6,940 reputation
23352
bio website
location Northern Spain, Europe
age
visits member for 3 years, 10 months
seen 6 hours ago

Theoretical Physics B.Sc. + M.Sc. and soon Mathematics doctorate student. 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
reviewed Approve suggested edit on $\forall p>0$ 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
Sep
11
reviewed Approve suggested edit on experimental-mathematics tag wiki excerpt
Aug
28
reviewed Approve suggested edit on Direct evaluation of a series from Euler's identity.
Aug
27
reviewed Approve suggested edit on Is there a nice way to find this integral $\int_0^1\frac{ \arcsin x}{x} \mathrm{d}x$?
Aug
27
reviewed Approve suggested edit on Complex numbers system of equations problem with 5 variables
Aug
27
reviewed Approve suggested edit on Linearity In Linear Algebra
Aug
27
comment Why study Algebraic Geometry?
@Christos, thanks! for some reason learning English I subconsciously tend to add a "d" to Stan·ford or Har·vard... typical misspellings.
Aug
27
revised Why study Algebraic Geometry?
added 205 characters in body
Aug
24
reviewed Approve suggested edit on Compactness of $L^p$ inclusion into $L^q$
Aug
19
awarded  Guru
Aug
15
revised Meaning of holomorphic Euler characteristics?
added 151 characters in body
Aug
5
awarded  Great Answer
Jul
27
reviewed Approve suggested edit on An integral domain and its field of fractions.
Jul
27
reviewed Approve suggested edit on Polynomial $f(x)$ degree problem.
Jul
27
comment Introductory texts on manifolds
@Bananeen: thank you. Yes, I do think that one should also learn at least the basics of the sheaf approach for manifolds via ringed spaces, and Ramanan is an excellent introduction to that. This is fundamental if one wishes to understand differential geometry in a similar language to modern algebraic geometry, although this approach is usually not required or even explained in most university courses. If you like algebraic-flavored treatments (but without sheaves), don't forget the advanced and formal book by Michor -"Topics in Differential Geometry".
Jul
25
reviewed Approve suggested edit on How to find confidence interval of quotient
Jun
25
reviewed Approve suggested edit on What is the minimum value of $\csc x - \sin x$?
Jun
25
reviewed Approve suggested edit on What is my total grade average?