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The main focus of this paper is on models of quartic surfaces, especially so-called complex surfaces. These are special fourth-degree surfaces that Julius Plucker introduced in the 1860s for visualizing the local structure of a quadratic line complex. Pluckers complex surfaces turned out to be closely related to Kummer surfaces and both of these types of quartics are examples of caustic surfaces, which arise in geometrical optics. Indeed, Kummer surfaces represent a natural generalization of the wave surface, first introduced by Augustin Fresnel to explain double refraction in biaxial crystals.
David Mumford made groundbreaking contributions in many fields, including the pure mathematics of algebraic geometry and the applied mathematics of machine learning and artificial intelligence. His work in both fields influenced my career at several key moments.
Scientific research is and was at all times a transnational (global) activity. In this respect, it crosses several borders: national, cultural, and ideological. Even in times when physical borders separated the scientific community, scientists kept t
Transformer architectures show significant promise for natural language processing. Given that a single pretrained model can be fine-tuned to perform well on many different tasks, these networks appear to extract generally useful linguistic features.
We present some episodes from the history of interactions between geometry and physics over the past century.
Eta Carinae (Eta Car) is one of the most massive binary stars in the Milky Way. It became the second-brightest star in the sky during its mid-19th century Great Eruption, but then faded from view (with only naked-eye estimates of brightness). Its eru