AIS Aspects of Galois Theory (2012)

 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.

Syllabus

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 http://www.hri.res.in/contact.html for the address and phone number of the City Guest House, and http://www.hri.res.in/∼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.