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In this short note we give a polynomial-time quantum reduction from the vectorization problem (DLP) to the parallelization problem (CDHP) for group actions. Combined with the trivial reduction from pa...
We give a new signature scheme for isogenies that combines the class group actions of CSIDH with the notion of Fiat-Shamir with aborts. Our techniques allow to have signatures of size less than one ki...
Let be a compact orientable surface with genus g andnboundary components ∂1,..., ∂n. Let b = (b1,...,bn) ∈ [−2,2] n. Then the mapping class group Mod() acts on the relative SU(2)-...
A survey of finite group actions on symplectic 4-manifolds is given with a special emphasis on results and questions concerning smooth or symplectic classification of group actions, group actions and ...
We show that coincidence of the full and reduced crossed product $C^\ast$-algebras of a group action on a unital commutative $C^\ast$-algebra implies amenability of the action whenever the group is ex...
For a countable group G and a standard Borel G-space X, a countable Borel partition P of X is called a generator if {gA : g in G, A in P} generates the Borel sigma-algebra of X. For G=Z, the Kolmogoro...
Abstract: We prove that the number of distinct group actions on compact Riemann surfaces of a fixed genus $\sigma \geq 2$ is at least quadratic in $\sigma$. We do this through the introduction of a co...
A refined form of the ‘Folk Theorem’ that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type is proved in the context of manifolds ...
Previously we gave a proof of the Feigin–Fuchs character formula for the irreducible unitary discrete series of the Virasoro algebra with 0 < c < 1. The proof showed directly that the mutliplicity sp...
We show that every effective smooth action of a Lie group G on a manifold M is a diffeomorphism from G onto its image in Diff(M), where the image is equipped with the subset diffeology of the functio...
We produce for each natural number n  3 two 1–parameter fam-ilies of Riemann surfaces admitting automorphism groups with two cyclic sub-groups H1 and H2 of orden 2n, that are conjugate in the group o...
Let $G$ be a finite $p$-group and $k$ a field of characteristic $p>0$. We show that $G$ has a \emph{non-linear} faithful action on a polynomial ring $U$ of dimension $n=\mathrm{log}_p(|G|)$ such that...
In his volume [5] on "Symmetry Breaking for Compact Lie Groups" Mike Field quotes a private communication by Jorge Ize claiming that any bifurcation problem with absolutely irreducible group action wo...
We construct holomorphic families of proper holomorphic embeddings of $\C^k$ into $\C^n$ ($0 so that for any two different parameters in the family no holomorphic automorphism of $\C^n$ can ...
If G is a finite ℓ-group acting on an affine space An over a finite field K of cardinality prime to ℓ, Serre [29] shows that there exists a rational fixed point. We generalize this to the ...

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