ATMW Lattices : Geometry and Dynamics (2014)

Venue: IISER, Mohali
Dates: 17th to 22nd Dec, 2014


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


School Convener(s)

Name Dr. Krishnendu Gongopadhyay Dr. Mahender Singh
Mailing Address Department of Mathematical Sciences, IISER Mohali,
Knowledge city, Sector 81, Ajit Garh, Punjab 140306, India
Department of Mathematical Sciences, IISER Mohali,
Knowledge city, Sector 81, Ajit Garh, Punjab 140306, India


Speakers and Syllabus 

Description of the Proposed Meeting
In the proposed meeting, we shall investigate geometric, arithmetic and dynamical aspects of lattices in Lie groups. The main component of the program will be an advanced school that would consists of around four courses on several topics related to lattices. The proposed courses are given below. Apart from these courses, there will also be some invited talks by experts on recent developments. Topics are chosen to cover the modern aspects of the area which are very much active presently. During the entire program, we shall have ample time to hold discussions among the young participants and the experienced researchers/speakers.The event would take place at IISER Mohali. The program would involve researchers from around the globe as well as enthusiastic young graduate and post-doctoral students.

The event would be centered around lattices in locally symmetric spaces, with special emphasis on lattices in hyperbolic geometry. On the other hand, a fundamental problem of symmetric spaces is the relationship between arithmetic groups and lattices. On the one hand, Borel and Harish-Chandra proved that in all symmetric spaces of non-compact type, all arithmetic groups are lattices and on the other hand Margulis proved the arithmeticity of all lattices of rank at least 2. It follows from the work of Corlette and, Gromov and Schohen [3] that all lattices in the quaternionic hyperbolic space and Cayley hyperbolic plane are arithmeti lattices. Gromov and Piateski-Shapiro [2] have given examples of non-arithmetic lattices for HnR . Complex hyperbolic space is the only class of symmetric spaces where it is not settled whether lattices are arithmetic. In a seminal paper, Mostow [4] constructed examples of non-arithmetic lattices in H2c . Deligne and Mostow [1] found a non-arithmetic lattice in H3C . For Hn C, n ≥ 4, the question is open and it is one of the most important question that is associated to complex hyperbolic space. Recently there are also many breakthroughs in the dynamics of lattices on homogeneous spaces. There is a striking similarity and also disparity between dynamics on homogeneous spaces of lattices and the so called Teichmuller dynamics. The aim of the workshop is to discuss all these geometric, arithmetic and dynamical aspects of lattices and to give the audience a unified view towards these beautiful objects.

Proposed Courses
The workshop would be aiming mostly to the young graduates and post-doctoral students who are either working or want to work in the related areas. The aim is to expose studets to this fascinating and active area of Mathematics that has tremendous potential for further growth. Here are the details of the courses that we plan in the workshop. The speakers without asterix are confirmed speakers.

Topic Instructor Affiliation Deatil of topic
Complex HyperbolicLattices John R. Parker Durham University Complex hyperbolic lattices may be constructed in (at least) four different ways. I will outline these methods and then illustrate them with some examples. The examples include lattices constructed by Mostow, Livné and Deligne-Mostow in the 1980s, including a description given by Thurston. The most important aspect of all these constructions is that they contain examples that are non-arithmetic. I will then outline a more recent project concerning triangle groups and how it is possible to use them to find new examples of non-arithmetic lattices. The latter work is joint with Martin Deraux and Julien Paupert. Background material for the course can be found in the survey article here.
Dynamics of Lattice actions S. G. Dani IIT Bombay TBA
Complex hyperbolic lattices-I  Julien Paupert ASU This course will be an introduction to discrete groups and lattices acting on hyperbolic spaces. More specifically, we will begin by introducing (real and complex) hyperbolic spaces, their isometries and subspaces. We will then review definitions and general properties of discrete groups of isometries and lattices, including properly discontinuous groups actions, fundamental domains and quotient spaces. Finally, we will survey two general methods for constructing lattices: via algebra and number theory, to obtain arithmetic lattices, and via geometry, to obtain reflection groups and Coxeter groups.
Knots and Lattices Kapil H. Paranjape IISER Mohali TBA

Research Talks

  • C. S. Aravinda (TIFR-CAM)
  • Siddhartha Bhattacharya (TIFR Mumbai)
  • Pralay Chatterjee (IMSc Chennai)
  • Jens Funke (Durham University)
  • Anish Ghosh (TIFR Mumbai)
  • C. S. Rajan (TIFR Mumbai)
  • Riddhi Shah (JNU Delhi)
  • B. Sury (ISI Bangalore)



  1. P. Deligne and G.D. Mostow, Monodromy of hypergeometric functions and non-lattice integral monodromy. Publ. Math. I.H.E.S. 63 (1986), 5–89.
  2. M. Gromov and I. Piatetski-Shapiro; Nonarithmetic groups in Lobachevsky spaces. Publ. I.H.E.S. 66 (1988) 93–103.
  3. M. Gromov and R. Schoen; Harmonic maps into singular spaces and p-adic superrigidity for lattices in groups of rank one. Publ. I.H.E.S. 76 (1992) 165–246.
  4. G.D. Mostow, On a remarkable class of polyhedra in complex hyperbolic space. Pacific Journal of Maths. 86 (1980) 171–276.
  5. Parker, J. R. ; Complex hyperbolic lattices, Discrete Groups and Geometric Structures, Contemporary Mathematics 501 AMS, (2009) 1–42.


Selected Applicants/Participants

 List of Participants (Outside)

Sr. SID Full name Gender Affiliation City, State Position in  College/ University Univ./ Inst.
M.Sc./ M.A.
Year of Passing M.Sc./ M.A Ph.D. Degree Date
1 7701 Mr. Arijit Ganguly Male Tata Institute of Fundamental Research


Research Scholar   Appeared/ Awaiting
2 7638 Mr. Sugato Mukhopadhyay Male Indian Institute of Technology, Kanpur Kanpur,
Uttar Pradesh
PhD Student Delhi University Appeared/ Awaiting
3 7651 Mr. Suman Paul Male IIT Kanpur Kanpur,
Uttar Pradesh
PhD IIT Kanpur Appeared/ Awaiting
4 7270 Mr. Sampat Sharma Male Tata Institute Of fundamental Research Mumbai,
Phd IISER MOHALI Appeared/ Awaiting
5 7372 Mr. Ramesh Kasilingam Male IIT BOMBAY Mumbai,
Research Scholar
Anna university,
6 7232 Mr Muna Naik Male Indian Statistical Institute, Kolkata Kolkata,
West Bengal
PhD National Institute Of
Science Education
and Research
7 6641 Mr. Vishal Gupta Male Zakir Husain Delhi College New Delhi,
Assistant Professor IIT Guwahati 2010  
8 6816 Dr. Shameek Paul Male Centre for Excellence in Basic Sciences Mumbai,
Research Associate University of Mumbai 2005 11 Jan 2012
9 6845 Dr Bibhas Chandra Saha Male Chandidas Mahavidyalaya Bolpur,
West Bengal
Assistant Professor Burdwan University 1995 2 Jul 2010
10 6300 Mr. Abhishek Mukherjee Male Kalna College

West Bengal

Assistant Professor Burdwan University 2007  
11 6304 Dr. Narinder Sharma Male Govt. Gandhi memeorial Science College Jammu

Jammu And Kashmir

Assistant Professor university of Jammu 2004 31 Oct 2012
12 7718 Mr Arghya Mondal Male The Institute of Mathematical Sciences, Chemnnai Chennai,
Tamil Nadu
PhD student   2012  
13 7748 Mr. Nitin Kumar Sharma Male Gautam Buddha University Greater Noida,
Uttar Pradesh
M.Sc Student GAUTAM BUDDHA UNIVERSITY Appeared/ Awaiting
14 7760 Ms. Sheela Verma Female Indian Institute Of Technology Kanpur India,
Uttar Pradesh
PhD IIT Kanpur 2012  
15 7814 Mr. Alok Kumar Yadav Male Jawaharlal Nehru University New Delhi,
PhD D.D.U. Gorakhpur
University, U.P.
16 7829 Mr. Yashpaul Male Malwa College Bondli Samrala Samrala, District Ludhiana, Punjab Assistant Professor Government College,
Hoshiarpur, Punjab (India)
17 7836 Ms. Asha Singh Female Himachal Pradesh University Shimla,
Himachal Pradesh
Himachal Pradesh University 2010  
18 7841 Mr. Brijesh Kumar Gupta Male Guru Ghasidas Vishwavidayalaya Bilaspur Bilaspur,
Ph. D. Deen Dyal Upadhaya Gorakhpur University 2011  
19 7842 Mr. Lovy Singhal Male TIFR Mumbai Mumbai,
Research Scholar Indian Institute of Technology Kanpur 2011  
20 7837 Asstprof. Ishpreet Kaur Female Guru hargobindsahib khalsa girls college Karhalisahib,
Punjab pan jab university chandigarh 2007  
21 7572 Ms. Anu Devgan Female Punjabi University Patiala,
Research Scholar Panjab University, Chandigarh 2010  
22 7237 Dr Rakesh Kumar Male Punjabi University, Patiala Patiala,
Assistant Professor Punjabi University, Patiala 2002 24 Dec 2008
23 7472 Mr. Sangeet Kumar Male Chitkara University, Rajpura Rajpura,
Assistant Professor

Guru Nanak Dev University,

24   Dr. Shrihari Sridharan   Assistant Professor, Chennai Mathematical Institute,          
List of Participants (Local)  
1 6348 Mrs. Priyanka Kaushal Female Rayat Bahra Group of Colleges, Kharar, Mohali, Punjab Mohali,
Associate Professor

Himachal Pradesh University, Shimla

2 6350 Ms. Brehmit Kaur Female Sri Guru Granth Sahib World University Sirhind,
Assistant Professor Panjab University,
3 7350 Ms. Geetika Gupta Female M.C.M D.A.V College for Women Chandigarh Assistant Professor Panjab University Chandigarh. 2010  
1 7845 Dr. Megha Goyal Female Punjabi University, Patiala Patiala,
Asst. Professor Panjab University,
2008 1 May 2014
2 7653 Ms. Rupali Rupali Female Punjabi University, Patiala Patiala,
Asst. Professor, PhD Panjab University ,
3 7803 Mrs. Garima Gupta Female College Of Engineering Patiala,
Assistant Professor Panjab University ,
4 7830 Ms. Rashmi Sachdeva Female Punjabi University, Patiala. Patiala,
Asst. Prof. Guru Nanak Dev
List of Participants  from IISERM  
1 7662 Ms Cigole Thomas Female IISER Mohali Mohali,
Integrated BS-MS student IISER Mohali Appeared/ Awaiting
2 7692 Mr. Shivam Arora Male IISER MOHALI Mohali,
Int. PhD IISER MOHALI Appeared/ Awaiting
3 7713 Ms. Divya Sharma Female IISER Mohali, Mohali. Mohali,
IISER Mohali Appeared/ Awaiting
4   Soumya Dey   IISER Mohali Mohali,
5   Arun Kumar   IISER Mohali Mohali,
6   Mr. Manoj Upreti   IISER Mohali Mohali,
7   Khushwant Singh   IISER Mohali Mohali,
8   Shiv Prasad   IISER Mohali Mohali,
9   Krishnendu Gongopadhyay   IISER Mohali Mohali,
10   Mahendra Singh   IISER Mohali Mohali,
11   Ms. Monika Kaushal   IISER Mohali Mohali,
12 7806 Mr Nitesh Bhardwaj Male IISER Mohali Mohali,
BS-MS integrated programme IISER, Mohali Appeared/ Awaiting



How To Reach

How to reach the venue: IISER MOHALI

  • By Air: Arrive at Chandigarh airport. There are many of connecting flights from Delhi/Mumbai to Chandigarh.
  • By Train: Nearest railway stations are
    1. Chandigarh (Station Code: CDG, 14 Km from IISER)
    2. Ambala (Station Code: UMB, 50 Km from IISER)
    3. Mohali (Station Code: SASN, 2 Km from IISER): There are very few connections to Mohali. One useful connection from Delhi is Una Jan-Shatabdi (Train No. 12057)
  • From Airport/Chandigarh Railway station to IISER: Take a Radio taxi/auto (phone numbers: 0172-4141414, 0172-4242424, 0172-4646464) to IISER Mohali. Almost all the drivers know the location and way to IISER. Neighbouring locations are Indian School of Business (ISB) Mohali and National Institute of Pharmaceutical Education and Research (NIPER) Mohali.  The distance between airport and IISER is about 10 kms and between Chandigarh Railway station and IISER is about 14 Kms. Mohali Railway station (called Sahibzada Ajit Singh Nagar station or SAS Nagar station) is just 2 km from IISER.