ISL Geometric Measure Theory (2013)

Venue:  CEMS, Almora
Dates: 9th to 21st December, 2013


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


School Convener(s)

Name C S Aravinda H.S.Dhami Sanjay Kumar (Pant)
Mailing Address Associate Professor,
Department of Mathematics,
TIFR CAM ,Sharadanagar,
GKVK Post, Bangalore-560065
Professor and Head,
Department of Mathematics,
SSJ Campus, Kumaun University
Almora, Uttarakhand-263601
Associate Professor,
Department of Mathematics,
Deen Dayal Upadhyaya College,
New Delhi-110015


Speakers and Syllabus 

Overview: To give a foundational course in Measure theory with geometric applications.


Date 9.30-10.30 11.00-12:00 12.15-13.15 14.30-15.30 16.00-17:00
09/12/13 L1(CSA) L2(SS) L3(GN) T1(HP) T2(HP)
10/12/13 L4(CSA) L5(SS) L6(GN) T3(SP) T4(SP)
11/12/13 L7(CSA) L8(AM) L9(SS) T5(HP) T6(HP)
12/12/13 L10(CSA) L11(GN) L12(SS) T7(SP) T8(SP)
13/12/13 L13(CSA) L14(GN) L15(SS) T9(HP) T10(HP)
14/12/13 L16(GN) L17(AM) L18(CSA)  --  --
S  U  N  D  A  Y
16/12/13 L19(AM) L20(VA) L21(KB) T11(CSA) T12(CSA)
17/12/13 L22(JA) L23(AG) L24(VA) T13(SP) T14(SP)
18/12/13 L25(JA) L26(AG) L27(KB) T15VA) T16(VA)
19/12/13 L28(JA) L29(AG) L30(VA) T17(SP) T18(SP)
20/12/13 L31(JA) L32(AG) L33(KB) T19(VA) T20(VA)
21/12/13 L34(JA) L35(AG) Valedictory --  --

Ln: Lecture n
Tn: Tutorial n
Tea Breaks: 10:30 - 11:00 and 15:30 - 16:00
Lunch Break: 13:15 - 14:30

Speakers and Syllabus

  • C S Aravinda (CSA): Basic diophantine approximation: Theorems of Dirichlet, Hurwitz and Liouville, Liouville numbers, badly approximable numbers, Schmidt games, winning sets and Hausdorff dimensions of winning sets. Introduce the notion of ergodicity. (6 lectures)
  • K Gowri Navada (GN): Continued fractions and a proof of Khinchine’s theorem (5 lectures)
  • Shrihari Sridharan (SS): Brief discussion of limsup and liminf, Lebesgue and Hausdorff measures, Cantor sets, Borel-Cantelli lemma, computing measures and Hausdorff dimensions of Cantor sets. (5 lectures)
  • Anandateertha Mangasuli (AM): Riesz representation theorem, Topological groups and Haar measures (briefly sketching the general construction but discussing a couple of simple examples explicitely). (3 lectures)
  • Vikram Aithal (VA): Kakeya needle problem, Besicovich sets and Hausdorff dimension of Besicovich sets. (3 lectures)
  • Jayadev Athreya (JA) and Anish Ghosh (AG): Will describe the notion of lattices in Euclidean space, and show how one can form a space of lattices in n-dimensional Euclidean space by considering the coset space Xn = SL(n, R)/SL(n, Z). Will describe and compute a finite invariant measure on this space, and show how to compute the volume using simple tools from number theory. Will discuss applications to the geometry of numbers,diophantine approximation, and counting problems like the Gauss circle problem. Will also discuss Khintchine’s theorem using Sullivan’s argument and the hyperbolic analogue of the lattice point counting problem. The second half of the course will describe how these problems connect to dynamical systems on the space Xn , and in particular discuss simple ex-amples of a phenomenon now know as the Dani correspondence. (5 lectures each)
  • Kingshook Biswas (KB): Self-similar sets and computations of Hausdorff dimensions. (3 lectures)

 Course Associates:

  • Vikram Aithal (VA) CBS, Mumbai
  • Harish Chandra Pathak (HP) BHU, Varanasi
  • Sanjay Pant (SP) DU and CEMS, Almora

Reference Books: The following books are the suggested references:

(1) Measure theory and Integration By G de Barra.
(2) Geometry of Fractal sets By K J Falconer.
(3) Continued Fractions (3rd Edition) By A I Khinchin.



Selected Applicants

List of selected applicants.

  1. Main List Participants are requested to confirm their participation in the School positively by 20th August, 2013 by sending email to sanjpant AT or by sending SMS to 9810528236

  2. On 21st August , 2013 wait-listed candidats will be inform depending on the confirmation received from the main list.

  3. Final List will be displayed in atmschools web -page on 27th August , 2013.

  4. University Guest House accommodation is on sharing basis (no guest(s) of selected participants will be entertained in UGH).


Sr. SID Full Name Gender Affiliation State Position in College/ Univ. Univ./Institute M.Sc./M.A. Year of Passing M.Sc./M.A Ph.D Degree Date
1 3885 Dr. Sag Ram Verma Male Gurukula Kangri Univ. Uttarakhand/ Uttaranchal Asst. Professor BHU Varanasi 2005 30 Jun 2009
2 3983 Dr Bankteshwar Tiwari Male BHU Varanasi Uttar Pradesh Asso.Professor Gorakhpur Univ. 1997 6 Nov 2001
3 3990 Dr. Gauree Shanker Male Banatshali Univ. Rajasthan Asst. Professor DDU Gorakhpur Univ. Gorakhpur (U.P.) 2000 8 Oct 2005
4 4036 Mr. Amit Sharma Male Himachal Pradesh Univ. Himachal Pradesh Gold medalist H.P.U 2004  
5 4054 Ms. Jita Parida Female Priyadarshini Indira Mahavidyalaya Orissa lecturer in college Sambalpur Univ. 2004  
6 4082 Ms Tejaswi Vilas Bane Female Sathaye college, vile parle, mumbai Maharashtra lecturer Univ. of   Mumbai. 2009  
7 3950 Mr. Deepak Kumar Porwal Male DU Delhi Research Scholar Univ. of Delhi 2010  
8 4111 Dr. Srijanani Anurag Prasad Female ISI Delhi Delhi Post - Doctoral Fellow ANNA Univ. 2004 29 Nov 2011
9 4114 Dr. Anugraha Nidhi Mohapatra Male Goa Univ. Goa Associate Professor Sambalpur Univ. 1985 13 Feb 1992
10 4118 Dr. Abhijit Pal Male CMI Tamil Nadu INSPIRE Faculty Calcutta Univ. 2004 24 Mar 2011
11 4123 Mr. Tapas Kumar Mondal Male Dr. Bhupendra Nath Dutta Smriti Mahavidyalaya West Bengal Assistant Professor The Univ. of Burdwan, West Bengal 2004  
12 4154 Mrs Sushma Virendrasinh Parmar Female AISSMS COE PUNE   Asst. Professor North Maharashtra Univ. Jalgoan Maharashtra 1999  
13 4159 Mr Mahadeo Kedari Nikam Male AISSMS COE PUNE Maharashtra Associate Professor Shivaji Univ. Kohlapur 1998 1 Mar 2008
14 4178 Mr. Vishal Gupta Male Swami Vivekananda Subharti Univ. Uttar Pradesh Asst. Professor IIT GUWAHATI 2010  
15 4256 Mr. Ashok Kumar Sah Male Kirori Mal College Delhi Asst. Professor Univ. OF DELHI 2010  
16 4280 Prof. Santosh Kumar Kumar Male S.G.G.S collge sector 26 chandigarh Chandigarh Asst. Professor   2008  
17 4319 Ms. S B T Sundari Katakam Female Rajiv Gandhi Univ. Of Knowledge Technologies Andhra Pradesh LECTURER ANDHRA Univ., VISAKHAPATNAM 2010  
18 4380 Dr Gururaja Ananthakrishna Male IISER Bhopal Madhya Pradesh Visiting Faculty Kuvempu Univ. 2004 22 Jun 2012
19 4381 Mr Vidyasagar Mysoremath Male Rani Channamma Univ. Karnataka Asst. Professor Karnatak Univ. 2008  
20 4396 Ms. Preeti Sharma Female Univ. Engineering College, Kota Rajasthan Asst. Professor IIT GUWAHATI 2012  
21 4397 Mr Dilip Jain Male G.I.E.T. Ranpur, Kota Rajasthan Asst. Professor IIT DELHI 2012  
22 4032 Mr Ramu Geddavalasa Male NITK Surathkal Karnataka Research Scholar Andhra Univ. 2007  
   Waiting List      
1 4365 Ms. Arnapurna Panda Female IIT Bhubaneswar Orissa Ph.d PG Dept. of mathematics, Utkal Univ.. vanivihar 2009  
2 4420 Mr. Anuj Kumar Male IIT Delhi Delhi Ph.d IIT Delhi 2011  
3 4435 Mr Tarun Kumar Chakra Male IIT Bhubaneswar Orissa PhD PG Dept. of mathematics, Utkal Univ.. vanivihar 2007  
4 4174 Mr. Asif Khan Male AMU Uttar Pradesh Persuing Ph.D (also working as guest faculty) A.M.UI 2005  
5 3882 Ms. Kousalyaparasakthi M Female Sri sarada college for women Tamil Nadu Ph.d Goverment arts college salem-8 2011  
6 3883 Ms. Saranya P Female Sri sarada college for women Tamil Nadu Ph.d sri sarada college for women 2011