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Delooping generated groups in homotopy type theory
Camil Champin, Samuel Mimram, Emile Oleon
https://arxiv.org/abs/2405.03264 https://

Delooping generated groups in homotopy type theory
Homotopy type theory is a logical setting based on Martin-Löf type theory in which one can perform geometric constructions and proofs in a synthetic way. Namely, types can be interpreted as spaces (up to continuous deformation) and proofs as homotopy invariant constructions. In this context, the loop spaces of types with a distinguished element (more precisely, pointed connected groupoids), provide a natural representation of groups, what we call here internal groups. The construction which in…

Spinoptics in a curved spacetime
Valeri P. Frolov
https://arxiv.org/abs/2405.01777 https://arxiv.org/pdf/2405.01777

Spinoptics in a curved spacetime
In this paper we study propagation of the high frequency electromagnetic waves in a curved spacetime. We discuss a so call spinoptics approach which generalizes a well known geometric optics approximation and allows one to take into account spin-dependent corrections. A new element proposed in this work is the use of effective action which allows one to derive spinoptics equations. This method is simpler and more transparent than the earlier proposed methods. It is explicitly covariant and can …

This https://arxiv.org/abs/2310.16701 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Odd-Sunflowers
Extending the notion of sunflowers, we call a family of at least two sets an odd-sunflower if every element of the underlying set is contained in an odd number of sets or in none of them. It follows from the Erd\H os--Szemerédi conjecture, recently proved by Naslund and Sawin, that there is a constant $μ<2$ such that every family of subsets of an $n$-element set that contains no odd-sunflower consists of at most $μ^n$ sets. We construct such families of size at least $1.5021^n$. We also char…

On the isomorphism problem for power semigroups
Salvatore Tringali
https://arxiv.org/abs/2402.11475 https://arxiv.org/pdf/2402.11475<…

On the isomorphism problem for power semigroups
Denote by $\mathcal P(S)$ the semigroup obtained by equipping the family of all non-empty subsets of a (multiplicatively written) semigroup $S$ with the operation of setwise multiplication induced by $S$ itself. We call a subsemigroup $P$ of $\mathcal P(S)$ downward complete if any element of $S$ lies in at least one set $X \in P$ and any non-empty subset of a set in $P$ is again in $P$. We prove, for a commutative semigroup $S$, a characterization of the cancellative elements of a downward c…