Specialization: Analysis
This group specializes in applied functional analysis and operator theory, harmonic analysis, and analysis of partial differential equations (PDEs) that emerge in probability, mathematical physics, and various real-world phenomena. Our research encompasses a broad range of topics, including:
- Investigating the structure and properties of the Heisenberg group and the metaplectic group via classical harmonic analysis. This includes applications in representation theory, time-frequency analysis, and quantum mechanics.
- Analyzing nonlinear and nonlocal elliptic and parabolic PDEs which are fundamental in modelling of Heterogeneous media, in Complex fluid dynamics and in Biological systems.
- Exploring PDEs governed by nonlocal operators, including the fractional Laplacian and logarithmic Laplacian, which are essential for anomalous diffusion, image processing applications such as noise reduction and edge detection and phase transition phenomena including nonlocal models in materials science.