Assuming a conjectural upper bound for the least prime in an arithmetic progression, we show that n-bit integers may be multiplied in O(n logn 4 ∗ n) bit operations.

In this paper we give a conjectural refinement of the DavenportHeilbronn theorem on the density of cubic field discriminants. Our refinement is plausible theoretically and agrees very well with computational data.

Cohen and Cohen-Jones-Segal have written about how to lift Floer-type invariants to spectra in the sense of stable homotopy theory. We'll talk about new and conjectural ways to lift Floer-type invariants to spectra.

We propose two conjectural relationships between the equivariant Gromov–Witten invariants of resolved conifold under diagonal and anti-diagonal actions $$\mathbb {P}^1$$ verify their validity in genus zero approximation. also provide evidences to support these one two.

We present new probabilistic and combinatorial identities relating three random processes: the oriented swap process (OSP) on n particles, corner growth process, last passage percolation (LPP) model. prove one of identities, a vector LPP times to its dual, using duality between Robinson–Schensted–Knuth Burge correspondences. A second identity, those two vectors “last times” in OSP, is conjectur...

Three conjectural directions in Gromov-Witten theory are discussed: Gorenstein properties, BPS states, and Virasoro constraints. Each points to basic structures in the subject which are not yet understood. 2000 Mathematics Subject Classification: 14N35, 14H10 .

We give Andrews-Gordon type series for the principal characters of level 5 and 7 standard modules affine Lie algebra $A^{(2)}_{2}$. also conjectural some 2 $A^{(2)}_{13}$.

We formulate and discuss two conjectures concerning recursive formulae for Branson’s Q-curvatures. The proposed formulae describe all Qcurvatures on manifolds of all even dimensions in terms of respective lower order Q-curvatures and lower order GJMS-operators. They are universal in the dimension of the underlying space. The recursive formulae are generated by an algorithm which rests on the th...