Events

In 1998, Goresky, Kottwitz, MacPherson introduced a class of $(S^1)^k$-actions on smooth manifolds with degenerate odd-dimensional cohomologies. They calculated the corresponding ring of equivariant cohomologies in terms of so-called GKM-graphs. Roughly speaking, a GKM-graph of type $(n,k)$ is an $n$-valent graph with labels from the lattice $\Z^k$ on its edges.

This talk will contain a review of some approaches and results of W. Chen, R. Yang, and their collaborators concerning nonexistence of solutions for a nonlinear Dirichlet problem with a fractional power of the Laplace operator in a half-space that belong certain functional classes depending on the growth order of the nonlinear term.

By the method of weighted metrics, in various cones of the space of continuous functions on the positive semiaxis, we study integro-differential equations of Volterra type of various orders with difference kernels and power nonlinearity.

The contraction mechanics of cardiac muscle, the stresses and strains developed, are closely related to the processes of muscle electrical activation.

The authors will discuss nonexistence results they obtained in the recent years for some nonlinear partial differential equations and inequalities containing fractional powers of the Laplace operator.

The talk is devoted to the operator-theoretic (spectral) approach to homogenization suggested by M. Birman and T. Suslina.

In the talk we consider traces of Fourier integral operators (V.P. ​​Maslov, L. Hörmander). More precisely, we study the situation when the trace of the Fourier integral operator on the submanifold is again the Fourier integral operator. The results obtained are used to study the Fredholm solvability of some Sobolev problems with nonlocal boundary conditions.