ATMW Analysis and Geometry (2014)
Venue: | TIFR-CAM, PB 6503, Chikkabommsandra, Sharadanagar, GKVK Post, Bangalore -560065 |
Dates: | 6^{th} to 10^{th} Jan 2014 |
Convener(s) | Speakers, Syllabus and Time table | Applicants/Participants |
Name | P.N. Srikanth | Sagun Chanillo | K. Sandeep |
Mailing Address | TIFR CAM, PB 6503, Chikkabommsandra, Sharadanagar, GKVK Post, Bangalore |
Rutgers University, USA | TIFR CAM, PB 6503, Chikkabommsandra, Sharadanagar, GKVK Post, Bangalore |
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.
References
( pdf ﬁles of [1], [2], [3], [4]) are available at www.math.princeton.edu/ 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
http://www.math.rutgers.edu/~chanillo/crduke.pdf
and
http://www.math.rutgers.edu/~chanillo/contemp_math_final.pdf
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
http://www.math.rutgers.edu/~chanillo/malchiodi.pdf - 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 |
T |
X.Huang | L U N C H |
P.Yang | T E A |
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:
- Professor Sun-Yung Alice Chang, Department of Mathematics, Princeton University, USA
Title of lecture:- Prescribing Gaussian curvature, Q-curvature equations and related PD - Professor Paul Yang, Department of Mathematics, Princeton University, USA
Title of lecture: - CR Yamabe problem and CR conformal Geometry. - Professor Xiaojun Huang, Department of Mathematics, Rutgers University, USA
Title of lecture:-Chern-Moser invariants and Normal forms. - 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 - 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. - 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 Bengal |
||||||
24 | Vijay Kumar Sohani | Dept. of Mathematics, IISc. Bangalore | |||||||
25 | .Priyankur Chaudhuri | ISI Bangalore | |||||||
26 | Kuntal Banerjee | Harish-Chandra Research Institute, | Allahabad |
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 http://math.tifrbng.res.in/contactus for links to the route maps.