What does “control of a deformation problem” mean?

Is the expression “control of a deformation problem’ ever defined? There are of course many examples relating a dg-Lie or L-infty algebra to a deformation problem, and the phrase is evocative. Is it ever defined? Answer AttributionSource : Link , Question Author : Jim Stasheff , Answer Author : Community

Natural transformations of A∞A_\infty-functors (between dg-categories) are “directed homotopies” (reference?)

Let A and B be dg-categories over a field, viewed as A∞-categories. The A∞-category (actually, dg-category) of strictly unital A∞-functors A→B will be denoted by Fun∞(A,B). It is described explicitly (in the non-unital case) for example in P. Seidel’s book (“Fukaya category and Picard-Lefschetz theory”). Let Δ1 be the 1-simplex category, namely, the linear category … Read more

Conjectured new primality test for Mersenne numbers

How to prove that this conjecture about a new primality test for Mersenne numbers is true ? Definition: Let M_{q}=2^{q}-1 , S_{0} = 3^{2} + 1/3^{2} , \ and: \ S_{i+1} = S_{i}^{2}-2 \pmod{M_{q}} Conjecture: M_{q}\text{ is a prime iff: } \ S_{q-1} \equiv S_{0} \pmod{M_{q}} \text{ and iff: } \prod_{0}^{q-2} S_i \equiv 1 \pmod{M_{q}} … Read more

Has unconditional convergence ever been proved other than by deducing it from absolute convergence?

Nobody’s answering this question so I’ll try it here. This is really a reference request: Has a certain kind of proof ever been used? A series ∑nan converges absolutely if ∑n|an|<∞. It converges unconditionally if it converges to a finite number and all of its rearrangements converge to that same number. For series of real … Read more

Modules over an Azumaya algebra and modules over the associated Brauer-Severi variety

Assume A is an Azumaya algebra of rank r2 on a smooth projective scheme Y over C. Let f:X→Y be the Brauer-Severi variety associated to A. I read here in a comment that the category of modules over A is equivalent to the categroy of modules on X which restrict to every fiber as a … Read more

Rational connectedness of certain subvarieties of the linear series

Let X be a smooth projective hypersurface in P3, |OX(a)| be the complete linear system for some integer a>0. Ofcourse, a general element of the linear system is a smooth curve. Denote by V the subvariety of |OX(a)| parametrizing reducible curves (i.e., with at least 2 irreducible components). Is any irreducible component of V rationally … Read more

Cannot multivectors be classified more easily than general tensors?

This is sort of a spinoff of Is there a useful generalization of the Schmidt decomposition to the tensoring together of 3 or more vector spaces? – seems to be almost hopeless, but maybe some partial results are known. Recall that multivectors are elements of exterior powers: an n-dimensional k-vector is an element of Λk(Cn). … Read more

Characterization of L[T2n+1]L[T_{2n+1}] as a direct limit of mice

I am asking for a reference request/proof sketch for the result of Steel that characterizes L[T2n+1] as a direct limit of mice. Given that both L[T2n+1] and M2n have a Σ2n+2 well-ordering of the reals, I think the result should be that L[T2n+1] is the direct limit of iterable mice with 2n Woodin cardinals, but … Read more

Faster (than normal) convergence of the normalized Ricci flow on surfaces

Consider a compact surface M of genus γ>1 (I am using the more usual letter “g” to denote metric), and the normalized Ricci flow on it. It is known that at time t, the scalar curvature R satisfies |R−r|<Cert, where r=∫MRdμ∫Mdμ is the average scalar curvature of M, and C is a constant depending only … Read more

Laplacian Spectra on Nearly Nodal Riemann Surfaces

Consider a family of complex curves C→D such that the central fibre is a nodal Riemann surface while other fibres are smooth Riemann surfaces. We choose a family of conformal metrics by restricting a smooth metric on C. So near the nodes (with local models xy=t, where t is the coordinate on D), the metric … Read more