Higher-dimensional Clifford–Severi equalities

Homotopy Type Theory: A synthetic approach to higher equalities

Ask an average mathematician or philosopher today about the foundations of mathematics, and you are likely to receive an answer involving set theory: an apparent consensus in marked contrast to the foundational debates of the early 20th century. Now, at the turn of the 21st century, a new theory has emerged to challenge the foundational ascendancy of sets. Arising from a surprising synthesis of...

Higher Dimensional

Determination of subrepresentations of the standard higher dimensional shearlet group

‎This paper is devoted to definition standard higher dimension shearlet group $ mathbb{S} = mathbb{R}^{+} times mathbb {R}^{n-1} times mathbb {R}^{n} $ and determination of square integrable subrepresentations of this group‎. ‎Also we give a characterisation of admissible vectors associated to the Hilbert spaces corresponding to each su brepresentations‎.

Higher Dimensional Trees, Algebraically

In formal language theory, James Rogers published a series of innovative papers generalising strings and trees to higher dimensions.Motivated by applications in linguistics, his goal was to smoothly extend the core theory of the formal languages of strings and trees to these higher dimensions. Rogers’ definitions focussed on a specific representation of higher dimensional trees. This paper pres...

Structures in Higher - Dimensional

This is an exposition of some of the constructions which have arisen in higher-dimensional category theory. We start with a review of the general theory of operads and multicategories (cf. Bur], Her], Lei1]). Using this we give a new deenition of n-category (a variation on Batanin's); we also give an informal dee-nition in pictures. Next we discuss Gray-categories and their place in coherence p...