This is an advanced workshop in harmonic analysis with lecture series' on four different themes. For registration, please follow instructions available at https://www.atmschools.org/school/2019/NCMW/ha

Speaker: Luca Fanelli (SAPIENZA Università di Roma, Italy)
Description: First set of lectures will be on Uniform Resolvent Estimates for Laplace and Dirac operators and applications. The plan of these lectures is as follows:
i) Introduction, non self-adjoint Hamiltonians and eigenvalue problems. The Birman-Schwinger Principle and absence of eigenvalues, as a consequence of uniform resolvent estimates for the free Hamiltonian. An overview of recent results in the non-relativistic case (Frank, Seiringer, Simon et al).
ii) The uniform Sobolev Estimate for the resolvent of the free Schrödinger Hamiltonian by Kenig-Ruiz-Sogge. Proof, and failure of the estimate for the Dirac Hamiltonian.
iii) A new Agmon-Hörmander-type estimate for the free Dirac operators. As a consequence, absence of eigenvalues for Dirac operators with almost scaling invariant complex potentials. The results are obtained in collaboration with P. D’Ancona, and N. Schiavone (Roma Sapienza).


Speaker: Bent Orsted (Aarhus University, Denmark)
Description: Second set of lectures will be on Branching problems for unitary representations and Poisson transforms. An interesting problem studied in the literature is to investigate how certain unitary representations of semi-simple Lie groups decompose when restricted to subgroups. This is known as Branching problem and it leads to structures that shed new light on certain elliptic boundary value problems. For example, for the groups O(1,n+1) and U(1,n+1) the branching theory leads to the well known Poisson transforms associated to symmetric spaces. Studying this problem in the general context one is led to Symmetric Breaking operators of Kobayashi and Speh providing new examples of Poisson transforms.


Speaker: Sanghyuk Lee (Seoul National University, South Korea)
Description: Third set of lectures will be on Bochner-Riesz conjecture and related problems. The Bochner-Riesz conjecture is an attempt to understand the convergence of multidimensional Fourier series and integral, which is one of the most fundamental questions in the classical harmonic analysis. Though the conjecture is settled in 2-dimensions, it is still open in higher dimensions. As is well known to experts in this field, the progresses in the Bochner-Riesz conjecture are closely tied to those of Fourier restriction problems, where we have witnessed rapid developments in recent years. Bilinear and multilinear generalizations of linearestimates turned out to be the most efficient tools. In this series of lectures we will cover developments in the Bochner-Riesz conjecture and its related problems in connection with the Fourier restriction problem.


Speaker: Tao Mei (Baylor University, Texas, USA)
Description: Fourth set of lectures will be on Noncommutative Harmonic Analysis, as per the following details:
i) Positive definite functions and group C* algebra: This will be on Haagerup's characterization of completely (positive) bounded multipliers on group C* algebras. References 1, 2, 3.
ii) Semigroup-BMO spaces: Junge-Mei's BMO interpolation theory in the noncommutative setting, References 4, 5.
iii) Schatten p classes and noncommutative Lp spaces: Introduction of noncommutative Lp spaces. Reference 6.
iv) Hilbert transform and Lp Fourier Multipliers: Mei-Ricard's free Hilbert transforms and Junge-Mei-Parcet's Lp fourier mutlipliers theory through cocycles. References 7, 8.
v) Free Group von Neuman algebras and Connes' quantum differential forms. Ref 3, 9.

References:
1. Haagerup, Uffe; An example of a nonnuclear C∗-algebra, which has the metric approximation property. Invent. Math. 50 (1978/79), no. 3, 279–293.
2. Haagerup, Uffe; Knudby, Søren A Lévy-Khinchin formula for free groups. Proc. Amer. Math. Soc. 143 (2015), no. 4, 1477–1489.
3. Brown, Nathanial P.; Ozawa, Narutaka C∗-algebras and finite-dimensional approximations. Graduate Studies in Mathematics, 88.
4. Junge, M.; Mei, T. BMO spaces associated with semigroups of operators. Math. Ann. 352 (2012), no. 3, 691–743.
5. Mei, Tao Tent spaces associated with semigroups of operators. J. Funct. Anal. 255 (2008), no. 12, 3356–3406.
6. Gilles Pisier and Quanhua Xu, Non-commutative Lp-spaces, Handbook of the geometry of Banach spaces, Vol. 2, North-Holland, Amsterdam, 2003, pp. 1459–1517.
7. Junge, Marius; Mei, Tao; Parcet, Javier Smooth Fourier multipliers on group von Neumann algebras. Geom. Funct. Anal. 24 (2014), no. 6, 1913–1980.
8. Mei, Tao; Ricard, Éric Free Hilbert transforms. Duke Math. J. 166 (2017), no. 11, 2153–2182.
9. Connes, Alain Noncommutative geometry. Academic Press, Inc., San Diego, CA, 1994. xiv+661 pp. ISBN: 0-12-185860-X


List of selected outstaion participants:

SID Name
     
SID Name
28332 Mr. Pritam Ganguly
     
30226 Ms. Surbhi  
28909 Mr Partha Sarathi Patra
     
30229 Mr Manoj Kumar
29043 Mr. Jayanta Sarkar
     
30234 Mr. Arup Kumar Maity
29096 Mr. Yasser K.T
     
30246 Mr. Ryu Jae Hyeon
29181 Mr Muna Naik
     
30261 Mr. Salman Ashraf
29291 Mr. Ramesh Manna
     
30288 Ms. Hyerim Ko
29376 Mr. Santanu Debnath
     
30289 Dr. Chuhee Cho
29492 Mr. Arun Kumar Bhardwaj
     
30303 Mr Tapendu Rana
29559 Mr. Shubham Rameshsingh Bais
     
30304 Mr. Ankit Bhojak
29722 Mr. Md Nurul Molla
     
30307 Mr. Rajesh Kumar Singh
29798 Mr. Dhiraj Patel
     
30308 Dr. Kanailal Mahato
29849 Mr. Anoop V P
     
30390 Mr. Sumit Kumar Rano
30031 Mr Somnath Ghosh
     
30399 Mr. Santi Ranjan Das
30061 Mr. Rupak Kumar Dalai
     
30413 Mr. Md Hasan Ali Biswas
30091 Mr. Duranta Chutia
     
30419 Mr. Yehyun Kwon
30115 Mr Shyam Swarup Mondal
     
30431 Dr. Anupam Gumber
30136 Mr. Naman Kumar
     
30439 Mr. Shubham Namdeo
30163 Mr Rattan Lal Lal
     
30466 Mr. Abhishek Ghosh
30208 Mr. Sewook Oh
     
30531 Dr. Eunhee Jeong
30214 Mr Juyoung Lee
     
30538 Dr. Choiti Bandyopadhyay


List of selected local participants:

SID Name
     
SID Name
29015 Mr Kalachand Shuin
     
29307 Dr. Neha Choubey
29027 Mr Riju Basak
     
30381 Mr. Muzammil Khan
29236 Prof Manisha Udit Jain
     
30462 Mr. Sonu Kurmi


List of invited participants:

Name Affiliation
     
Name Affiliation
Ashisha Kumar IIT Indore
     
Pratyoosh Kumar IIT Guwahati
E.K. Narayanan IISc Bangalore
     
Radoun Daher University of hassan II, Casablanca, Morocco
Ionnis Parissis Universidad del País Vasco, Spain
     
Sajith G Sullamussalam Science College
Joachim Toft Linnaeus University, Sweden
     
Sanjay P K NIT Calicut
Jotsaroop Kaur IISER Mohali
     
Sanjoy Pusti IIT Bombay
Kangwei Li Tianjin University, China
     
Sayan Bagchi IISER Kolkata
Lakshmi Lavanya IISER Tirupati
     
Senthil Raani K S IISER Berhampur
Luz Roncal BCAM- Basque Center for Applied Mathematics, Spain
     
Shobha Madan IIT Goa
Mithun Bhowmik IIT Bombay
     
Sundaram Thangavelu IISc Bangalore
Oscar Blasco Universidad de Valencia, Spain
     
Suparna Sen Calcutta University
P K Ratnakumar HRI Allahabad
     
Venku Naidu Dogga IIT Hyderabad
Parasar Mohanty IIT Kanpur
     
Vijay kumar Sohani IIT Indore