T. Tao and the Syracuse conjecture

Algorithmes pour Vérifier La Conjecture De Syracuse

The Structure of Boolean Derivatives in TAO and Meta-TAO

Following the ecological epistemology of Gregory Bateson, we have modeled mental process as the flow of differences in a richly connected network. Bateson also suggested that taking differences in this flow of differences would produce higher order knowledge. Finally, Bateson considered symmetry to be the basis for the pattern which connects living forms and, while he never connected taking dif...

The Endpoint Case of the Bennett-carbery-tao Multilinear Kakeya Conjecture

We prove the endpoint case of the multilinear Kakeya conjecture of Bennett, Carbery, and Tao. The proof uses the polynomial method introduced by Dvir. In [1], Bennett, Carbery, and Tao formulated a multilinear Kakeya conjecture, and they proved the conjecture except for the endpoint case. In this paper, we slightly sharpen their result by proving the endpoint case of the conjecture. Our method ...

9 Syracuse : 1949 – 1952

The year 1949 saw the publication of two papers by Peter Bergmann: Non-Linear Field Theories in the Physical Review [1] and, together with Johanna Brunnings, in the Reviews of Modern Physics [2], with the ambitious title Non-Linear Field Theories II: Canonical Equations and Quantization. These papers lay the foundation for the research of the Syracuse group working to quantize Einstein's theory...

The Inverse Conjecture for the Gowers Norm over Finite Fields via the Correspondence Principle Terence Tao and Tamar Ziegler

The inverse conjecture for the Gowers norms U(V ) for finite-dimensional vector spaces V over a finite field F asserts, roughly speaking, that a bounded function f has large Gowers norm ‖f‖Ud(V ) if and only if it correlates with a phase polynomial φ = eF(P ) of degree at most d− 1, thus P : V → F is a polynomial of degree at most d− 1. In this paper, we develop a variant of the Furstenberg cor...