About:

Lectures:

• Lecture Series by Prof. S. Thangavelu: "Bargmann and Fock meet Hardy: An uncertainty principle for operators"

In these lectures, we discuss certain bounded linear operators on Fock/twisted Fock spaces leading to the definition of twisted Heisenberg groups $ H^n_\lambda(\C)$. We construct a certain unitary representation of this group and use an operator analogue of Hardy's theorem proves that this representation is irreducible. --:References:--

° The lectures are held on Tuesdays and Thursdays from 11:15 a.m. to 12:30 p.m. in the seminar room next to Higgs Hall.

• Lecture Series by Prof. S. Thangavelu: "Fourier analysis: L^2 theory, Schwartz space, Tempered distributions"

Colloquium Talk:

• Bargmann and Fock meet Hardy: An uncertainty principle for operators : Prof. S. Thangavelu, IISc B'luru, 01-04-2024

Valentine "Valya" Bargmann (April 6, 1908 – July 20, 1989) was a German-American mathematician and theoretical physicist.

Vladimir Aleksandrovich Fock (December 22, 1898 – December 27, 1974) was a Soviet physicist, who did foundational work on quantum mechanics and quantum electrodynamics.

Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis.

Workshops/Conferences:

• Workshop on Harmonic Analysis: Fourier Multipliers and Related Topics at HRI, Feb 19 - Mar 02, 2024.

Singular Integrals -Lp boundedness, Spectral estimates on the sphere: Prof. S. Thangavelu.

Basics on Fourier multipliers: Prof. P.K. Ratnakumar

Unique Continuation Principle (UCP) for Partial Differential Equations: Dr. Tuhin Ghosh.

Preprints:

• On the boundedness of Dunkl multipliers: Suman Mukherjee, Sundaram Thangavelu

• On the boundedness of certain operators of convolution type on Fock spaces: Sundaram Thangavelu

Seminar/Colloquium:

• Adaptive Finite element methods for contact problems : Dr. Tanvi, HRI Allahabad.

• Microlocal analysis through continuous shearlet and Radon transform : Dr. Swaraj Paul, SRMIST, Chennai.

• Quantitative uniqueness for parabolic operators with applications to nodal sets : Dr. Agnid Baneerjee, Arizona State University.

• Strong unique continuation for parabolic operators with Hardy type potential : Dr. Agnid Baneerjee, Arizona State University.

• Invariant Submanifolds for Stochastic Partial Differential Equations : Dr. Rajeev Bhaskaran, ISI Bangalore & IISER TVM.

• The Monotonicity Inequality for Linear Stochastic PDEs : Dr. Suprio Bhar, IIT, Kanpur.

• On fractal dimensions of fractal functions and fractional integrals : Dr. Subhas Chandra, HRI, Allahabad.

• Connection on Lie groupoids and Chern-Weil theory : Dr. Saikat Chatterjee, IISER TVM.

• On Homogenizazion of Maxwell equations : Swapnil Sanap, HRI, Allahabad.

• Long time behavior of evolution equations using Entropy methods : Susovan Pramanik, HRI, Allahabad.

• Homogenisation of a Poro-elastic Model : Dr. Hari Shankar Mahato, IIT Kharagpur.

• Linear and Bilinear Multipliers for the Dunkl Transform : Dr. Suman Mukherjee, NISER Bhubaneswar.

• Functions operating on modulation spaces in connection with the fractional Fourier transform: Dr. Hasan Ali Biswas, IISc Bangalore.

• Turbulent flow dynamics in the world's oceans: Dr. Jim Thomas, ICTS & TIFR Bangalore.

• On Solitons to Ambient Obstruction Flow: Dr. Rahul Poddar, HRI Allahabad.

• Spectra of negatively curved Riemannian manifolds: Dr. Mayukh Mukherjee, IIT Bombay.

• Hypocoercivity and Optimal Decay Rate Analysis for Goldstein Taylor Model: Dr. Saumyajit Das, IIT Bombay.

• Degeneracies in triangular reaction-diffusion systems: Dr. Saumyajit Das, IIT Bombay.

• Counting Rational Points near Manifolds: Dr. Rajula Srivastava, University of Bonn.

• Randomness, Rational Points, and Oscillatory Integral: Dr. Niclas Technau, Max Planck Institute, Bonn.

• On Bilinear Bochner-Riesz Problem: Dr. Saurabh Srivastava, IISER-Bhopal.

• On point-wise convergence of the solution of the heat equation on the torus : Dr. Divyang Bhimani, IISER-Pune.

• The fractional KPI saga: Low regularity well-posedness analysis : Dr. Akansha Sanwal, University of Innsbruck, Austria.

• Visibility and Invisibility in Inverse problems : Dr. Ashwin Tarikere, University of California, USA.

Links:

• HRI Library.

• Symposium on Celebrating International Women in Mathematics Day

• PhD-Postdoc Math Meet

• Seminar series (online) on Prismatic Cohomology

• Workshop on Harmonic Analysis: Fourier Multipliers and Related Topics