Javier Álvarezless info
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Theoretical Physicist and now Mathematics graduate student. My main interest is on Algebraic Geometry, especially in higher-dimensional varieties, motives and any kind of enumerative problems of intersection theory; but I am also very interested in how Riemannian, Kählerian and Symplectic Geometry are interrelated through, e.g., mirror symmetry or quantum cohomology. Topology is wonderful when appears in the form of majestic theorems like the Atiyah-Singer index. Number theory, disguised as Diophantine and Arakelov Geometries, is fascinating too: from the Weil conjectures and the modularity theorem beyond Fermat-Wiles, to the arithmetic Grothendieck-Riemann-Roch; now intriguing correlations between prime numbers and knots are emerging in the new field of Arithmetic Topology, perhaps closely related to Anabelian Geometry. Noncommutative Geometry along with mixed motives bridge mysterious links between arithmetics and perturbative quantum field theory via Feynman path integrals and motivic integration. On the Physics side I like everything about applications of gauge theory in mathematics, (non-stringy) Quantum Gravity and Foundations of Quantum Mechanics, especially its relational and categorical/topoi formulations. My philosophy is a kind of Ontic Structural Empiricism whereby Mathematics is epistemologically a Natural Science: the universal study of patterns (above all meta-patterns!). In response to Wigner, its success is evident, as any phenomena in the Cosmos can only be understood from necessarily information-theoretic models of their net of correlations of empirical perceptions. Thus, ontologically, nothing can be said about the 'final nature' of the world except the structurality of what can be represented from within itself, hence any TOE discoverable will be purely mathematical. Physics and mathematics, despite using different methods to acquire certainty and knowledge, are just different manifestations of one and the same unified, structured and cognizable empirical reality. Transcendental metaphysics is a void byproduct of language misusage due to ill-defined concept extrapolations.
"Whereof one cannot speak, thereof one must remain silent" - Wittgenstein
Check out my Listmanias about Geometry at Amazon.