We explain how rank two Frobenius extensions of commutative rings lead to link homology theories and discuss relations between these theories, Bar-Natan theories, equivariant cohomology and the Rasmussen invariant. AMS Subject Classification: 57M27 Frobenius systems. Suppose ι : R −→ A is an inclusion of commutative rings, and ι(1) = 1. The restriction functor Res : A−mod −→ R−mod has left and ...

We give a simple derivation of the spectrum Dirac magnetic monopole on unit sphere S2 based geometric quantization and Frobenius reciprocity formula. The starting point is calculation by Novikov Schmelzer canonical symplectic structure coadjoint orbits isometry group 3-dimensional Euclidean space E(3), which showed appearance term.

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

We introduce fusion bialgebras and their duals systematically study Fourier analysis. As an application, we discover new efficient analytic obstructions on the unitary categorification of rings. prove Hausdorff-Young inequality, uncertainty principles for duals. show that Schur product property, Young's inequality sum-set estimate hold bialgebras, but not always If ring is Grothendieck a catego...

We develop techniques of mimicking the Frobenius action in study universal homeomorphisms mixed characteristic. As a consequence, we show characteristic Keel's base point free theorem obtaining applications towards Minimal Model Program, generalise Kollár's on existence quotients by finite equivalence relations to characteristic, and provide new proof affine group schemes.

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...