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visits member for 2 years, 6 months
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Theoretical Physics Licenciado, starting Mathematics Ph.D. at CSU, Fall 2015. My major interest is in Algebraic and Arithmetic Geometry, specifically higher-dimensional varieties, 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, 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.

"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

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

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


Sep
11
awarded  Custodian
Sep
11
reviewed Edit suggested edit on Can general relativity be completely described as a field in a flat space?
Sep
11
revised Can general relativity be completely described as a field in a flat space?
Removing some opinionated statements.
May
4
awarded  Yearling
Mar
12
revised Intuitive meaning of the Hilbert Space formalism
added 279 characters in body
Feb
24
revised Can general relativity be completely described as a field in a flat space?
added 791 characters in body
Feb
21
awarded  Nice Answer
Sep
6
revised Can general relativity be completely described as a field in a flat space?
deleted 1766 characters in body
Sep
6
revised Can general relativity be completely described as a field in a flat space?
reorganized a paragraph and added reference link
Sep
6
comment Can general relativity be completely described as a field in a flat space?
@Anixx: regarding your first comment on constructing the underlying manifold to correspond to physical space at large scale: that is indeed what is actually done in the standard cosmological models nowadays. It is possible because of the Copernican principle at large scale: a homogeneous matter field permeates space-time so one can gauge-fix the underlying manifold to the physical space-time measured by comoving coordinates at those scales. BUT! Minkowski's flat space-time is not a solution of the field equations when there is a nonzero cosmological constant! So, the global space is never flat
Sep
6
comment Can general relativity be completely described as a field in a flat space?
@BenCrowell: the answer does not wander because the concepts at hand are more subtle and philosophically laden than many want to admit, so a long deep discussion is required. I have added a clarification about Deser's work and others and how they all actually agree and emphasize my point. It amounts to a semantical fuzziness, but an important one: what, I believe, misleads readers incorrectly are comments like those which assume equivalence between physical space-time and the mathematical underlying manifold needed to formulate a field theory. Everyone is half-right and half-wrong in this case
Sep
6
revised Can general relativity be completely described as a field in a flat space?
added 839 characters in body
Sep
6
comment Can general relativity be completely described as a field in a flat space?
Added a long clarification at the end of my answer about the work of Deser and others as mentioned in other answers which may seem to contradict mine. I hope to be of any help clarifying these issues.
Sep
6
revised Can general relativity be completely described as a field in a flat space?
Added clarification about comments and other answers which seem to conflict with this one
May
4
awarded  Yearling
Feb
8
awarded  Custodian
Feb
8
reviewed Satisfactory Are Carnot engine efficieny and Fourier heat trasmission law related?
Feb
8
reviewed Satisfactory What are the 't Hooft papers about classical models underlying QM?
Feb
8
reviewed Satisfactory Causality in a gedanken experiment on the hydrogen atom
Feb
8
reviewed Satisfactory Banach Space representations of physical systems