A 4-valent first-kind Frobenius circulant graph is a connected Cayley graph DLn(1, h) = Cay(Zn, H) on the additive group of integers modulo n, where each prime factor of n is congruent to 1 modulo 4 and H = {[1], [h],−[1], −[h]} with h a solution to the congruence equation x + 1 ≡ 0 (mod n). In [A. Thomson and S. Zhou, Frobenius circulant graphs of valency four, J. Austral. Math. Soc. 85 (2008)...

Abstract Gendo-Frobenius algebras are a common generalisation of Frobenius and gendo-symmetric algebras. A comultiplication is constructed for gendo-Frobenius algebras, which specialises to the known comultiplications on In addition, shown be precisely those that have counit compatible with this comultiplication. Moreover, new characterisation given. This key constructing

Using the sieve for Frobenius developed earlier by the author, we show that in a certain sense, the roots of the L-functions of most algebraic curves over finite fields do not satisfy any non-trivial (linear or multiplicative) dependency relations. This can be seen as an analogue of conjectures of Q-linear independence among ordinates of zeros of Lfunctions over number fields. As a corollary of...

We consider in this work the enumeration of involutions by descent sets, and based on that, by descent numbers. Formulas of the number of involutions with a prescribed descent set, with a prescribed descent number and Frobenius-type formulas are given.

Primitive digraphs on n vertices, k arcs and girth s are considered. By a(n, k, s) we mean the minimum exponent taken over all such digraphs. We estimate the number a(n, k, s) using the Frobenius number for special values of k and s.

By invoking the concept of twisted Poincaré symmetry of the algebra of functions on a Minkowski space-time, we demonstrate that the noncommutative space-time with the commutation relations [xμ ,xν ] = iθμν , where θμν is a constant real antisymmetric matrix, can be interpreted in a Lorentzinvariant way [1]. The implications of the twisted Poincaré symmetry on QFT on such a spacetime is briefly ...

These notes were taken at the NSF-CBMS conference on topological and geometric Methods in QFT at Montana State University in summer 2017. Most of the lectures were given by Dan Freed. I live-TEXed these notes using vim, and as such there may be typos; please send questions, comments, complaints, and corrections to [email protected]; any mistakes in the notes are my own. Thanks to Nilay K...

We construct a holographic map between asymptotically AdS5 × S5 solutions of 10d supergravity and vacuum expectation values of gauge invariant operators of the dual QFT. The ingredients that enter in the construction are (i) gauge invariant variables so that the KK reduction is independent of any choice of gauge fixing; (ii) the non-linear KK reduction map from 10 to 5 dimensions (constructed p...

Philosophers of physics should be more attentive to the role energy conditions play in GR. I review the changing status of energy conditions for quantum fields – presently there are no singularity theorems for semiclassical GR. So we must re-evaluate how we understand the relationship between GR, QFT and singularities. Moreover, on our present understanding of what it is to be a “reasonable” fi...