Related papers: Notes on Laver Tables

These are notes for a very rapid introduction to the basics of exterior differential systems and their connection with what is now known as Lie theory, together with some typical and not-so-typical applications to illustrate their use.

We improve the error terms of some estimates related to counting lattices from recent work of L. Fukshansky, P. Guerzhoy and F. Luca (2017). This improvement is based on some analytic techniques, in particular on bounds of exponential sums…

A new kind of diagrams is presented, showing the causal structure of bimetric interactions.

Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…

We obtain a lower bound for a number of primes in tuples. As applications, we obtain a lower bound for the Romanoff type representation functions.

We give an axiomatic framework for studying the representation theory of towers of algebras. We introduce a new class of algebras, contour algebras, generalising (and interpolating between) blob algebras and cyclotomic Temperley-Lieb…

After recalling the notion of Lie algebroid, we construct these structures associated with contact forms or systems. We are then interested in particular classes of Lie Rinehart algebras.

These Lecture Notes are a brief introduction to the Malliavin calculus. In particular, different notions of Malliavin derivative found in the literature are considered and compared.

In this paper we study underlying graphs corresponding to a set of halving lines. We establish many properties of such graphs. In addition, we tighten the upper bound for the number of halving lines.

We develop a random model for relation algebras. We prove some preliminary results and pose questions that lay out a new direction of research.

Computations in renormalizable perturbative quantum field theories reveal mathematical structures which go way beyond the formal structure which is usually taken as underlying quantum field theory. We review these new structures and the…

Let L be a restricted Lie algebra over a field of positive characteristic. We survey the known results about the Lie structure of the restricted enveloping algebra u(L) of L. Related results about the structure of the group of units and the…

In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.

Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.

A novel definition of the Laplacian of 1/r is presented, suitable for advanced undergraduates.

Informal lecture notes with examples on sheaf theory and the derived category of sheaves; sheaves and Morse theory; perverse sheaves, and some applications to representation theory. Added Oct 2021: cellular perverse sheaves. Proofs are…

In this article we present a new method to obtain polynomial lower bounds for Galois orbits of torsion points of one dimensional group varieties.

New notions are introduced in algebra in order to better study the congruences in number theory. For example, the <special semigroups> makes an important such contribution.

We establish derivative estimates of solution of elliptic system in narrow regions.

We attempt to survey recent results and open problems connected to Lieb-Thirring inequalities.