Inspired by the geometry of wrapped Fukaya categories, we introduce the notion of wrapped microlocal sheaves. We show that traditional microlocal sheaves are equivalent to functionals on wrapped microlocal sheaves, in analogy with the expected relati...
A novel optimization strategy, Info-Evo, is described, in which natural gradient search using nonparametric Fisher information is used to provide ongoing guidance to an evolutionary learning algorithm, so that the evolutionary process preferentially...
The main topic of the paper is the construction of various explicit flat families of border bases. To begin with, we cover the punctual Hilbert scheme Hilb^μ(A^n) by border basis schemes and work out the base changes. This enables us to control flat...
We give an overview of several of the mathematical works of Gilles Lachaud and provide a historical context. This is interspersed with some personal anecdotes highlighting many facets of his personality....
We show that the F-theory dual of the heterotic string with unbroken Spin(32)/Z_2 symmetry in eight dimensions can be described in terms of the same polyhedron that can also encode unbroken E_8\times E_8 symmetry. By considering particular compacti...
A variational principle is applied to 4D Euclidean space provided with a tensor refractive index, defining what can be seen as 4-dimensional optics (4DO). The geometry of such space is analysed, making no physical assumptions of any kind. However,...
It is the author's belief that a perfect theory will eventually be formulated, where geometry and physics become indistinguishable, so that the complete understanding of space properties, together with proper assignments between geometric and physi...
The supersymmetric generalization of dilatations in the presence of the dilaton is defined. This is done by defining the supersymmetric dilaton geometry which is motivated by the supersymmetric volume preserving diffeomorphisms. The resulting model...
Given a solution to 4D Einstein gravity with an isometry direction, it is known that the equations of motion are identical to those of a 3D $σ$-model with target space geometry $SU(1,1)/U(1)$. Thus, any transformation by $SU(1, 1) \cong SL(2,\mathbb...
We provide exposition into the field of projection theory, which lies at the intersection of incidence geometry and geometric measure theory. We first give the necessary preliminaries in Chapter 2, focusing on incidences between points and lines and...
Using a Kaluza-Klein-type lift, it is shown how Killing-Yano forms with torsion can remain symmetries of a higher-dimensional geometry, subject to an algebraic condition between the Kaluza-Klein field strength and the Killing-Yano form. The lift cond...
Given the complex geometry of white matter streamlines, Autoencoders have been proposed as a dimension-reduction tool to simplify the analysis streamlines in a low-dimensional latent spaces. However, despite these recent successes, the majority of en...
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omg guys orbit placement yeeaa111...
I'm tired of seeing people say that Orbit is a new top 1 when its projected to be in the top 10 or possibly even lower. ...
We investigate the correspondence between the geometry of a smooth compact Lie group action on a manifold $\mathrm{M}$ and the intrinsic smooth structure of the orbit space $\mathrm{M}/\mathrm{G}$. While the action on $\mathrm{M}$ is classically orga...
it seems people are hyped about orbit being verified. why? is it new top 1, or some significant level in the gd history? (i am genuerly asking i do not engade with gd comunity that much)...
ask me anything i completed the first 7 clicks in orbit...