# ATMW Topological Combinatorics (2014)

 Venue: Harish-Chandra Research Institute, Chhatnag Road,  Jhunsi,  Allahabad Dates: 6th to 11th Oct, 2014

 Speakers and Syllabus

Brief Description: The topics covered will be on application of Topological Dynamics, Ergodic Theory and Algebraic Topology in the areas of Combinatorics, Diophantine approximation and Combinatorial Number Theory.

Objective:To introduce advanced topics in ‘Topological and Ergodic methods’ in Combinatorics and Number Theory to young researchers in India. We give the details below.

Introductory lectures on Topological Dynamics, Ergodic Theory, Diophantine approximation and Combinatorics, followed by interaction of these areas of mathematics. Each speaker will give two to four talks and there will be some discussion hours.

Titles and abstracts of the topics covered are as follows:

1. Abstract: We shall first discuss some basic facts about Diophantine approximation. Afterwards, we shall see its connection with solutions of Diophantine equations.
2. Application of topological dynamics in Diophantine approximation by S. G. Dani:
Abstract: We discuss certain general principles of applying topological dynamics to address questions in Diophantine approximation, relating especially to studying values of linear and quadratic forms at integer points. The case of binary quadratic forms will be considered in detail.
3. Fractal methods in Diophantine approximation by Anish Ghosh
Abstract: In this course, we will discuss techniques to compute the Hausdorff measure and dimension of sets of arithmetic interest. We will also discuss Diophantine properties of a large class of measures including fractal measures, a subject which has seen rapid advances recently.
4. Ordered permutations in topological dynamics, Counting conjugacy classes and Partitions for classification by V. Kannan.
5. G- indices and the Topological Tverberg Theorem by Satya Deo:
Abstract: Starting from the classical Tvergerb Theorem we will introduce the notion of G-indices for a finite group G. With some review of algebraic topology,
will will state and prove the Topological Tverberg Theorem and the BMZ colored Tverberg Theorem.
6. large sets in amenable group and mixing properties by Dibyendu De:
Abstract: Mixing properties for dynamical systems via largeness properties of various “typical” return times sets or independent return times sets, have been studied by various authors.
In the current discussions we consider a hierarchy of notions of largeness for subsets of arbitrary amenable groups (such as thick sets, syndetic sets, IP-sets, etc., as well as some new classes) and study them in conjunction with recurrence in topological dynamics and ergodic theory. We use topological dynamics and topological algebraic properties of the Stone-Cech compactification (βG, ·) where G is an amenable group, to establish the connections between various notions of largeness.
List of speakers.
1. Prof. S. G. Dani, IIT Bombay, Mumbai
2. Prof. Anish Ghosh, TIFR and University of East Anglia
3. Prof. V. Kannan, University of Hyderabad.
4. Prof. Satya Deo, Harish - Chandra Research Institute, Allahabad.
7. Prof. Dibyendu De, Kalyani University, Kolkata

Lecture Notes. We shall be giving lecture notes, related materials to the participants during the school.

Time Table (Tentative) :In the morning two and after noon one 1 and 1/2 hours talks meant for main topics.the speakers will cover their topics. The last one hour talk is meant for Discussion and Tutorials. We shall give the tentative time-table as below.

 Date 09:30 - 11:00 11:15 - 12:45 14:15 - 15:45 16:00-17:00 06.10.14 Dibyendu Satyadeo Thangadurai Adhikari 07.10.14 Dibyendu Satyadeo Adhikari Thangadurai 08.10.14 Kannan Satyadeo Anish Tut/Discussion 09.10.14 Kannan Dani Anish Tut/Discussion 10.10.14 Kannan Dani Anish Tut/Discussion 11.10.14 Kannan Dani Anish Tut/Discussion

 Selected Applicants

 Sr. SID Full Name Gen der Affiliation State Position in College/ University University /Institute M.Sc./M.A. Year of Passing M.Sc./ M.A Ph.D. Deg. Date 1 6446 Mr. Rameez Raja M University of Kashmir J & K Ph.D. Student University of Kashmir 2009 2 6447 Mr Sameer Ahmad Gupkari M JK Institute Of Mathematical Sciences J & K Assistant Professor University of Kashmir 2003 3 6475 Mr. Soumya Dey M IISER Mohali Punjab PhD Student RKM Vivekananda University 2013 4 6483 Ms Rashmirekha Patra F Sambalpur University Orissa PhD student Utkal University 2010 5 6490 Mr. Subhash Chand M Rohilkhand University, Bareilly UP M.Sc S M.A. Awaiting Result 6 6502 Mr. Biplab Basak M Indian Institute of Science Bangalore Karnataka PhD Student IIT Kanpur 2010 7 6544 Mr. Lovy Singhal M Tata Institute of Fundamental Research Maharashtra Shyama Prasad Mukherjee Fellow IIT Kanpur 2011 8 6553 Dr. Jitendra Kumar Maitra M Rani Durgavati University, Jabalpur. MP Associate Professor Rani Durgavati University, Jabalpur. 1991 9 Nov 1998 9 6577 Mr Subhajit Jana M UNIVERSITY OF KALYANI WB PhD research schoolar IIT Bombay 2010 10 6592 Mr. Surojit Ghosh M Ramakrishna Mission Vivekananda University WB PhD I.I.T. Kanpur 2012 11 6593 Dr. Kunhanandan Mailattu M GOA UNIVERSITY Goa Assistant Professor UNIVERSITY OF CALICUT 1989 20 Jan 2012 12 6594 Ms. Arpita Ghosh F I.I.T.Kanpur U.P M.Sc I.I.T.Kanpur 2013 13 6596 Dr. Kamran Alam Khan M V.R.A.L. Govt. Mahila Degree College U.P ASSISTANT PROFESSOR Rohilkhand University, Bareilly 1997 19 Oct 2012 14 6597 Mr. Sajal Kumar Mukherjee M Vivekananda University WB PhD student Ramakrishna Mission Vivekananda University 2013 15 6600 Mr. Subramani Muthukrishnan M CMI Tamil Nadu PhD University of Madras 2009 16 6618 Mr. Nabajyoti Bhattacharjee M Assam University Assam M.Sc. student Assam University 2012 17 6619 Mr. Biman Kanti Nath M Assam University Assam M.Sc. student Assam University 2012 18 6621 Mr Nongthombam Dhyanchand M Jiri College Manipur Asst. Proffesor Assam University 2013 19 6643 Mr L Bimolchand Singh M Jiri college Manipur Asst. Proffesor Manipur University 2009 20 6653 Dr Geetanjali Sharma F Banasthali University Rajasthan Asst. Proffesor Jiwaji University 2007 12 Oct 2012 21 6656 Dr Satya Prakash Tripathi M Kirori Mal College, University of Delhi Delhi Associate Professor University of Delhi, St. Stephen's College 1991 16 Sep 2000

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.

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.