Station (3km) and it is most convenient while coming from Mumbai side, but one should make sure that the train stops there. The autorickshaw fare is about 10 times the meter reading.
From airport the University is about 16 km.
When one enters the university there are 2 roads, take the right road to go to Mathematics Dept. or to University Guest House/ Univ. SET Guest House. Dept. of Math. comes first on this road on the left side, and it is a building with Green Colour Fence. To go to SET Guest House, one goes ahead and at the end turns to the
left, to go near main Guest House. The main Guest House is very near the main building (with Flag) and is next to VC Bungalow and from the main Guest House, a road goes to IUCAA. The SET Guest House is located on this road about 150 meters from main Guest House on the right side.