This text discusses the Euler class, the intersection number, the Lefschetz number, and the Thom class. The aim of discussing these well-known concepts is to describe them in a "computable" way. These will be expressed in differential or integral forms, giving formulae, generali…
Grassmannian geometry of scattering amplitudes
Tau functions are a central tool in the modern theory of integrable systems. This volume provides a thorough introduction, starting from the basics and extending to recent research results. It covers a wide range of applications, including generating functions for solutions of i…
A thorough introduction to tau functions, from the basics through to the most recent results, with applications in mathematical physics.
This paper is devoted primarily to the study of properties of the Grassmannian of oriented 2-planes in [double-struck capital]ℝ[superscript]n and to applications of these properties to understanding minimal surfaces in [double-struck capital]ℝ[superscript]n via the generalized G…