Convener(s)
| Name: | Dr. Jotsaroop Kaur | Dr. Santhosh K. Pamula |
| Mailing Address: | Assistant Professor Department of Mathematics, Indian Institute of Science education and Research, Mohali |
Assistant Professor Department of Mathematics, Indian Institute of Science education and Research, Mohali |
| Email: | jotsaroop at iisermohali.ac.in | santhoshkp at iisermohali.ac.in |
This workshop is organised before the Discussion meeting in Harmonic analysis conference organised once every two years. The main aim of this NCMW is to introduce the recent developments in Harmonic analysis and also its relation with operator theory. This program is intended for Ph.D. students, post-doctoral fellows, and young teachers interested in working in Harmonic analysis and operator theory. The overall theme of this workshop will be inequalities in Harmonic analysis ,restriction theory, uncertainty principle with applications to data science, rough singular integral operators, uniform resolvent estimates and Rokhlin property for inclusion of C* algebras. All the above themes are very exciting in the field of analysis. We are having experts from abroad and within the country to present these topics.
Dates:
Venue:
Venue Address:
Dr.Jotsaroop Kaur
Assistant Professor Department of Mathematics
Indian Institute of Science education and Research,Mohali
Sector 81 SAS Nagar, Mohali 140306,
Punjab
Venue State:
Venue City:
PIN:
Chrono Order:
Syllabus:
|
Name of Speakers with Affiliations |
No of Lecture Hours |
Detailed Syllabus |
|
Jonathan Bennett |
4 |
Title: Brascamp—Lieb inequalities in harmonic analysis
Abstract: The Brascamp—Lieb inequalities are a broad generalisation of a host of important inequalities in mathematics, such as the H\"older, sharp Young's convolution, and Loomis—Whitney inequalities. While they naturally arise across the mathematical sciences, they have found remarkable applications in harmonic analysis over the last decade. In these lectures we will provide an accessible introduction to this area, placing emphasis on applications to well-known themes in modern harmonic analysis, from the restriction theory of the Fourier transform to Radon-like transforms. |
|
Hiroyuki Osaka |
4 |
Title: “ The Rokhlin property for inclusion of C*-algebras” Abstract: Let A ⊂ B be an inclusion of unital C*-algebras. It is a natural question which C*-algebraic permanent properties (simplicity, finiteness, real rank zero condition, stable rank one condition, nuclearity, strictly comparison property with respect to projections (resp.positive elements), the Jang-Su absorption, etc) are inherited to a small C*-algebra from a large C*-algebra . The typical example is the inclusion A ⊂ A XαΓ of a C*-algebra and its C*-crossed product A XαΓ by a discrete group and an action from on . In case of has the Rokhlin property (strong or weak), then we know that several permanent properties are inherited to a small C*-algebra from a large C*-algebra. In these lectures at first, we present basic operator algebras theory and classification theory of operator algebras. Then, we present Rokhlin property (strict, tracial, weak) for actions of C*-crossed products by discrete groups. After that we introduce the Rokhlin property for inclusion A ⊂ B of C*- algebras and show that several permanent properties are inherited to from under the condition that the Watatani index is finite which is C*-version of Jones index theory. Finally, we introduce several future problems. |
|
Parasar Mohanty |
3 |
Title: Rough singular Integral operator Abstract: In this short course, we will try to cover the following topics: (i) The ideas behind the proofs of Christ, Rubio de Francia, and Seeger. (ii) Recent developments in the boundedness in the weighted setting (iii) Recent advancements in research concerning endpoint results of maximal rough singular operators |
|
Jotsaroop Kaur |
3 |
Title: Uniform Resolvent estimates for Laplacian Abstract: The plan of the lectures is to first introduce the classical result by C. Kenig, A. Ruiz and C. Sogge in 1987 regarding Uniform resolvent estimates and unique continuation of Laplacian. We will also do the sharp result by S. Lee, E. Jeong and Y. Kwon regarding uniform resolvent estimates for non elliptic constant coefficient differential operators and its applications. We will also discuss the analogue resolvent estimates in the hypo elliptic setting, namely Grushin operator and Heisenberg Sub Laplacian. development . |
|
Alex Iosevich |
4 |
Title: ”Restriction theory, uncertainty principle, spectral synthesis, signal recovery and applications to data science".
Abstract: We are going to discuss a variety of connections between the restriction theory for the Fourier transform, the Fourier uncertainty principle, spectral synthesis, signal recovery, and the imputation of missing values in time series. Throughout the lectures, we are going to go back and forth between purely theoretical and highly applied concepts to present a continual symbiosis that channels techniques and ideas in both directions. |
References:
- Bennett, J., Carbery, A., Christ, M., Tao, T. The Brascamp–Lieb Inequalities: Finiteness, Structure and Extremals. GAFA Geom. funct. anal. 17, 1343–1415 (2008). https://doi.org/10.1007/s00039-007-0619-6.
- Seeger, Andreas Singular integral operators with rough convolution kernels. J. Amer. Math. Soc. 9 (1996), no. 1, 95-105.
- Bhojak, Ankit; Mohanty, Parasar Weak type bounds for rough maximal singular integrals near L^1.J. Funct. Anal. 284 (2023), no. 10.
- C.E. Kenig, A. Ruiz, C.D. Sogge, Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators, Duke Math. J., 55 (2) (1987), pp. 329-347
- E. Jeong, Y. Kwon, S. Lee, Uniform Sobolev inequalities for second order non-elliptic differential operators, Advances in Mathematics, Volume 302, 2016, Pages 323-350.
- Kodaka, K., Osaka, H., and Teruya, T., The Rokhlin property for inclusions of C*-algebras with a finite Watatani Index. In: Operator structures and Dynamical Systems, Contemporary Mathematics , 503, American Mathematical Society, Providence, RI, 2009, pp. 177–195.
- H. Osaka and T. Teruya, The Rokhlin property for inclusion of C* -algebras, Rocky Mount. J. Math. 50 (2020), no. 5. 1785 –1792.
- H. Osaka, K. Kodaka, T. Teruya, The Rokhlin property for inclusion of C*-algebras with a finite Watatani index , Contem. Math. 503(2009), 177–195.
- Y. Watatani, Index for C*-subalgebras, Mem. Amer. Math. Soc. 424(1990), AMS.
Names of the tutors with their affiliation:
1. Utsav Dewan (ISI Kolkata)
2. Rifat Siddique (IISER Mohali)
3. Riju Basak (NTU Taiwan)
Time Table:
|
Day |
Date |
Lecture 1 9.30 – 11.00 |
Tea 11.05 - 11.25 |
Lecture 2 11.30 - 1.00 |
Lunch 1.05 – 1.55 |
Lecture 3 2.00 - 3.30 |
Tea 3.35 - 3.55 |
Discussion 4.00 - 5.00 |
Snacks 5.05 - 5.35 |
|
|
|
(name of the speaker) |
|
(name of the speaker) |
|
(name of the speaker) |
|
(Name of the tutor) |
|
|
Mon |
08/12 |
JB |
|
HO |
|
AI |
|
RB & JB |
|
|
Tues |
09/12 |
HO |
|
PM |
|
JK |
|
RS & HO |
|
|
Wed |
10/12 |
JB |
|
PM |
|
AI |
|
RB & JB |
|
|
Thu |
11/12 |
HO |
|
JK |
|
JB |
|
RS & HO |
|
|
Fri |
12/12 |
JB |
|
AI |
|
HO |
|
UD & AI |
|
|
Sat |
13/12 |
PM |
|
JK |
|
AI |
|
UD & AI |
|
Full forms for the abbreviations of speakers and tutors:
JB: Jonathan Bennett
HO: Hiroyuki Osaka
PM:Parasar Mohanty
AI: Alex Iosevich
JK:Jotsaroop Kaur
UD:Utsav Dewan
RS:Rifat Siddique
RB:Riju Basak
Selected Applicants:
How to Reach:
TBA