Extended Abstracts 2021/2022

Part I Analysis.- A note on a Capelli operator and its resonance.- Schatten-von Neumann classes Sp on the torus for 0 < p = 2.- Log-Sobolev and Nash inequalities on graded groups.- One-sided Hardy-Littlewood maximal function on generalised Lorentz spaces.- Remarks on gradient Yamabe solitons.- Boundedness of Fourier multipliers on fundamental domains of lattices.- Pointwise domination and weak L 1 boundedness of Littlewood-Paley operators via sparse operators.- Hp Lp boundedness of Fourier multipliers on graded Lie groups.- On a reverse integral Hardy inequality on polarisable metric measure space.- Logarithmic Sobolev inequalities of fractional order on noncommutative tori.- The Prabhakar fractional q -integral and q -differential operators.- A note on weak type boundedness of pseudo-differential operators on rank one symmetric spaces of noncompact type.- Lp - Lq norms ofspectral multipliers.- Estimates for oscillatory integrals with discontinuous amplitude.- The unitary dual of the Heisenberg group over Rp.- Critical Sobolev-type identities and inequalities on stratified Lie groups.- Part II Partial differential equations.- Anisotropic Picone type identities for general vector fields and some applications.- An equivalence between the Neumann problem and its boundary domain integral equation systems for Stokes equations.- Short note on generalised bivariate Mittag-Leffler-type functions.- Inverse problems for time-fractional mixed equation involving the Caputo fractional derivative.- Time dependent inverse source problems for integrodifferential Kelvin-Voigt system.- A nonlocal initial conditional boundary value problem on metric graph.- Second-order semiregular non-commutative harmonic oscillators: the spectral zeta function.- Global well-posedness with loss of regularity for a class of singular hyperbolic Cauchy problems.- On a mixed equationinvolving Prabhakar fractional order integral-differential operators.- Inverse problem of determining a time-dependent source in a fractional Langevin-type partial differential equation.- Very weak solution of the discrete wave equation for harmonic oscillator.- An estimate for the multivariate Mittag-Leffler function.- Part III Mathematical modelling.- Mathematical modelling of the Lomb-Scargle method in astrophysics.- The application of physics informed networks to solve hyperbolic partial differential equations with nonconvex flux function and diffusion term.- Fractional differential equations: a primer for structural dynamics applications.- Text matching as time series matching.- Performing Particle Image Segmentation on an Extremely Small Dataset.- Two-dimensional dispersed composites on a square torus.