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)

 

References

  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

Mumbai,
Maharashtra

 Research Scholar   Appeared/ Awaiting
Result		  
2 7638 Mr. Sugato Mukhopadhyay Male Indian Institute of Technology, Kanpur Kanpur,
Uttar Pradesh		 PhD Student Delhi University Appeared/ Awaiting
Result		  
3 7651 Mr. Suman Paul Male IIT Kanpur Kanpur,
Uttar Pradesh		 PhD IIT Kanpur Appeared/ Awaiting
Result		  
4 7270 Mr. Sampat Sharma Male Tata Institute Of fundamental Research Mumbai,
Maharashtra		 Phd IISER MOHALI Appeared/ Awaiting
Result		  
5 7372 Mr. Ramesh Kasilingam Male IIT BOMBAY Mumbai,
Maharashtra		 Research Scholar
(PhD)		 Anna university,
chennai		 2006  
6 7232 Mr Muna Naik Male Indian Statistical Institute, Kolkata Kolkata,
West Bengal		 PhD National Institute Of
Science Education
and Research		 2013  
7 6641 Mr. Vishal Gupta Male Zakir Husain Delhi College New Delhi,
Delhi		 Assistant Professor IIT Guwahati 2010  
8 6816 Dr. Shameek Paul Male Centre for Excellence in Basic Sciences Mumbai,
Maharashtra		 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

Burdwan,
West Bengal

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

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
Result		  
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,
Delhi		 PhD D.D.U. Gorakhpur
University, U.P.		 2011  
16 7829 Mr. Yashpaul Male Malwa College Bondli Samrala Samrala, District Ludhiana, Punjab Assistant Professor Government College,
Hoshiarpur, Punjab (India)		 2005  
17 7836 Ms. Asha Singh Female Himachal Pradesh University Shimla,
Himachal Pradesh		 Ph.D.
student		 Himachal Pradesh University 2010  
18 7841 Mr. Brijesh Kumar Gupta Male Guru Ghasidas Vishwavidayalaya Bilaspur Bilaspur,
Chhattisgarh		 Ph. D. Deen Dyal Upadhaya Gorakhpur University 2011  
19 7842 Mr. Lovy Singhal Male TIFR Mumbai Mumbai,
Maharashtra		 Research Scholar Indian Institute of Technology Kanpur 2011  
20 7837 Asstprof. Ishpreet Kaur Female Guru hargobindsahib khalsa girls college Karhalisahib,
Punjab		 asst.prof. pan jab university chandigarh 2007  
21 7572 Ms. Anu Devgan Female Punjabi University Patiala,
Punjab		 Research Scholar Panjab University, Chandigarh 2010  
22 7237 Dr Rakesh Kumar Male Punjabi University, Patiala Patiala,
Punjab		 Assistant Professor Punjabi University, Patiala 2002 24 Dec 2008
23 7472 Mr. Sangeet Kumar Male Chitkara University, Rajpura Rajpura,
Punjab		 Assistant Professor

Guru Nanak Dev University,
Amritsar

 2008  
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,
Punjab		 Associate Professor

Himachal Pradesh University, Shimla

 2001  
2 6350 Ms. Brehmit Kaur Female Sri Guru Granth Sahib World University Sirhind,
Punjab		 Assistant Professor Panjab University,
Chandigarh		 2009  
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,
Punjab		 Asst. Professor Panjab University,
Chandigarh		 2008 1 May 2014
2 7653 Ms. Rupali Rupali Female Punjabi University, Patiala Patiala,
Punjab		 Asst. Professor, PhD Panjab University ,
Chandigarh		 2006  
3 7803 Mrs. Garima Gupta Female College Of Engineering Patiala,
Punjab		 Assistant Professor Panjab University ,
Chandigarh		 2008  
4 7830 Ms. Rashmi Sachdeva Female Punjabi University, Patiala. Patiala,
Punjab		 Asst. Prof. Guru Nanak Dev
University		 2009  
List of Participants  from IISERM  
1 7662 Ms Cigole Thomas Female IISER Mohali Mohali,
Punjab		 Integrated BS-MS student IISER Mohali Appeared/ Awaiting
Result		  
2 7692 Mr. Shivam Arora Male IISER MOHALI Mohali,
Punjab		 Int. PhD IISER MOHALI Appeared/ Awaiting
Result		  
3 7713 Ms. Divya Sharma Female IISER Mohali, Mohali. Mohali,
Punjab		 MSc
Student		 IISER Mohali Appeared/ Awaiting
Result		  
4   Soumya Dey   IISER Mohali Mohali,
Punjab		        
5   Arun Kumar   IISER Mohali Mohali,
Punjab		        
6   Mr. Manoj Upreti   IISER Mohali Mohali,
Punjab		        
7   Khushwant Singh   IISER Mohali Mohali,
Punjab		        
8   Shiv Prasad   IISER Mohali Mohali,
Punjab		        
9   Krishnendu Gongopadhyay   IISER Mohali Mohali,
Punjab		        
10   Mahendra Singh   IISER Mohali Mohali,
Punjab		        
11   Ms. Monika Kaushal   IISER Mohali Mohali,
Punjab		        
12 7806 Mr Nitesh Bhardwaj Male IISER Mohali Mohali,
Punjab		 BS-MS integrated programme IISER, Mohali Appeared/ Awaiting
Result		  

 

 

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.