4 papers
Towards Hodge-Riemann relations for non-Archimedean analogs of valuations on convex sets
Semyon Alesker
In [8], a non-Archimedean analogue of the space of translation-invariant even valuations on convex sets was introduced. In [7], motivated by a further analogy with the classical th…
Non-commutative linear algebra and plurisubharmonic functions of quaternionic variables
Semyon Alesker
We recall known and establish new properties of the Dieudonné and Moore determinants of quaternionic matrices.Using these linear algebraic results we develop a basic theory of plu…
Non-Archimedean analogue of the space of valuations on convex sets
Semyon Alesker
In the last two decades a number of structures on the classical space of translation invariant valuations on convex bodies were discovered, e.g. product, convolution, a Fourier typ…
Octonionic Calabi-Yau theorem
Semyon Alesker, Peter Gordon
A new class of Riemannian metrics, called octonionic Kähler, is introduced and studied on a certain class of 16-dimensional manifolds. It is an octonionic analogue of Kähler metr…