ATMW Local Cohomology (2016)
| Venue: |
St. Joseph College, Irinjalakuda, Kerala |
| Dates: |
20th June - 2nd July 2016 |
| Convener(s) | Speakers, Syllabus and Time table | Applicants/Participants |
| Name | Dr. Sr. Christy | Mangalambal N.R | Prof. J.K. Verma | Markus Brodmann |
| Mailing Address | St. Joseph College, Irinjalakuda, Kerala | St. Joseph College, Irinjalakuda, Kerala | IIT Bombay | - |
Speakers
- H. Ananthnarayan (IIT Bombay)
- Markus Brodmann (University at Zurich)
- N. T. Cuong (Institute of Mathematics, Hanoi)
- Krishna Hanumanthu (CMI, Chennai)
- Le Tuan Hoa (Institute of Mathematics, Hanoi)
- Manoj Kummini (CMI, Chennai)
- Dilip Patil (IISc, Bangalore)
- Tony J. Puthenpurakal (IIT Bombay)
- Peter Schenzel (Martin-Luther-University at Halle-Wittenberg)
Tutors
- H. Ananthnarayan (IIT Bombay)
- Markus Brodmann (University at Zurich)
- N. T. Cuong (Institute of Mathematics, Hanoi)
- Krishna Hanumanthu (CMI, Chennai)
- Le Tuan Hoa (Institute of Mathematics, Hanoi)
- Manoj Kummini (CMI, Chennai)
- Dilip Patil (IISc, Bangalore)
- Tony J. Puthenpurakal (IIT Bombay)
- Peter Schenzel (Martin-Luther-University at Halle-Wittenberg)
Course Plan in Brief
1. Manoj Kummini (CMI, Chennai) Manoj Kummini delivered 3 lectures on the following topics: Injective modules: Injective Modules, existence of injective hull, structure theorem for irreducible injective modules, examples of injective modules, Matlis duality.
2. Tony Puthenpurakal (IIT Bombay) Tony Puthenpurakal delivered 7 lectures on the following topics: Local cohomology: Resolutions and derived functors, Local Cohomology functor, direct limit of Ext modules, direct limit of Koszul cohomology modules. Depth, non-vanishing and vanishing theorems. Ring of differential operators on K [[X1 ...Xd]] where K is a field of characteristic zero. Application to local cohomology modules over Regular rings containing a field of characteristic zero. Associated primes of local cohomology modules. Finiteness of Bass numbers of local cohomology modules. Bounds on injective dimension of local cohomology modules.
3. Dilip Patil (IISc, Bangalore) Dilip Patil delivered 4 lectures on the following topics: Cohen-Macaulay rings: Koszul complex, regular sequences, characterisation of depth via Ext modules, Cohen-Macaulay modules and their characterisations, unmixedness theorems, examples of CM rings, Auslander Buchsbaum formula. Ferrand-Vasconceos theorem about I=I2.
4. H. Ananthnarayan (IIT Bombay) H Anathnarayan delivered 4 lectures on the following topics: Gorenstein rings: various definitions of Gorenstein rings, Bass numbers, injective resolutions, canonical module, local duality, examples of Gorenstein rings, Serre's theorem.
5. Krishna Hanumanthu (CMI, Chennai) Krishna Hanumanthu delivered 3 lectures on the following topics: Serr'e FAC paper: : Sheaves, Cech cohomology, Flasque sheaves, relation between local cohomology and sheaf cohomology, Grothendieck-Serre difference formula for Hilbert functions, projective Varieties: graded local cohomology, sheaves on projective varieties, global sections and cohomology.
6. Markus Brodmann (Univ. Zurich) Markus Brodmann delivered 4 lectures on the following topics: D-modules: Filtered algebras, derivations, Weyl algebra, the standard basis, weighted degrees and filtrations, weighted associated graded rings, filtered modules, D-modules, Grobner bases, weighted orderings, standard degree and Hilbert polynomials.
7. N.T. Cuong (Institute of Mathematics, Hanoi) N T Cuong delivered 4 lectures on the following topics: Sequentially Cohen-Macaulay modules: Filtrations and good systems of parameters, sequentially Cohen-Macaulay modules, characterization of sequentially Cohen-Macaulay modules by good systems of parameters.
8. Le Tuan Hoa (Institute of Mathematics, Hanoi) Le Tuan Hoa delivered 4 lectures on the following topics: Castelnuovo-Mumford regularity: Characterisations of Castelnuovo-Mumford regularity via local cohomology, Mumford's characterization of regularity of sheaves on projective space and its extension by Eisenbud-Goto, regularity and reduction numbers of large powers of ideals, bounding regularity in terms of degrees of defining equations, regularity and Hilbert coefficients, complexity of Grobner bases, some open problems.
9. Peter Schenzel (Univ. Halle) Peter Schenzel delivered 3 lectures on the following topics: Bezout's Theorem and local cohomology: Rees and form rings, Hilbert function, Hilbert polynomial, multiplicities, Auslander-Buchsbaum-Serre formula for multiplicities of parameter ideals, subcomplexes of Koszul and Cech-complexes, inequalities for local intersection numbers in Bezout's, theorem, corrections of results of Pritchard and Greuel-Lossen-Justin.
10. J. K. Verma (IIT Bombay) J. K. Verma delivered 1 lecture on the following topic: Stanley's solution of the ADG conjecture.
Researchers
- Clare D'Cruz (CD)
- Dipankar Ghosh (DG)
- Jyoti Singh (JS)
- Rakesh Reddy (RR)
- Parangama Sarkar (PS)
- Kumari Saloni (KS)
- Mandira Mondol (MM)
- R. Bhattacharyya (RB)
- Jai Laxmi (JL)
- Rajiv Kumar (RK)
- A.V. Jayanthan (AVJ)
Schedule of Lectures and Tutorials
| Day | Date | 9.30 | 11.00 | 11.30 | 1.00 | 2.00 | 3.30 | 4.00-4.50 (tut) | 4.50 | 5.10-.6.00 (tut) |
| Mon | 20-6 | DP |
T E A |
TP |
L U N C H |
MK |
T E A |
DP, mk, tp |
S N A C K S |
MK,dp,tp |
| Tue | 21-6 | DP | TP | MK | TP, mk, dp | MK, dp, tp | ||||
| Wed | 22-6 | DP | TP | MK | DP, tp, mk | MK, dp, tp | ||||
| Thu | 23-6 | DP | TP | PS | TP, dp, ps | PS, dp, tp | ||||
| Fri | 24-6 | MB | HA | PS | MB, ha, ps | HA, mb, ps | ||||
| Sat | 25-6 | MB | HA | PS | HA, mb, ps | PS, mb, ha | ||||
| Sun | EXCURSION | |||||||||
| Mon | 27-6 | MB |
T E A |
HA | L
U N C H |
KH |
T E A |
MB,ha,kh |
S N A C K S |
CD, DG |
| Tue | 28-6 | MB | HA | KH | JKV | JS, RR | ||||
| Wed | 29-6 | LH | NC | KH | LH, nc,kh | PS, KS | ||||
| Thu | 30-6 | LH | NC | TP | NC, lh,tp | MM, RB | ||||
| Fri | .1-7 | LH | NC | TP | LH, nc, tp | JL, RK | ||||
| Sat | .2-7 | LH | NC | TP | NC, lh, tp | Val | ||||
| Researcher | Institute | Research Paper |
| Clare D'Cruz (CD) | CMI, Chennai | Castelnuovo-Mumford regularity |
| Dipankar Ghosh (DG) | IIT Bombay | Asymptotic linear bounds of Castelnuovo- Mumford regularity in multi-graded modules |
| Jyoti Singh (JS) | IIT Bombay | Coisotropic Property of Characteristic Varieties |
| Rakesh Reddy (RR) | IISER, Trivandrum | de Rham Cohomology of Local Cohomology modules |
| Parangama Sarkar (PS) | IIT Bombay | Local cohomology of multi-Rees algebras & joint reduction numbers and product of complete ideals |
| Kumari Saloni (KS) | IIT Guwahati | On Hilbert coe_cients of parameter ideals |
| Mandira Mondol (MM) | TIFR, Mumbai | Hilbert Kunz Multiplicity and Hilbert Kunz density function of Segre product and tensor product of rings |
| R. Bhattacharyya (RB) | DA College, Kolkata | Behaviour of _niteness of associated primes of Lyubeznik functor under ring extensions |
| Jai Laxmi (JL) | IIT Bombay | Decomposing Gorenstein Rings as Connected Sums |
| Rajiv Kumar (RK) | IITBombay | Extremal Rays of the Betti Cones |
| A.V. Jayanthan (AVJ) | IITMadras | Regularity of binomial edge ideals of block graphs |
| 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. Deg. Date |
| 1 | 6793 | Ms. Kriti Goel | Female | IIT Bombay | PhD | IIT Bombay | 2015 | |
| 2 | 6989 | Mr. Rajiv Kumar | Male | IIT Bombay | PhD | Guru Nanak Dev University Amritsar | 2009 | |
| 3 | 7027 | Ms. Sudeshna Roy | Female | IIT Bombay | PhD | Jadavpur University | 2013 | |
| 4 | 7048 | Mr. Joydip Saha | Male | Ramakrishna Mission Vivekananda University | Ph.D. | Ramakrishna Mission Vivekananda University | 2010 | |
| 5 | 7327 | Mr. Rajib Sarkar | Male | CMI | PhD | IIT MADRAS | 2014 | |
| 6 | 7333 | Mr. Ram Shila | Male | JNU | PhD | UM DAE CBS, Mumbai University | 2014 | |
| 7 | 7348 | Ms Mitra Koley | Female | CMI | PhD | IIT Guwahati | 2011 | |
| 8 | 7475 | Mr. Rijul Saini | Male | TIFR | PhD | Integrated PhD | 2015 | |
| 9 | 7531 | Mr. Sujoy Chakraborty | Male | TIFR | Research Scholar | Chennai Mathematical Institute | 2015 | |
| 10 | 7600 | Mr. Sampat Kumar Sharma | Male | TIFR MUMBAI | PhD | IISER MOHALI | 2014 | |
| 11 | 7670 | Ms. Parangama Sarkar | Female | IITB | Phd | IIT Madras | 2011 | |
| 12 | 7690 | Mr. Subhajit Chanda | Male | IIT MADRAS | PhD | IIT MADRAS | 2015 | |
| 13 | 7812 | Ms. Jai Laxmi | Female | IIT BOMBAY | PhD | University of Hyderabad | 2012 | |
| 14 | 7859 | Mr. Selvaraja S | Male | IIT MADRAS | PhD | Indian Institute of Technology Kanpur | 2013 | |
| 15 | 7882 | Mr. Dipankar Ghosh | Male | IIT BOMBAY | PhD | Indian Institute of Technology Guwahati | 2011 | |
| 16 | 7921 | Mr. Amith K Shastri | Male | TIFR | PhD | University Of Madras | 2014 | |
| 17 | 7922 | Mr Ravitheja Vangala | Male | TIFR | PhD | Chennai Mathematical Institute | 2014 | |
| 18 | 8016 | Mr. Anoop Singh | Male | HRI | PhD | University of Allahabad | 2013 | |
| 19 | 8036 | Ms. Kumari Saloni | Female | IIT Guwahati | PhD student | IIT Guwahati | 2010 | |
| 20 | 8140 | Dr. Jyoti Singh | Female | IIT bombay | Post-doctoral Fellow | University of Lucknow | 2009 | 8/4/2015 |
| 21 | 8141 | Ms Mandira Mondal | Female | TIFR | PhD Student | |||
| 22 | 8145 | Mr. Ajay Kumar | Male | Dav University Jalandhar | Assistant Professor | Panjab University | 2008 | 5/29/2015 |
| 23 | 8180 | Dr. Rajsekhar Bhattacharyya | Male | Dinabandhu Andrews College | Associate Professor | |||
| 24 | 7520 | Mr. Soumitra Das | Male | North-Eastern Hill University | PhD | North-Eastern Hill University | 2012 | |
| 25 | 7847 | Mr. Prabakaran P | Male | Periyar University | PhD | M.Sc. | 2012 | |
| 26 | Ms. Dhanya V S | Female | St. Joseph's College | Assistant Professor | ||||
| 27 | Dr. Rakhesh Reddy | Male | ||||||
| 28 | Mr.Bibekananda | Male | ||||||
| 29 | Ms. Sabna K S | Female | ||||||
| 30 | Ms. Clare D'Cruz | Female |
How to reach
Venue: St. Joseph’s College, Irinjalakuda, Thrissur, Kerala 680121
Accommodation: Chand V Regency, Munnupedika, Thrissur, Kerala, India 680681 (9.4 kms from the venue)
How to Reach to Chand V Regency
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Thrissur Railway |
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Thrissur- Irinjalakkuda- |
Rs. 720 |
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Moonupedika(30km) |
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Bus |
Reach Sakthan Thampuran Bus |
Rs. 30 |
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Rs. 80 |
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stand By Auto (2 km), |
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Catch bus to Kodungaloor via |
Rs. 30 |
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Vadanapilly/Thriprayar , get down |
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at Munnupedika stop (33 km) |
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Get Auto to Chand V Regency |
Rs. 20 |
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Auto |
Thrissur- Irinjalakkuda- |
Rs. 600 |
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Moonupedika(30km) |
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Irinjalakkuda |
Taxi |
Kalletumkara-Irinjalakkuda- |
Rs. 450 |
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Railway Station |
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Moonupedika(18km) |
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(Kalletumkara) |
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Auto |
Kalletumkara-Irinjalakkuda- |
Rs. 360 |
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Moonupedika(18km) |
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Cochin (Nedumbassery) |
Taxi |
Nedumbassery- Angamaly-Chalakudy- Potta- |
Rs. 1200 |
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International |
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Irinjalakuda-Munnupedika (50 km) |
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Airport |
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