Javier Álvarezless info
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Theoretical Physics Lic. and now Mathematics postgraduate student. My major interest is in Algebraic and Arithmetic Geometry, specifically higher-dimensional varieties, rational points and L-functions, motives and any kind of enumerative results from intersection theory. I switched from physics after finding out how Riemannian, Kählerian and Symplectic Geometry are interrelated through, e.g., mirror symmetry and quantum cohomology. Topology is wonderful when it 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, making fascinating the subject of Operator Algebras and its Functional Analysis. On the Physics side I like applications of gauge theory to mathematics, Quantum Gravity and Foundations of Quantum Mechanics, especially its relational and topoi formulations. My philosophy is a kind of Structural Realism (or Model-dependent Realism) 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 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. I fully endorse Carlo Rovelli's philosophy of science, emphasizing the need of conceptual understanding to advance like the great scientists of the past.
"Science is not about certainty, it's about finding the most reliable way of thinking at the present level of knowledge", Rovelli
"It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what can be said about Nature", Bohr
"Whereof one cannot speak, thereof one must remain silent", Wittgenstein