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location Northern Spain, Europe
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visits member for 4 years
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Theoretical Physics Licenciado to start Pure Mathematics Ph.D. at CSU, Fall 2015.

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 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 gauge theory applied to mathematics, Quantum Gravity and Foundations of Quantum Mechanics, especially its relational and topoi formulations. My philosophy is in-between Constructive Empiricism and 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 the 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. 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 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


11h
revised String Theory: What to do?
added 332 characters in body
11h
comment String Theory: What to do?
@Did the link to Woit's blog has been added to the first paragraph of my answer, as you suggested and we discussed. I had been uninterested in the "string theory" topic for long, but recently I have found Woit's blog as a very useful reference to keep updated.
11h
revised String Theory: What to do?
Included Woit's blog reference as suggested by some commentator
Dec
8
awarded  Caucus
Dec
7
reviewed Approve Finding the number of Spanning Trees of a Graph $G$
Dec
7
reviewed Approve When is the quotient ring of a multivariable polynomial ring over a field an integral domain?
Dec
4
reviewed Approve Proving and identity with the normalized sine function
Dec
4
reviewed Approve What is an example of a lower semicontinuous function that is not continuous?
Dec
1
awarded  Necromancer
Nov
25
awarded  Yearling
Nov
22
awarded  Popular Question
Nov
15
reviewed Approve Finding the inverse function.
Nov
15
comment Why study Algebraic Geometry?
Dear @GeorgesElencwajg, thanks a lot for all your support: sometimes small nice gestures can help big transcendental changes. I am looking forward to doing algebraic geometry "officially" at last, and hoping to do research in the coming years!
Nov
15
comment Why study Algebraic Geometry?
@GeorgesElencwajg: Dear Georges, I have sent you a thanking personal email to your university address, I hope you can receive it and read it.
Nov
15
comment Why study Algebraic Geometry?
@Marek: hope you get your chance to study abroad and keep on with your math career, I just wanted to tell you that I have just been admitted in a Ph.D. program in the USA; so don't surrender and struggle hard to achieve your dreams!
Nov
13
reviewed Approve How to find the area inside $x^2+y^2+\sin(4x)+\sin(4y)=4$ using Green's Theorem
Oct
23
reviewed Approve Evaluating Limit - $(1-\cos(x^2))/(x^3\sin(x))$
Sep
11
reviewed Approve $\forall p>0$ we get $\displaystyle \lim_{n\to \infty} n^{a_{p}}\sum _{i=0}^{n}|B_{\frac{i+1}{n}}-B_{\frac{i}{n}}|^{p}=c_{p}$
Sep
11
revised String Theory: What to do?
Improving for less opinionated statements
Sep
11
awarded  Nice Answer