This section contains some of the (mathematical) things I wrote, including my Bachelor's thesis. Warning: there may be many typos so one should be careful!
Rough notes for a talk for the Friday Fish on the geometric structure of wavefront sets of an oscillatory integral. In addition to this, we discuss the pullback and pushfoward operators and see that they define Fourier integral operators. We finish by discussing how some operations (namely pullback of distributions, product of distributions and composition of operators) can be defined for distributions, as long as their wavefronts are disjoint.
The final project in the Symplectic Geometry course I took in my Master's course. It concerns the study of the group of Hamiltonian symplectormorphisms of a symplectic manifold using the flux homomorphism.
The final project (in Portuguese) in the Harmonic Analysis course I took in my Master's course. It concerns lacunary Fourier series, which are Fourier series such that its consecutive frequencies have "big gaps" between them, in some more precise sense.
Such Fourier series were used by W. Rudin to study the following general problem: given some arithmetic property P, what is an estimate for the biggest number of elements in an arithmetic progression of size N which satisfy property P?
The final project (in Portuguese) in the Homotopy Theory course I took in my Master's course. It is a brief introduction to topological complex K-theory. The second part concerns applications of topological K-theory, in particular to proving the Hopf invariant 1 problem and the non-existence of an almost complex structure on the 4-sphere.
My Bachelor's thesis on Milnor's construction of an exotic 7-sphere, that is, a manifold homeomorphic to the usual 7-sphere but not diffeomorphic to it. It also contains an introduction to the theory of fibre bundles and characteristic classes. This thesis was done under the supervision of Gustavo Granja.