Advanced commutative algebra (2019)

  Convener(s)
Name: Prof. Mousumi Mandal
 Prof. Ramakrishna Nanduri Prof. Manoj Kummini      
Mailing Address:

Department of Mathematics
IIT Kharagpur
West Bengal-721302

 Department of Mathematics
IIT Kharagpur
West Bengal-721302		 Chennai Mathematical Institute
Email: mousumi at maths.iitkgp.ac.in nanduri at maths.iitkgp.ac.in mkummini at cmi.ac.in

 This school covers topics in an advanced course in commutative algebra. Topics to be discussed include: flatness, criterion for flatness, fibres of flat maps, generic flatness theorem; Kahler differentials, fundamental exact sequences; completion; smoothness; jacobian criterion; Cohen structure theorem (equicharacteristic case); excellent rings; Lichtenbaum-Schlessinger functors. The prerequisite for this school is a course in introductory commutative algebra (associated primes and primary decomposition; integral extensions; dimension theory of noetherian local rings).

Please Note:  Participants have to arrange for their own travel.

Dates: 

Monday, December 2, 2019 - 09:00 to Saturday, December 14, 2019 - 18:45

Venue: 

Venue Address: 

Department of Mathematics
Indian Institute of Technology Kharagpur
West Bengal-721302

 

Venue State: 

Venue City: 

PIN: 

721302

Chrono Order: 

331

Syllabus: 

 

Syllabus: (Each speaker is required to deliver minimum 6 lectures).

 

Name of the Speaker with affiliation

No. of Lectures

Detailed Syllabus

Utsav Choudhury

ISI Kolkata

6

Flatness, going down theorem, local criteron for flatness,fibres of flat maps,, generic flatness theorem

Prof Sarang Sane

IIT-Madras

6

Derivations, Module of Kahler differentials, fundamental exact sequences, relation to conormal modules, completions and complete rings

Prof Suresh Nayak

ISI Bengaluru

6

Formal smoothness and smoothness, separable field extensions, Cohen structure theorem (equichar. Case) jacobian criterion, relation to flatness and Kahler differentials

Prof Manoj Kummini

CMI

6

Excellent rings; Lichtenbaum-Schlessinger functors.

 

References:

  1. Matsumura, Commutative Algebra
  2. Eisenbud, Commutative algebra with a view towards algebraic geometry
  3. Hartshorne, Algebraic geometry
  4. Hartshorne, Deformation theory.

 

Time Table: 

 Time-Table (with names of speakers and course associates/ tutors):

Day

Date

Lecture 1

(9.30
to
11.00)

Tea

(11.05
to
11.25)

Lecture 2

(11.30
to
1.00)

Lunch

(1.05
to
2.25)

Tutorial

(2.30
to
3.30)

Tea

(3.35
to
3.55)

Tutorial

(4.00
to
5.00)

Snacks

5.05
to
5.30

 

 

(name of the speaker)

 

(name of the speaker)

 

(name of the speaker + tutors)

 

(name of the speaker + tutors)

 

Mon

2/12//2019

UC

 

SS

 

UC+2

 

SS+2

 

Tues

3/12/19

UC

 

SS

 

UC+2

 

SS+2

 

Wed

4/12/19

UC

 

SS

 

UC+2

 

SS+2

 

Thu

5/12/19

UC

 

SS

 

UC+2

 

SS+2

 

Fri

6/12/19

UC

 

SS

 

UC+2

 

SS+2

 

Sat

7/12/19

UC

 

SS

 

UC+2

 

SS+2

 

 SUNDAY : OFF

Mon

9/12/19

SN

 

MK

 

SN+2

 

MK+2

 

Tues

10/12/19

SN

 

MK

 

SN+2

 

MK+2

 

Wed

11/12/19

SN

 

MK

 

SN+2

 

MK+2

 

Thu

12/12/19

SN

 

MK

 

SN+2

 

MK+2

 

Fri

13/12/19

SN

 

MK

 

SN+2

 

MK+2

 

Sat

14/12/19

SN

 

MK

 

SN+2

 

MK+2

 

 

Tutorial Assistants:

S. No.

Name

Affiliation

1

Ramakrishna Nanduri

IIT Kharagpur

 

 

Selected Applicants: 

Final list

Out Station
sr.n SID Full Name Gender Affiliation Position in College/University University/Institute M.Sc./ M.A. Year of Passing M.Sc./M.A Phd deg date
1 26774 Mr. Kamalesh Saha Male IIT Gandhinagar PhD Aliah University 2017  
2 27173 Mr Sourav Sen Male Ramakrishna Mission Vidyamandira PhD Ramakrishna Mission Vivekananda University 2013  
3 27459 Mr. Arindam Das Male Bits Pilani PhD NIIT Rourkela 2016  
4 28069 Mr. Om Prakash Male Indian Institute Of Technology, Gandhinagar PhD Maharshi Dayanand University, Rohtak 2016  
5 28074 Mr Pranjal Srivastava Male IIT Gandhinagar PhD University of Allahabad    
6 28122 Mr. Kanoy Kumar Das Male Ramakrishna Mission Vivekananda Educational and Research Institute PhD Ramakrishna Mission Vidyamandira 2018  
7 28178 Dr. Dishari Chaudhuri Female Indian Institute of Science Education and Research Mohali Post Doctoral Fellow Indian Institute of Technology Kharagpur 2010 10/01/09
8 28254 Ms. Saipriya Dubey Female IIT Bombay PhD M.S. Baroda University 2016  
9 28442 Mr. Rajib Sarkar Male IIT Madras PhD IIT Madras 2014  
10 28457 Mr. Arvind Kumar Male Indian Institute of Technology Madras Ph.D. IIT,Madras 2016  
11 28486 Mr. Subhajit Chanda Male IIT MADRAS PhD IIT Madras 2015  
12 28491 Mr Dibyendu Mondal Male Indian Institute of Technology Bombay PhD IIT Bombay 2015  
13 28592 Mr Provanjan Mallick Male IIT Bombay Ph.D IIT Madras 2012 31/12/18
14 28600 Mr. Ankit Mishra Male IIT Bombay Ph.D. University of Allahabad 2015 NA
15 28733 Ms. Thulasi K R Female Pondicherry University PhD Student Pondicherry University Integrated M.Sc. 2017  
16 28735 Ms. Kriti Goel Female IIT Bombay PhD student IIT Bombay 2015  
17 28757 Mr. Sudip Pandit Male IIT Gandhinagar PhD IIT Gandhinagar 2018  
18 28763 Mr. Amit Roy Male IISER Mohali PhD Student CMI 2015  
19 28782 Mr. Dharm Veer Male Chennai Mathematical Institute PhD Student Chennai Mathematical Institute 2016  
20 28786 Mr. Nirmal Kotal Male Chennai Mathematical Institute PhD IIT Kharagpur 2017  
21 28811 Mr. Soham Mondal Male IIT Madras PH.D VISVA-Barti 2017  
22 28833 Dr. Parangama Sarkar Female Chennai Mathematical Institute Postdoc IIT Madras 2011  
23 28841 Mr. Sanjay Singha Male IIIT Vadodara PhD VISVA-Barti 2018  
24 28865 Mr Gopinath Sahoo Male Harish-Chandra Research Institute PhD University of Hyderabad, Hyderabad 2015  
25 28876 Mr Chandramouli Chakraborty Male Indian Institute Of Technology Madras Ph.d Indian Institute of Technology Madras 2018  
26 28908 Ms. Rakhi Pratihar Female IIT Bombay PhD Jadavpur University 2016  
27 28915 Ms. Sudeshna Roy Female IIT Bombay PhD Jadavpur University 2013  
28 28934 Dr. Kumari Saloni Female Chennai mathematical institute Visiting fellow IIT Guwahati 2010 28/11/02
29 28606 Ms. Parnashree Ghosh Female Indian Statistical Institute, Kolkata PhD IIT Kharagpur 2018  
30 28764 Mr. Amit Patra Male IIT Bombay PhD IIT Bombay 2017 N/A
Local
1 28787 Mr. Dipak Kumar Pradhan Male IIT KGP PhD IIT Kahragpur 2018  
2 28868 Mr. Bidwan Chakraborty Male IIT Kharagpur PhD IIT Kanpur 2016  
3 28883 Ms. Rimpa Nandi Female IIT Kharagpur PhD The University of Burdwan 2014  
4 28906 Mr. Anindya Ganguly Male IIT Kharagpur MS(by Research) IIT Kharagpur 2016 NA
5 28932 Mr. Harshit Jitendra Motwani Male IIT KGP Integrated MSc Student IIT KGP    
7 28544 Ms. Poulami Mandal Female Indian Statistical Institutes, Bangalore Centre PhD Student Indian Statistical Institute, Bangalore Centre 2017  
Waiting list
1 28871 Mr. Dibyendu Biswas Male IIT Bombay PhD IIT Bombay 2017  
2 27436 Mr. Subham Bhakta Male Georg-August-Universität Göttingen PhD student Chennai Mathematical Institute 2018  
3 27806 Ms. Sulakhana Chowdhury Female IISER TVM Integrated PhD 2nd Year IISER,TVM Awaiting Result  
4 28912 Ms. Jigyasa Gaurav Female IIT Bombay PhD Indian Institute of Science, Bangalore 2017  
5 28921 Mr. Biman Roy Male Indian Statistical Institute PhD Student Indian Statistical Institute 2018  
6 27361 Mr Saravanan S Male Pondicherry University Ph.D. Scholar pondicherry University 2018  
7 28292 Mr. Soumitra Das Male North-Eastern Hill University PhD North-Eastern Hill University 2012  
8 28599 Mr. Kushal Bhowmick Male Harish Chandra Research Institute. PhD Indian Statistical Institute. 2016  
9 28613 Mr Santanu Tantubay Male Harish-Chandra Research Institute PhD Hyderabad Central University 2018  
10 28636 Dr Aftab Hussain Shah Male Central University of Kashmir Assistant Professor Aligarh Muslim University 2004 Thesis Title On Epimorphisms dominions and semigroup identities
11 28689 Mr. Prajnan Kumar Bhagawati Male Gauhati University PhD Pondicherry University 2017  
12 26587 Mr Soumik Ghosh Male Indian Statistical Institute, Kolkata M Math Student Indian Statistical Institute    
13 28860 Mr. Abdul Hannan Male Indian Statistical Institute, M. Math Student Indian Statistical Institute, Kolkata    
14 28886 Mr. Sarbajit Dey Male Indian Statistical Institute M.Math student Indian Statistical Institute    
15 28911 Ms. Poornima B Female IISER Pune BS-MS student Indian Institute of Science Education and Research Awaiting Result  
16 28889 Mr Supravat Sarkar Male Indian Statistical Institute B.Stat Student      
17 28861 Dr. Selvaraja S Male Institute of Mathematical Sciences, Chennai Post Doctoral Fellow Indian Institute of Technology Kanpur 2013 26/03/18

 

 

How to Reach: 

Kharagpur is known world over for two landmarks. One, the longest railway platform, and the other, the Indian Institute of Technology, more commonly known as IIT. Situated about 120 km west of Kolkata, Kharagpur is well connected to Kolkata by Road and Rail transport. Kharagpur can be reached in about 2 hours by train or 3 hours by car from Howrah railway station of Kolkata. Kharagpur is also connected by direct train services to most major cities of the country. The Institute is about 10 minutes drive (5 km) from the Kharagpur railway station. Private taxi, autorickshaw or cycle-rickshaw can be hired to reach the Institute.

By Air

The nearest airport to Kharagpur is the Netaji Subhas Chandra Bose International Airport (CCU), Kolkata. You can get a flight to Kolkata airport on regular basis. It is widely connected to almost all the major destinations of the country.
From Kolkata Airport you can take a cab from the Airport taxi stand to Kharagpur. The distance is almost 140KM. The travel time is approximately 2.30 hrs. It costs roughly Rs. 3000/- (depending on the taxi type). OR
You can take a cab and reach Howrah railway station. Take a taxi to Howrah Station (UBER and OLA is available). The cost is approximately Rs. 300. It takes around 1.30 Hrs (if you get Traffic Jam) to reach Howrah station. There is regular Express and Local (choice is yours) trains to Kharagpur. It takes 2 hrs by an express train - Fare - Rs 60/- to 150/- depending on class and train type. The Institute is 5 km from Kharagpur railway station. (Kharagpur Rly stn.-IIT campus: Taxi fare Rs. 150 /-, Rickshaw Fare Rs. 60/-, Auto rickshaw Fare Rs.100/-)

By train

Kharagpur is well connected to most major cities of India by rail. There are frequent trains to Kharagpur. Check http://www.indianrail.gov.in/ for train details. Alternatively, you can reach the Howrah Railway station and take a local or express train to Kharagpur. OR
Book a cab to reach Kharagpur via road. The distance is almost 140KM. The travel time is approximately 2.30 hrs. It costs roughly Rs. 3000/- (depending on the taxi type).
The Institute is 5 km from Kharagpur railway station. (Kharagpur Rly stn.-IIT campus: Taxi fare Rs. 150 /-, Rickshaw Fare Rs. 60/-, Auto rickshaw Fare Rs.100/-)

School Short Name: 

aca

Last Date Application: 

Wednesday, March 13, 2019

School Type: 

AIS