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Cohen and Glashow introduced the notion of very special relativity as viable space-time symmetry of elementary particle physics. As a natural generalization of their idea, we study the subgroup of the conformal group, dubbed very special…
Let G be a reductive groups over an algebraically closed field k. Let P^{(i)} be associated parabolic subgroups, and X^{(i)}:=T^*G/P^i. The bounded derived categories of coherent sheaves on X^{(i)} are equivalent, but there is no canonical…
Cortical surface reconstruction (CSR) from MRI is key to investigating brain structure and function. While recent deep learning approaches have significantly improved the speed of CSR, a substantial amount of runtime is still needed to map…
This article investigates the complex symplectic geometry of the deformation space of complex projective structures on a closed oriented surface of genus at least 2. The cotangent symplectic structure given by the Schwarzian parametrization…
This paper reviews predictive coding, from theoretical neuroscience, and variational autoencoders, from machine learning, identifying the common origin and mathematical framework underlying both areas. As each area is prominent within its…
In visual cognition, illusions help elucidate certain intriguing latent perceptual functions of the human vision system, and their proper mathematical modeling and computational simulation are therefore deeply beneficial to both biological…
Functional magnetic resonance imaging (fMRI) reveals complex brain functional networks with hierarchical topologies crucial for cognitive processing. Standard Euclidean Graph Neural Networks (GNNs) often struggle to represent these…
We study smooth projective varieties with small dual variety using methods from symplectic topology. We prove the affine parts of such varieties are subcritical, and that the hyperplane class is invertible in their quantum cohomology. We…
In this paper we find a unique normal form for the symplectic matrix representation of the conjugacy class of a prime order element of the mapping-class group. We find a set of generators for the fundamental group of a surface with a…
We classify the group of birational automorphisms of Hilbert schemes of points on algebraic K3 surfaces of Picard rank one. We study whether these automorphisms are symplectic or non-symplectic and if there exists a hyperk\"ahler birational…
How does the neocortex learn and develop the foundations of all our high-level cognitive abilities? We present a comprehensive framework spanning biological, computational, and cognitive levels, with a clear theoretical continuity between…
We study the neural field equations introduced by Chossat and Faugeras in their article to model the representation and the processing of image edges and textures in the hypercolumns of the cortical area V1. The key entity, the structure…
We introduce Correlational Image Modeling (CIM), a novel and surprisingly effective approach to self-supervised visual pre-training. Our CIM performs a simple pretext task: we randomly crop image regions (exemplars) from an input image…
Using the method of C. V\"or\"os, we establish results in hyperbolic plane geometry, related to triangles and circles. We present a model independent construction for Malfatti's problem and several trigonometric formulas for triangles.
We propose a normative model for spatial representation in the hippocampal formation that combines optimality principles, such as maximizing coding range and spatial information per neuron, with an algebraic framework for computing in…
This article aims to review a selection of central topics and examples in logarithmic conformal field theory. It begins with a pure Virasoro example, critical percolation, then continues with a detailed exposition of symplectic fermions,…
We treat the problem of defining, and characterising in a practical way, an appropriate class of distinguished curves for Poincar\'e-Einstein manifolds, and other conformally singular geometries. These "generalised geodesics" agree with…
As Vision Transformers (ViTs) are increasingly adopted in sensitive vision applications, there is a growing demand for improved interpretability. This has led to efforts to forward-align these models with carefully annotated abstract,…
We present a formulation of the coupling of vector multiplets to N=2 supergravity which is symplectic covariant (and thus is not based on a prepotential) and uses superconformal tensor calculus. We do not start from an action, but from the…