Annual Foundation School - Part II (2014 @ CEMS Almora)
Venue: | CEMS, Department of Mathematics, SSJ Campus, Kumaun University, Almora. |
Dates: | 1^{st} - 28^{th }May, 2014 |
Convener(s) | Speakers, Syllabus and Time table | Applicants/Participants |
Name | K.N. Raghavan | H.S. Dhami | Sanjay K Pant |
Mailing Address | Professor, Institute of Mathematical Sciences (IMSc), CIT Campus, Taramani, Chennai - 600113 |
Vice-Chancellor, Kumaun University, Nainital-263001 |
Associate Professor, Deen Dayal Upadhyaya College, (University of Delhi),Shivaji Marg, Karampura, New Delhi-110015 |
1. Ring Theory.
- Modules over Principal Ideal Domains Modules, direct sums, free modules, finitely geneover a PID, structure of finitely generated abelian groups, rational and Jordan canonical form.
- Basics Commutative rings, nil radical, Jacobson radical, localization of rings and modulrings, primary decomposition of ideals and modules.
- Integral extensions of rings, Going up and going down theorems, finiteness of intdiscrete valuation rings, Krull's normality criterion, Noether normalization lemma, Hilbert's Nullstellensatz
- Semisimple rings Wedderburn's Theorem, Rings with chain conditions and ArWedderburn’s main theorem.
Speakers: Parvati Shastri (Mumbai University), Ronnie Sebastian (IISER,Pune), K.N.Raghavan (IMSc, Chennai)
Course Associates: TBA (To Be Announced)
References:
S. Lang, Algebra, 3rd edition, Addison-Wesley.
- D. S. Dummit and R. M. Foote, Abstract Algebra, 2nd edition John-Wiley.
- N. Jacobson, Basic Algebra, Vol. 1 and 2, Dover, 2011.
- A. W. Knapp, Advanced Algebra, Birkhauser, 2011.
2. Functional Analysis.
- Normed linear spaces, Continuous linear transformations, application to differential equBanach theorems-analytic and geometric versions, vector valued integration.
- Bounded Linear maps on Banach Spaces Baire's theorem and applications: Uniformprinciple and application to Fourier series, Open mapping and closed graph theoremscomplemented subspaces, unbounded operators and adjoints.
- Bounded linear functionals Weak and weak* topologies, Applications to reflexive sepauniformly convex spaces, Application to calculus of variations.
- Hilbert spaces, Riesz representation theorem, Lax-Milgram lemma and applicationinequalities, Orthonormal bases, Applications to Fourier series and examples of special funcLegendre and Hermite polynomials.
Speakers: Anant R Shastri (IIT,Mumbai), R. Srinivasan (CMI,Chennai), Sanjay K Pant (CEMS, Almora), Abhay Bhatt (ISI,Delhi)**
Course Associates: TBA
** to be confirmed.
References
- J. B. Conway, A Course in Functional Analysis, II edition, Springer, Berlin 1990.
- C. Goffman, G. Pedrick, First Course in Functional Analysis, Prentice-Hall, 1974.
- S. Kesavan, Functional Analysis Volume 52 of Texts and readings in mathematics, HAgency (India), 2009.
- B. B. Limaye, Functional Analysis, II edition New Age International, 1996.
- A. Tayor and D. Lay, Introduction to Functional Analysis, Wiley, New York, 1980.
3. Differential Topology.
- Review of differential calculus of several variables: Inverse and implicit function theoremsmooth functions; smooth partition of unity, Submanifolds of Euclidean spaces (withboundary) Tangent space, embeddings, immersions and submersions, Regular valutheorem, Transversality and Stability. [The above material should be supported amply by exand examples from matrix groups.]
- Abstract topological and smooth manifolds, partition of unity, Fundamental gluing lemmfor Hausdorffness of the quotient, classification of 1-manifolds. Definition of a vector bundbundle as an example. Sard's theorem. Easy Whitney embedding theorems.
- Vector fields and isotopies Normal bundle and Tubular neighborhood theorem. Omanifolds and on normal bundles. Vector fields. Isotopy extension theorem. Disc Theorem. neighborhood theorem.
- Intersection Theory: Transverse homotopy theorem and oriented intersection numbmaps both oriented and non oriented cases, winding number, Jordan Brouwer separation theorem, Borsuk- Ulam theorem.
Speakers: Amiya Mukherjee (ISI, Kolkata), Gautam Mukherjee (ISI, Kolkata), Samik Basu (RKMVU, Kolkata)
Course Associates: TBA
References:
- V. Gullemin and A. Pollack, Differential Topology, Englewood Cliff, N.J. Prentice Hall (19(2) W. Hirsch, Differential Topology, Springer-Verlag.
- Morris W. Hirsch: Differential Topology,Springer-Verlag, New York Inc., 1976.
- J. W. Milnor, Topology from the Differential Viewpoint, Univ. Press, Verginia.
- Anant R. Shastri, Elements of Differential Topology, CRC Press, 2011.
Time Table (tentative)
Time Table
Week - 1 | |||||||
Date | 09:30 to 11:00 | 11:00-11:30 | 11:30-13:00 | 13:00 -14:30 | 14:30 -15:30 | 15:30 - 16:00 | 16:00 -17:00 |
May 01, 2014 | RT1 |
T E A |
FA1 |
L U N C H |
TRT1 |
T E A |
TFA1 |
May 02, 2014 | FA2 | DT1 | TFA2 | TDT1 | |||
May 03, 2014 | DT2 | RT2 | TDT2 | TRT2 | |||
May 05, 2014 | RT3 | FA3 | TRT3 | TFA3 | |||
May 06, 2014 | FA4 | DT3 | TFA4 | TDT3 | |||
May 07, 2014 | DT4 | RT4 | TDT4 | TRT4 |
Week - 2 | |||||||
Date | 09:30 - 11:00 | 11:00 - 11:30 | 11:30 - 13:00 | 13:00 - 14:30 | 14:30 - 15:30 | 15:30 - 16:00 | 16:00 - 17:00 |
May 08, 2014 | RT5 |
T E A |
FA5 |
L U N C H |
TRT5 | T
E A |
TFA5 |
May 09, 2014 | FA6 | DT5 | TFA6 | TDT5 | |||
May 10, 2014 | DT6 | RT6 | TDT6 | TRT6 | |||
May 12, 2014 | RT7 | FA7 | TRT7 | TFA7 | |||
May 13, 2014 | FA8 | DT7 | TFA8 | TDT7 | |||
May 14, 2014 | DT8 | RT8 | TDT8 | TRT8 |
Week-3 | |||||||
Date | 09:30 - 11:00 | 11:00 - 11:30 | 11:30 - 13:00 | 13:00 - 14:30 | 14:30 - 15:30 | 15:30 - 16:00 | 16:00 - 17:00 |
May 15, 2014 | RT9 |
T E A |
FA9 |
L U N C H |
TRT9 |
T E A |
TFA9 |
May 16, 2014 | FA10 | DT9 | TFA10 | TDT9 | |||
May 17, 2014 | DT10 | RT10 | TDT10 | TRT10 | |||
May 19, 2014 | RT11 | FA11 | TRT11 | TFA11 | |||
May 20, 2014 | FA12 | DT11 | TFA12 | TDT11 | |||
May 21, 2014 | DT12 | RT12 | TDT12 | TRT12 |
Week - 4 | |||||||
Date | 09:30 - 11:00 | 11:00 - 11:30 | 11:30 - 13:00 | 13:00 - 14:30 | 14:30 - 15:30 | 15:30 - 16:00 | 16:00 - 17:00 |
May 22, 2014 | RT13 |
T E A |
FA13 |
L U N C H |
TRT13 |
T E A |
TFA13 |
May 23, 2014 | FA14 | DT13 | TFA14 | TDT13 | |||
May 24, 2014 | DT14 | RT14 | TDT14 | TRT14 | |||
May 26, 2014 | RT15 | FA15 | TRT15 | TFA15 | |||
May 27, 2014 | FA16 | DT15 | TFA16 | TDT15 | |||
May 28, 2014 | DT16 | RT16 | TDT16 | TRT16 |
RTn - nth lecture in ring theory | TFAn - nth tutorial in functional analysis |
TRTn - nth tutorial in ring theory | DTn - nth lecture in differential topology |
FAn - nth lecture in functional analysis | TDTn - nth tutorial in differential topology |
Selected Applicants |
Please read the following instructions carefully.
- All further inquiries/communications, regarding the school should be addressed to the respective local organizers.
- Selected candidates should communicate the confirmation of their participation on or before 05th March 2014, along with a copy of their onward journey ticket where-ever applicable, failing which their selection will be cancelled automatically.
- If you are a selected candidate and decide NOT to attend the school for any reason what-so-ever, at any stage even after after confirmation, please communicate this immediately to the organizers so that some wait-listed candidates may benefit.
- Organizers are requested to fill-up the vacancies as and when they occur by informing the candidates from the wait-list.
- Wait-listed candidates may therefore book their tickets so as not miss such a chance merely because they would not get a train-ticket.
Serial | SID | Full Name | Gender | Affiliation | State | Position | University/Institute M.Sc./M.A. | Year of Passing M.Sc./M.A | Ph.D. Degree Date |
1 | 5095 | Ms. Namita Sharma | Female | Department of mathematics, delhi university | Delhi | M.Phil | St. Stephen's college | 2012 | |
2 | 5100 | Mr. Uma Shankar Verma | Male | University of allahabad | Uttar Pradesh | Research Scholar | University of Lucknow, Lucknow | 2006 | |
3 | 5129 | Mr. Vijay Kumar Yadav | Male | Ndian school of mines | Jharkhand | Ph.D | Dr. RAM MANOHAR LOHIYA AVADH UNIVERSITY, FAIZABAD | 2003 | |
4 | 5187 | Mr Sumit Kumar | Male | Imsc, chennai | Tamil Nadu | JRF | IISC | 2013 | |
5 | 5203 | Mr Anindya Ghatak | Male | National institute and science education and research | Orissa | PhD | Calcutta University | 2012 | |
6 | 5226 | Mrs Priyanka Ashok Harjule | Female | Mnit jaipur | Rajasthan | Ph.D | Bangalore University | 2012 | |
7 | 5244 | Mr. Ashish Kumar Kesarwany | Male | Iit guwahati | Assam | Ph.D. | IIT Kanpur | 2012 | |
8 | 5279 | Ms Sueet Millon Sahoo | Female | National institute of science education and research,bhubaneswar | Orissa | PhD | NATIONAL INSTITUTE OF TECHNOLOGY | 2012 | |
9 | 5289 | Ms Moni Kumari | Female | Niser bhubanswar | Orissa | Phd | BHU | 2012 | |
10 | 5292 | Mr. Suraj Krishna M S | Male | Chennai mathematical institute | PhD | University of Hyderabad | 2013 | ||
11 | 5305 | Ms Moni Kumari | Female | Niser | Orissa | Ph.D | BHU | 2012 | |
12 | 5309 | Mr Sapan Kumar Das | Male | Nit jamshedpur research scholar | Jharkhand | RESEARCH SCHOLAR | fakir mohan (auto) college | 2012 | |
13 | 5335 | Ms. Anupam Gumber | Female | Indian institute of technology indore | Madhya Pradesh | PhD Student | G.N.D.U Amritsar/Lyallpur Khalsa College Jalandhar | 2007 | |
14 | 5372 | Mr Harish D | Male | Department of mathematics, bangalore university. | Karnataka | PhD | Bangalore University | 2012 | |
15 | 5384 | Ms. Kavita Khandelwal | Female | Malaviya national institute of technology jaipur | Rajasthan | PhD | University of Rajasthan | 2008 | |
16 | 5403 | Ms. Sheela Verma | Female | Indian institute of technology kanpur | Uttar Pradesh | PhD | IIT Kanpur | 2012 | |
17 | 5406 | Ms Poonam Rani | Female | Department of mathematics | Delhi | phD | Jamia Millia Islamia | 2012 | |
18 | 5437 | Ms. Sweta Kumari | Female | University of allahabad, allahabad | Uttar Pradesh | D. Phil. Student | University of Allahabad | 2009 | |
19 | 5444 | Ms. Shelly Verma | Female | University of delhi | Delhi | M.Phil student | University of Delhi | 2010 | |
20 | 5448 | Mr. Ganga Prasad Yadav | Male | University of allahabad, allahabad | Uttar Pradesh | D.Phil. Student | University of Allahabad, Allahabad | 2011 | |
21 | 5457 | Mr. Sanjeev Kumar Maurya | Male | Indian institute of technology (bhu) varanasi | Uttar Pradesh | Ph.D | VBS PURVANCHAL UNIVERSITY JAUNPUR | 2010 | |
22 | 5459 | Mr. Alok Kumar Yadav | Male | Jawaharlal neharu university (jnu) | Delhi | Research Scholar | D.D.U. Gorakhpur University (U.P.) | 2011 | |
23 | 5466 | Mr. Nitin Bisht | Male | Indian institute of technology indore | Madhya Pradesh | PhD | H.N.B. GARHWAL UNIVERSITY | 2011 | |
24 | 5470 | Ms. Debaroti Das | Female | Nit silchar | Assam | PhD Student | Tripura University | 2011 | |
25 | 5471 | Mr. Krishanu Roy | Male | Institute of mathematical sciences | Tamil Nadu | Integrated Ph.d student | Appeared / Awaiting Result | ||
26 | 5486 | Mr. Avijit Nath | Male | Institute of mathematical sciences | Tamil Nadu | NBHM Ph.D. coursework student | Ramakrishna Mission Vivekananda University | 2013 | |
27 | 5502 | Ms Poonam Kesarwani | Female | IIT Kanpur | Uttar Pradesh | PhD | IIT Kanpur | 2012 | |
28 | 5507 | Ms. Meena Pargaei | Female | IIT Kanpur | Uttar Pradesh | PhD | G.B.P.U.A.&T. Pantnagar | 2012 | |
29 | 5510 | Ms. Meena Pargaei | Female | IIT Kanpur | Uttar Pradesh | PhD | G.B.P.U.A.&T. Pantnagar | 2012 | |
30 | 5512 | Mr Dillip Kumar Pradhan | Male | National institute of technology, rourkela | Orissa | PhD | Sambalpur University | 2011 | |
Waiting List | |||||||||
Serial | SID | Full Name | Gender | Affiliation | State | position | University/Institute M.Sc./M.A. | Year of Passing M.Sc./M.A | Ph.D. Degree Date |
1 | 5288 | Mr. Bikramaditya Sahu | Male | Niser , bhubaneswar | Orissa | PhD | Indian Institute of Technology Bombay | 2013 | |
2 | 5388 | Mr. Ranadip Gangopadhyay | Male | Banaras hindu university | Uttar Pradesh | PhD | NETAJI SUBHAS OPEN UNIVERSITY | 2013 | |
3 | 5400 | Ms. Meena Kumari Gurjar | Female | Malaviya national institute of technology, jaipur | Rajasthan | Research Scholar | University of Rajasthan Jaipur | 2008 | |
4 | 5511 | Mr. Ratan Kumar Giri | Male | Nit rourkela | Orissa | PhD | IIT Guwahati | 2012 | |
5 | 5517 | Mr Gireesh D.S | Male | Bangalore university | Karnataka | PhD | Bangalore University | 2011 | |
6 | 5521 | Mr. Arun Kumar | Male | Indian institute of science education and research, mohali | Punjab | Int.Phd | MOHALI | Awaiting Result | |
7 | 5534 | Mr. Abhishake Rastogi | Male | IIT Delhi | Delhi | Ph.D. | IIT Delhi | 2013 | |
8 | 5538 | Mr. Anuj Kumar | Male | IIT Delhi | Delhi | PhD | IIT Delhi | 2011 | |
9 | 5543 | Ms. Saroj Rani | Female | IIT Delhi | Delhi | Ph.D. Student | KURUKSHETRA UNIVERSITY | 2007 | |
10 | 5544 | Mr Aranya Lahiri | Male | IISER Bhopal | Madhya Pradesh | BS-MS 5th year student | IISER Bhopal | Appeared / Awaiting Result |
More Information
Advice to participants:
- Keep up with updates to this pageand follow instructions posted here.
- 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: The syllabi (pdf file available at the end of page) 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 (listed, as is customary in mathematics literature, by alphabetical order on last name):
Ring theory: K. N. Raghavan (IMSc), Ronnie Sebastian (IISER, Pune), Parvati Shastri (University of Mumbai)
Functional Analysis: Sanjay Pant (Delhi University), Anant Shastri (IITB), R. Srinivasan (CMI)
Differential topology: Samik Basu (RKMVU), Amiya Mukherjee (ISI, Kolkata), Gautam Mukherjee (ISI, Kolkata)
General advice to participants about RT-I: Revise linear algebra and basic facts about PIDs. The theorems will be proved for modules over a general PID although in the applications the PID will invariably be either the ring of integers or the ring of polynomials in one variable over a field. Specifically come prepared with knowledge of the following material:
- PIDs (as, for example, in Artin's algebra text)
- definitions and very basics of commutative rings (again as, for example, in Artin's algebra text)
- matrices over commutative rings: determinants, cofactors, invertibility
- linear algebra (including eigenvalues and canonical forms) from any standard book on linear algebra, e.g., Hoffman and Kunze.
Note on references for RT-II and RT-III: The following text is suggested as an additional important reference:
M. F. Atiyah and I. G. Macdonald: Introduction to Commutative Algebra, 1969.
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 (All notes are available as single download zip file at the end of the page):
Samik Basu: Additional problems for DT.
Amiya Mukherjee: Part 1, Part 2, Part 3, Part 4 of DT; Tutorial problems
K. N. Raghavan: Integral extensions, Simple and semisimple finite dimensional algebras
Anant Shastri: Normed linear spaces, Hahn-Banach theorems, Hilbert spaces
Parvati Shastri: Lectures on modules over PIDs
Ronnie Sebastian: Chapters 1 and 2 (of Atiyah-Macdonald), Chapter 3
R. Srinivasan: tutorial sheet 1, sheet 2
How to reach CEMS Almora
By Air:
The nearest airport is New Delhi. From Delhi one can reach Almora by train or by road as given below.
By Train:
The nearest train station is Kathgodam. Several important rail stations in India have direct connection to Kathgodam. From Delhi, there three main trains run almost daily from Delhi to Kathgodam: 12040 ANVT-KGM Shatabdi (06:15 AM), 15013 Ranikhet Express (22:40) and 15035 UTR-SAMPARK Express (16:00). We recommend the first two connections. One may also get down at Haldwani (the station just before Kathgodam). Please note that train number 12040 starts from ANAND VIHAR railway station at Delhi and the other two trains depart from OLD DELHI railway station. So, if you plan to reach Kathgodam by train, after arriving at the airport or New Delhi railway station, you should direct yourself towards the Anand Vihar railway terminus or the Old Delhi rail station in Delhi. The metro stops most nearest to these rail stations are Anand Vihar and Chandni Chowk respectively.
Summary of trains:
- *Delhi - Kathgodam by Ranikhet Express. (Train No. 15013)
- *Anand Vihar (ANVT)-Kathgodam (KGM) Shatabdi (Train o. 12040)
- Delhi - Kathgodam by Uttarakhand Smprk Kranti Express (Train No.15035)
- Delhi - Lal Kuan by Pooja Express. (Train No. 0517)
Trains with asterix are recommended.
By Road:
This option is little expensive, but direct and in many cases, would be flexible. This option is to travel to Almora from New Delhi Airport by road. You can book a (private) taxi at the airport or in advance. By car it generally takes 8-10 hours to Almora (from Delhi airport) assuming that you will take one or two breaks in between the journey.
AC Volvo buses are also available from ISBT Delhi to Kathgodam.
Car Direction:
Delhi - Hapur bypass - Moradabad bypass - Rampur - Bilaspur - Rudrapur - Haldwani - Kathgodam [approximately 270 kms]- Ranibagh - Bhimtal - Bhowali - Khairna Bridge - Kwarah Bridge - Almora. From Kathgodam/Haldwani to Almora: One has to travel this route by car or bus. It takes sround 3 hrs to reach Almora from Kathgodam. We recommend you to hire a car or shared taxi at Kathgodam/Haldwani. If you intend to travel by a shared taxi, it is better to get down at Haldwani since the availability of shared taxis are better there.