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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, 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 method of questioning her!", Heisenberg

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


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?
Jun
17
reviewed Approve suggested edit on Prove this identity…
Jun
17
reviewed Approve suggested edit on use theorrem 1.8.2 to show that T is a matrix transformation
Jun
17
reviewed Approve suggested edit on Solving the equation $a ^ b + b ^ a = 200$
Jun
17
awarded  Announcer
Jun
15
reviewed Approve suggested edit on Transformations order?
Jun
10
reviewed Approve suggested edit on Algebra - solve given inequality
Jun
3
reviewed Approve suggested edit on Math Olympiad Algebraic Question Comprising Square Roots
May
26
reviewed Approve suggested edit on Counting problem and probability
May
20
reviewed Approve suggested edit on Product of two matrices with simple spectrum
May
18
reviewed Approve suggested edit on application of c*algebras
May
14
awarded  Good Answer
May
5
reviewed Approve suggested edit on What will the integration be ?
May
3
reviewed Approve suggested edit on 2 questions about counting and permutation
Apr
28
reviewed Approve suggested edit on Solving second order nonlinear ODE