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[CT071]

CT071 (1/1) : Global differential geometry (53C) / Partial differential equations on manifolds; differential operators (58J) / Manifolds and cell complexes (57-)

Session Time & Room : 5D (Aug.25, 15:30-17:10) @F402
Type : Contributed Talk
Abstract : Finsler manifolds are important generalizations of Euclidean and Riemannian ones with applications in different domains of mathematics, physics and engineering. In the present talk we are going to present some recent results concerning Finsler connections, curvature and relation with statistical models in the real world. We suggest possible development of information geometry on Finsler manifolds that would allow a wide range of applications.
Classification : 53C60
Format : Talk at Waseda University
Author(s) :
- Sorin Sabau (Tokai University)

Session Time & Room : 5D (Aug.25, 15:30-17:10) @F402
Type : Contributed Talk
Abstract : Learning from data that live in Riemannian manifolds has become central to many applications, ranging from radar signal processing to neuroscience. In this talk, we present a generalisation of Gaussian distributions to Riemannian symmetric spaces of non-positive curvature, which include hyperbolic spaces, as well as spaces of real, complex and quaternion positive definite matrices, and spaces of structured Toeplitz or block-Toeplitz positive definite matrices and discuss applications to geometric statistics on such spaces.
Classification : 53C22, 53B20, 53B50, 53C80, 53C35, Geometric statistics, probability on manifolds
Format : Talk at Waseda University
Author(s) :
- Cyrus Mostajeran (Nanyang Technological University)
- Salem Said (Université Grenoble-Alpes)

Session Time & Room : 5D (Aug.25, 15:30-17:10) @F402
Type : Contributed Talk
Abstract : Poincaré integral operators give explicit potential and provide an inverse of differential operators in the sense of null-homotopy. These operators play a key role in the mathematical and numerical analysis of fluid and electromagnetic problems. Consequences include the well-posedness of the Stokes problem and the p-robustness of high-order finite element methods. In this talk, we derive such operators for the Bernstein-Gelfand-Gelfand (BGG) complexes with potential applications in elasticity and relativity. The idea is to carry over the results for the de-Rham complex by Costabel and McIntosh to these cases by homological algebra.
Classification : 58J10, 35N05, 58A12, 58A14, 65N30, finite element methods, Hilbert complexes, Bernstein-Gelfand-Gelfand construction, applied analysis
Format : Talk at Waseda University
Author(s) :
- Andreas Čap (University of Vienna)
- Kaibo Hu (University of Oxford)

Session Time & Room : 5D (Aug.25, 15:30-17:10) @F402
Type : Contributed Talk
Abstract : In this communication, we talk about the fractional controllability problem of internally controlled semilinear hyperbolic systems. in the first method, we show the controllability of the linear system using Hilbert uniqueness method HUM, and the fractional controllability problem is solved applying Schauder’s fixed point theorem. Secondly, the analytics study is then attempted by employing generalized inverse methods and changed also into a fixed point problem. Hence, we give an approximate approach to find a control that brings the Riemann-Liouville fractional attained position (resp. speed) to the required position yd1 (resp. speed yd2). Finally, computing simulations are used to confirm the obtained results.
Classification : 57-XX, 26-XX, 53-XX
Format : Online Talk on Zoom
Author(s) :
- Mustapha Benoudi (Moulay Ismail University)