The automorphisms of free groups with boundaries form a family of groups An,k closely related to mapping class groups, with the standard automorphisms of free groups as An,0 and (essentially) the symmetric automorphisms of free groups as A0,k . We construct a contractible space Ln,k on which An,k acts with finite stabilizers and finite quotient space and deduce a range for the virtual cohomolog...

Here, we present a survey concerning parabolic free boundary problems involving a discontinuous hysteresis operator. Such problems describe biological and chemical processes 'with memory' in which various substances interact according to hysteresis law. Our main objective is to discuss the structure of the free boundaries and the properties of the so-called 'strong solutions' belonging to the a...

We consider free higher derivative theories of scalars and Dirac fermions in the presence a boundary general dimension. establish method for finding consistent conformal conditions these by removing certain primaries from spectrum. A rich set renormalization group flows between various is revealed, triggered deformations quadratic primaries. compute energy on hemisphere, show that $a$-theorem g...

<p style='text-indent:20px;'>We study a class of free boundary systems with nonlocal diffusion, which are natural extensions the corresponding problems reaction diffusion systems. As before represents spreading front species, but here population dispersal is described by "nonlocal diffusion" instead "local diffusion". We prove that such problem has unique global solution, and for models L...

In this paper we investigate the spectrum of $OSp(n|2m)$ quantum spin chains with free boundary conditions. We compute surface energy these models which, similar to other properties in thermodynamic limit including effective central charge underlying conformal field theory, depends on $n-2m$ only. For several regime $n-2m< 2$ have studied finite-size subleading logarithmic corrections scaling. ...