AIS Aspects of Galois Theory (2012)

Venue: HRI, Allahabad
Dates: 10rh - 29th Dec, 2012.


Convener(s) Speakers, Syllabus and Time table Applicants/Participants


School Convener(s)

Name N. Raghavendra D. S. Ramana
Mailing Address Harish-Chandra Research Institute,
Chhatnag Road, Jhunsi,Allahabad – 211019

Harish-Chandra Research Institute,
Chhatnag Road, Jhunsi,Allahabad – 211019

Speakers and Syllabus 

 The proposed AIS will be devoted to the study of some aspects of Grothendieck’s generalization of Galois theory, and its relations with fundamental groups. This topic is fundamental to both number theory and algebraic geometry, and has numerous relationships with other areas in these two subjects. The AIS would be beneficial to students who wish to understand the basics of the topics. There has been a large amount of work in recent years on fundamental group schemes, Tannakian categories, and their interactions with the theory of moduli spaces of bundles over algebraic varieties. It is hoped that the AIS would help students to understand, and perhaps add to, some of that work.




Detailed Syllabus

K.N. Raghavan (KNR)


Separable algebras

N. Raghavendra (NR)


Recap of finite Galois theory and covering spaces; profinite groups

D.S. Ramana (DSR)


Classical infinite Galois theory

V. Balaji (VB)


Profinite fundamental group of a connected space; basic language of schemes

Amit Hogadi (AH)


Étale algebras, and Galois group actions on finite discrete spaces

V. Srinivas (VS)


Fundamental group of a connected scheme


Selected Applicants


Sr. SID Full Name Gender Affiliation State Position Univ/ Inst. MSc/ MA Year of passing MSc/ MA PHD degree date
1 1800 Mr. Guddu Kumar Male IISER Kolkata West Bengal MSc student IISER KOLKATA NA  
2 1820 Mr. Anurag Singh Male IISER Mohali Chandigarh Participant of AIS- Algebra IIT-Guwahati 2012  
3 1824 Mr. Suman Ahmed Male University of Burdwan West Bengal PhD Calcutta University 2008  
4 1856 Ms Purnima Satapathy Female NIT, Rourkela Orissa M.SC COMPLETED NIT, ROURKELA 2012  
5 1859 Mr Tushar Kanta Naik Male Chennai Mathematical Institute Tamil Nadu M.Sc Student Chennai Mathematical Institute NA  
6 1860 Mr. Bilal Ahmad Dar Male University Of Kashmir Jammu and Kashmir M.PHIL - RESEARCH SCHOLAR UNIVERSITY OF KASHMIR 2010  
7 1865 Dr Raja Durai Male Jaypee University of Information Technology Himachal Pradesh Assistant Professor I.I.T (Madras) 1997 30 Jul 2004
8 1870 Mr. Biswajyoti Saha Male University of Hyderabad Andhra Pradesh MSc Student University of Hyderabad 2012  
9 1876 Ms. Ekata Saha Female University of Hyderabad Andhra Pradesh MSc Student University of Hyderabad 2012  
10 1990 Mr. Manoj Kumar Patel Male Faculty of Engineering and Technology, Gurukula Kangri University. Uttarakhand/ Uttaranchal Asst. Professor U.P. College, Poorvanchal University Jaunpur 2004 1 Jul 2011
11 2010 Mr. Piyush Goyal Male S.C.D. Government College for Boys Punjab Lecturer Panjab University, Chaandigarh 2011  
12 2065 Mr. Sourav Das Male IIT Guwahati Assam STUDENT IIT GUWAHATI 2012  
13 2093 Ms Kritika Singhal Female IISER MOHALI Punjab MS STUDENT MS from IISER MOHALI NA  
14 2104 Mr. Shuddhodan Kadattur Vasudevan Male School of Mathematics, TIFR Maharashtra Research Scholar NA NA  
15 2114 Mr. Amit Kumar Singh Male University of Allahabad Uttar Pradesh MSc Student University of Allahabad 2011  
16 2211 Mr. N Annamalai Male Bharathidasan University Tamil Nadu MPhil Student University M.Sc. 2011  
17 2240 Mr. Dinesh Valluri Male Chennai Mathematical Institute. Tamil Nadu MSc Student BITS-Pilani, Goa campus. NA  
18 2305 Ms Saudamini Nayak Female NIT,Rourkela Orissa Ph.D Scholar Sambalpur University 2008  
19 2351 Mr Mohd Rafiq Mirza Male Sultan ul Arifeen Institute Jammu and Kashmir Lecturer University Of Kashmir 2003  
20 2372 Dr Deepak Kumar Tiwari Male H.O.D.,Mathematics Department, PSRDC College Uttar Pradesh H.O.D. Mathematics Kanpur University 2002 3 Mar 2012
21 2411 Mr. Neeraj Kumar Tripathi Male B.B.A University, lucknow Uttar Pradesh PhD B.H.U. Varansi 2009  
22 2428 Mr Rama Krishna Bandi Male IIT Roorkee Uttarakhand/ Uttaranchal Research Scholar Osmania University 2006  
23 2515 Mr. Tadkeshwar Nath Mishra Male DST – Centre For Interdisciplinary Mathematical Science, Baranas Hindu University Uttar Pradesh PhD AWADHESH PRATAP SINGH UNIVERSITY REWA (M.P)/M.SC 2010  


How to reach


1.By train

Allahabad is well connected by train from various parts of the country. The most convenient trains from New Delhi to Allahabad are 12418 Prayagraj Express, and 12276 Duronto Express. Trains passing through Allahabad include 12311 Howrah–Kalka Mail, 12322 Mumbai–Howrah Mail, and 12669 Chennai–Chhapra Ganga Kaveri Express. For detailed information on these and other trains to Allahabad, please see the Indian Railways Web sites.

2.By air

There is a single daily flight, AI 9811 of Air India, from Delhi to Allahabad on all days of the week except Sunday. For details, please see the Air India Web site.

3.By road

Allahabad is 238 km. from Lucknow, and 125 km. from Varanasi. There are frequent bus services between these cities and Allahabad, typically once every half hour. Private taxis also operate on these routes.

The road journey from Lucknow to Allahabad takes about 5 hours. Buses leave Lucknow from the Charbagh Bus Depot, and terminate at the Civil Lines Bus Depot in Allahabad.

The road journey from Varanasi to Allahabad takes about 3 hours. Most vehicles enter Allahabad along the Shastri Bridge over the river Ganga. In that case, one reaches Chak, a place near the Institute (see below), before Allahabad city.

4.From Allahabad city to HRI

The HRI campus is at Jhusi, about 13 km. from Allahabad city towards Varanasi. The Institute operates a regular bus service from the HRI City Guest House, to the campus. Please see for the address and phone number of the City Guest House, and∼yashpal/busschedule.pdf for the timetable of bus services between the City Guest House and the campus.

If you are coming to Allahabad by train, then come out through the Civil Lines Exit of the station, and take a rickshaw or a tempo from the station to the HRI City Guest House. The distance from the station to the City Guest House is about 4 km.

If you are coming from the city to HRI by a vehicle other than an HRI bus, the following information may be useful. To reach the campus from the city, one goes along the Shastri bridge over the river Ganga. Three km. beyond the end of the bridge, along the Grand Trunk Road (G. T. Road), there is an HRI sign, where one should turn right, off the highway and into Chhatnag Road. This point on the G. T. Road is called Chak. The HRI campus is a further 3 km. from Chak, along Chhatnag Road. The entrance to the campus is about 100 m. before the Birla Guest House, an establishment owned by a private industrial company.