Seminar
Approximation of fractional operators and fractional PDEs using a sinc-basis
We introduce a spectral method to approximate PDEs involving the fractional Laplacian with zero exterior condition. Our approach is based on interpolation by tensor products of sinc-functions, which combine a simple representation in Fourier-space with fast enough decay to suitably approximate the bounded support of solutions to the Dirichlet problem. This yields a numerical complexity of O(NlogN) for the application of the operator to a discretization with N degrees of freedom.
Constructing robust high order entropy stable discontinuous Galerkin methods
High order methods are known to be unstable when applied to nonlinear conservation laws whose solutions exhibit shocks and turbulence. Entropy stable schemes address this instability by ensuring that physically relevant solutions satisfy a semi-discrete entropy inequality independently of numerical resolution or solution regularization and shock capturing.
Singularity formation for reduced models of fluid equations
`Neural forecasting of high-dimensional dynamical Systems'
Images of skyscraper sheaves on toric resolutions: cohomology distribution
Zoom Meeting ID: 973 0230 7263
Shirsho Mukherjee - Minimax characterization of non-linear eigenvalue problems.
Moduli spaces of stable curves, Gromov-Witten varieties, and the quantum K-theory ring
The moduli space of pointed hyperelliptic curves over finite fields
Zagier’s formula for multiple zeta values and its odd variant revisited
Zoom Meeting ID: 973 0230 7263