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1900s–1930s: Branch Curves and the Italian School of Algebraic Geometry
In contrast to the separate beginnings during the nineteenth century presented in the previous chapter, the twentieth century saw the consolidation...
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Algebraic Dynamical Systems in Machine Learning
We introduce an algebraic analogue of dynamical systems, based on term rewriting. We show that a recursive function applied to the output of an...
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Information geometry of dynamics on graphs and hypergraphs
We introduce a new information-geometric structure associated with the dynamics on discrete objects such as graphs and hypergraphs. The presented...
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Algebra, Geometry and Topology of ERK Kinetics
The MEK/ERK signalling pathway is involved in cell division, cell specialisation, survival and cell death (Shaul and Seger in Biochim Biophys Acta...
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Counting intrinsic Diophantine approximations in simple algebraic groups
We establish an explicit asymptotic formula for the number of rational solutions of intrinsic Diophantine inequalities on simply-connected simple...
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Algebraic hyperbolicity of very general surfaces
Recently, Haase and Ilten initiated the study of classifying algebraically hyperbolic surfaces in toric threefolds. We complete this classification...
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FAITHFUL ACTIONS OF AUTOMORPHISM GROUPS OF FREE GROUPS ON ALGEBRAIC VARIETIES
Considering a certain construction of algebraic varieties X endowed with an algebraic action of the group Aut( F n ), n < ∞, we obtain a criterion for...
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Toric Degenerations in Symplectic Geometry
Toric degeneration in algebraic geometry is a process of degenerating a given projective variety into a toric one. Then one can obtain information...
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Algebraic capacities
We study invariants coming from certain optimisation problems for nef divisors on surfaces. These optimisation problems arise in work of the author...
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Local positivity and effective Diophantine approximation
In this paper we present a new approach to prove effective results in Diophantine approximation. This approach involves measures of local positivity...
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Detecting Affine Equivalences Between Implicit Planar Algebraic Curves
We present a complete algorithm for computing the affine equivalences between two implicit planar algebraic curves. We provide evidence of the...
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Towards Massively Parallel Computations in Algebraic Geometry
Introducing parallelism and exploring its use is still a fundamental challenge for the computer algebra community. In high-performance numerical...
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Grete Hermann and Effective Methods in Geometry
Sometimes in the history of science we can find scientists who were not acknowledged at their time and only later the scientific community has...
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Enumerative Geometry, Before and After String Theory
Throughout its long history, algebraic geometry has been enriched by the influences of invariant theory, abstract algebra, number theory, topology,...
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Algebraic hyperbolicity for surfaces in smooth projective toric threefolds with Picard rank 2 and 3
Algebraic hyperbolicity serves as a bridge between differential geometry and algebraic geometry. Generally, it is difficult to show that a given...
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Visual Representations of Euclidean Geometry: Diagrammatic Reasoning in Oliver Byrne’s Work
Around the half of the nineteenth century the Irish mathematician and civil engineer Oliver Byrne published a peculiar version of Euclid’s Elements...
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Physical Geometry by Plane-Based Geometric Algebra
Plane-based geometric algebra (PGA) offers a way to represent Euclidean motions that is directly built on the primitives of affine geometry, and thus...
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On the Geometry of the Anti-canonical Bundle of the Bott-Samelson-Demazure-Hansen Varieties
Let G be a semi-simple simply connected algebraic group over the field ℂ of complex numbers. Let T be a maximal torus of G , and let W be the Weyl...
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A characterization of the algebraic degree in semidefinite programming
In this article, we show that the algebraic degree in semidefinite programming can be expressed in terms of the coefficient of a certain monomial in...