ATMW Analysis and Geometry (2014)

Venue: TIFR-CAM, PB 6503, Chikkabommsandra, Sharadanagar, GKVK Post,   Bangalore -560065
Dates: 6th to 10th Jan 2014


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


School Convener(s)

Name P.N. Srikanth Sagun Chanillo K. Sandeep
Mailing Address TIFR CAM,  PB 6503, Chikkabommsandra,
Sharadanagar, GKVK Post,
Rutgers University, USA TIFR CAM,  PB 6503, Chikkabommsandra,
Sharadanagar, GKVK Post,


Speakers and Syllabus 

A brief  description of the Workshop

The subject Geometric Analysis has been  a very active area of research for the past several decades  and the  studies  in the area have  been instrumental   in solving several important problems in  Mathematics. To mention a few, Ricci flow and proof  of Poincare  Conjecture,  Study of harmonic maps, minimal surfaces,  Yamabe problem, prescribing the curvatures,   Complex  manifolds and CR Yamabe problem, General relativity, Positive mass theorem, etc.  Geometric analysis lies in the interface of several subjects like   Geometry, PDE, Harmonic analysis,  Topology and Nonlinear functional analysis.
The aim of this workshop is to expose  young mathematicians to the  state of the art in the subject  leading them to possible research career in the field and as such this workshop is a sequel to the workshop on the same topic being held from  8th to 27th  July 2013.

Apart from others the following are expected  to lecture in the workshop.

  • Speaker: Professor Sun-Yung Alice Chang, Department  of Mathematics, Princeton University, USA
    Title of lecture:-
    Prescribing Gaussian curvature, Q-curvature equations and related PDE
    Abstract and outline
    :-In this mini lecture series, I will cover some non-linear partial differential equations which arise in the study of prescribing curvature problems in conformal geometry.

Lecture I:We will discuss the classical problem of prescribing Gaussian curvature on compact surfaces; basic background and an analytic tool of sharp Moser-Trudinger Sobolev inequality.
(Reference [1])

Lecture II:Uniformization Theorem on compact surface, generalized Moser-Trudinger inequality on high dimensional manifolds, Polyakov formula, Log determinant functional and definition of Q curvature on 4-manifolds. (Reference [1])

Lecture III:Conformal covariant operators, Paneitz and GJMS operators, basic existence result of ”prescribing Q-curvature” problem.
(Reference [2], [3])

Lecture IV:Positivity of Paneitz operators, some geometric application of the Q-curvature equation.

(Reference [4], [5] and more recent literature). If time permits, I plan also to cover some relationship between Q-curvature and study of a class of symmetric functions of the Riccitensor called the σk of Schouten tensors.

( pdf files of [1], [2], [3], [4]) are available at chang)

[1] Sun-Yung A. Chang ”Nonlinear elliptic equations in conformal geometry”, Nachdiplom lectures in Mathematics, ETH, Zurich, Springer-Birkh¨auser, 2004.

[2] Sun-Yung A. Chang , Michael Eastwood, Bent Orsted, and Paul Yang), ”What is Q-curvature?” Acta Appl. Math. 102 (2008), no.2-3 119-125.

[3] Sun-Yung A. Chang and Paul Yang, “Extremal metrics of zeta function determinants on 4-manifolds,” Annals of Math. 142 (1995) pp. 171-212.

[4] [4] Sun-Yung A. Chang, J. Qing and P.C. Yang, “On the Chern-Gauss-Bonnet integral for conformal metrics on R4 ,” Duke Math. J., vol 102, no.3 (2000) pp. 523-544.
[5] Matthew Gursky,” The principal eigenvalue of a conformally invariant differential operator, with an application to semi-linear elliptic PDE” Comm. Math. Phys. 207
(1999), 131-143.

  • Speaker:- Professor Paul Yang, Department  of Mathematics, Princeton University, USA
    Title of lecture:-
    CR Yamabe problem and CR conformal Geometry.
    Abstract and Outline:-In this lecture series, I will discuss the CR Yamabe problem. This includes back ground material on CR structures, the CR embedding problem and the d-bar problem, and the CR Paneitz operator.
    Lecture 1: The CR structure. The Tanaka Webster connection, curvature and torsion. Holomorphic functions and the embedding problem.
    Lecture 2: The CR Paneitz operator and the solution of the embedding problem.
    Lecture 3: The CR positive mass theorem.
    Lecture 4: The solution of the CR Yambe problem.
    Material for Lectures 1 and 2 can be downloaded here
    References for Lectures 3 and 4:
    [1] R. Schoen and S.-T. Yau, Proof of the Positive Mass Theorem II, Communications in Math. Physics, 79 (1981), 231-260
    [2] E. Witten, A New Proof of the Positive Mass Theorem, Communications in Math. Physics, 80, (1981), 381-402.
    [3] J.-H. Cheng, A. Malchiodi and Paul Yang, slides on the proof of the CR Positive Mass Theorem and CR Yamabe Problem
  • Speaker: Professor Xiaojun Huang, Department of Mathematics, Rutgers University, USA
    Title of lecture:- Chern-Moser invariants and Normal  forms.
    Abstract and Outline: The equivalence problem in Several Complex Variables studies when two domains in a complex space  are holomorphically equivalent. When the domains are strongly pseudoconvex and have smooth boundaries, the result of Bochner and C. Fefferman can be applied to reduce this equivalence problem to that for real hypersurfaces. In this short course,we will introduce the Cartan-Chern-Moser method for solving the equivalence problem for real hypersurfaces. We will introduce the normal form method and the moving frame method. If time permits, we will also study the equivalence problem for real submanifolds with CR ( Cauchy-Riemann)singularities.
    Background for the lectures of Prof. Huang can be found in:

    [1] Xiaojun Huang, Local Equivalence Problems for Real Submanifolds in Complex Spaces, Springer Lecture Notes in Mathematics, 1848, Real methods in Complex and CR Geometry, 109-163, eds. D. Zaitsev, G. Zampieri, Lectures given at the CIME Summer school, Martina Franca, Italy, 2002.

  • Speaker:-Professor Rupert L. Frank, Department  of Mathematics, California Institute of Technology,USA
    Title of lecture:- Sharp inequalities

Each of the speakers above will give 5 hours of lectures (4+1).

Schedule of Lectures

Day 9:30-10:45   11:15-12:30   2:00-3:15   3:45-5:00
Monday A.Chang


X.Huang L
P.Yang T
K. Sandeep
Tuesday X.Huang P.Yang A.Chang C. Titarev
Wednesday P.Yang S.Chanillo    
Thursday A.Chang X.Huang P.Yang K. Sandeep
Friday A.Chang X.Huang C. Titarev S.Chanillo

Speakers and title of lectures:

  1. Professor Sun-Yung Alice Chang, Department of Mathematics, Princeton University, USA
    Title of lecture:- Prescribing Gaussian curvature, Q-curvature equations and related PD
  2. Professor Paul Yang, Department of Mathematics, Princeton University, USA
    Title of lecture: - CR Yamabe problem and CR conformal Geometry.
  3. Professor Xiaojun Huang, Department of Mathematics, Rutgers University, USA
    Title of lecture:-Chern-Moser invariants and Normal forms.
  4.  Professor Cyril Tintarev, Department of Mathematics, Uppsala University, Sweden
    Title of lectures:-Cocompactness and cocompactness of Sobolev-type imbeddings on manifolds & Compactness properties of Moser-Trudinger functional
  5.   Professor Sandeep K, Tata Institute of Fundamental Research-Centre for Applicable Mathematics, Bangalore
    Title of lecture:- Symmetry properties and uniqueness of extremals for the Sobolev and Hardy-Sobolev Maz’ya inequalities.
  6. The titles of lecture by Prof. Sagun Chanillo will be announced in due course.

VENUE:  Lecture Hall - 111, 1st floor, TIFR CAM, Bangalore


Selected Applicants


Sr. SID Full Name Gender Affiliation State Position in College/ University University/Institute M.Sc. / M.A. Year of Passing M.Sc. / M.A Ph.D. Deg.
1 4479 Dr. Shravan Kumar Pandey Male  A.P.S.University, Rewa (M.P.)486003 India MP Asst. Professor A.P.S.University, Rewa (M.P.)486003 India 2007 29 Jul 2013
2 4480 Dr. Giteshwari Pandey Female  A.P.S.University, Rewa (M.P.)486003 India MP Asst. Professor  A.P.S.University, Rewa (M.P.)486003 India 2007 2 Aug 2013
3 4486 Mr. Gorachand Chakraborty Male IIT Bhubaneswar Orissa Ph.D Student IIT Guwahati 2012  
4 4496 Dr Anisa Mohmad Husen Chorwadwala Female IISER Pune. Maharashtra Asst. Professor University of Mumbai 2001 10 Jul 2007
5 4505 Dr. Avijit Sarkar Male University of Kalyani West Bengal Asst. Professor University of Kalyani 2002 2 Feb 2010
6 4510 Mr Soutrik Roy Chowdhury Male IISER,Mohali Punjab int Phd student   Awaiting Result  
7 4511 Dr Sreenadh Konijeti Male IIT Delhi   Associate Professor Madras University 1997  
8 4516 Mr. Suhail Gulzar Mattoo Male Kashmir University J&K Research Scholar Kashmir University 2007  
9 4522 Mr. Priyadip Mondal Male Indian Statistical Institute, Bangalore Centre Karnataka MSc Student Indian Statistical Institute Awaiting Result  
10 4555 Mr. Aryaman Sensarma Male IIT KANPUR Uttar Pradesh Research Scholar VIisva Bharti 2011  
11 4558 Mr. Ramesh Manna Male Harish-Chandra Research Institute Uttar Pradesh Phd IITMadras 2010  
12 4559 Mr. Koushik Ghosh Male Indian Statistical Institute,Bangalore Karnataka Student Indian Statistical Institute, Bangalore Awaiting Result  
13 4579 Mr. Rahul Kumar Singh Male Harish-Chandra Research Institute Uttar Pradesh PhD M.S.University of Baroda 2009  
14 4621 Dr. Pak Tung Ho Male Sogang University   Asst. Professor The Chinese University of Hong Kong 2004 10 Aug 2010
15 4624 Mr. Subhadip Dey Male Indian Statistical Institute, Bangalore Center Karnataka M.Math Student InIndian Statistical Institute, Bangalore Center Awaiting Result  
16 4629 Ms Tawheeda Rasool Female National Institute of Technology, Srinagar J&K Research Scholar (Ph.d) University of Kashmir 2007  
17 4634 Ms. Rashmi Sachdeva Female Thapar University Punjab PhD   2009  
18 4641 Mr. Naveen Kumar Male UM-DAE-Centre For Excellence In Basic Sciences Maharashtra MSc. Student UM-DAE-CEBS Awaiting Result  
19   Mr.Gaurav Prabhakar Sawant   IISER, Pune          
20   Prof.Ratnakumar P K   Harish-Chandra Research Institute          
21   Mr.Divyang Bhimani   Harish-Chandra Research Institute          
22   Dr.Saugata Bandyopadhyay   IISER, Pune          
23   .Joydeep Sengupta   Dept. of Mathematics,University of Gour Banga West
24   Vijay Kumar Sohani   Dept. of Mathematics, IISc. Bangalore          
25   .Priyankur Chaudhuri   ISI Bangalore          
26   Kuntal Banerjee    Harish-Chandra Research Institute, Allahabad PDF      


How to reach

How to reach TIFR, Bangalore

* From Bangalore Internation Airport (Distance 28km)

You can hire a City taxi or private taxi from Airport to TIFR , Yelahanka new town.
Landmark : Yelahanka new town Dairy Circle

* From Bangalore City Railway Station or Majestic Bus Stand (Distance 16km)

You can hire a City Taxi or Auto Rickshaw and ask drop for Yelahanka new town. The fare for City Taxi will be approximately Rs.400. For Auto Rickshaw fare will be approximately Rs.200.

You can also use BMTC Bus service to reach TIFR. You can board into following buses which comes to Yelahanka new town bus stand.

Buses to Yelahanka new town : 402B, 402D, 284D

TIFR CAM is located walkable distance from Yelahanka new town bus stand.

You may also visit the link below for links to the route maps.