Javier Álvarez

Fort Collins, CO

Theoretical Physics Licenciado, now attending Math Ph.D. at CSU.

"Science is not about certainty, it's about finding the most reliable way of thinking at the present level of knowledge", C. 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", N. Bohr.

"What we observe is not Nature herself, but Nature exposed to our methods of questioning her!", W. Heisenberg.

"Whereof one cannot speak, thereof one must be silent", Wittgenstein.

My major interests are in Algebraic and Arithmetic Geometry, specifically higher-dim. varieties, L-functions, algebraic K-theory, motives and enumerative intersection theory in moduli of curves. I switched from physics after finding out how Riemann, Kähler and Symplectic Geometry are related 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 motives bridge mysterious links between arithmetics and QFT via Feynman path integrals, making fascinating the subject of Operator Algebras and its Functional Analysis. On the Physics side I like Gauge Theory, Quantum Gravity and Quantum Mechanics, especially its relational and topoi formulations. I fully endorse Carlo Rovelli's stance about Science, me being a Second Philosopher approaching Ontic Structural Realism, whereby Mathematics is epistemologically a Natural Science: the universal study of patterns (above all meta-patterns!). In response to Wigner, its success is tautological, as any phenomena in the Cosmos can only be understood from necessarily information-theoretic models of correlation structures from 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. Physics and Mathematics, despite using different methods to acquire knowledge, are just different 'regions' to grasp from one and the same unified, structured and cognizable empirical reality. Transcendental metaphysics is a void byproduct of language misusage due to operationally unjustified concept extrapolations.

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