Pure mathematics is, in its way, the poetry of logical ideas.
Seminars and papers:
Bitcoin Transaction Malleability
Bitcoin Transaction Malleability
A seminar talk about Bitcoin's Transaction Malleability, an example of a security issue in the Bitcoin global cryptocurrency system.
cryptocurrency
bitcoin
malleability-attack
Mt.Gox incident
The Banach-Tarski paradox
The Banach-Tarski paradox
One of the seminar talks I presented at University of Tours, about the Banach-Tarsky Paradox, one of the most famous and disturbing results in mathematics.
Pathology
Non-measurable_sets
Axiom_of_choice
Banach_Tarski
Wild automorphisms of the complex field
Wild automorphisms of the complex field
A fun little presentation I made during my bachelor degree, exploring the dark parts of the group of automorphisms of the complex field.
Pathology
Wild_automorphisms
Zorn's_Lemma
complex_automorphisms
Hilbert's 5th problem
Hilbert's 5th problem
Probably one of the first short talks I gave during my Differential Geometry class. This one is about characterizing linear Lie groups by Von Neumann's theorem (actually, in the case of closed linear topological groups).
Lie_groups
Hilbert_problem
differentiable_manifolds
The Octahedral group
The Octahedral group
Little presentation about the study of the isometry group of the Octahedron.
Octahedral_group
isometry_group
Octahedron
Academic papers:
Master thesis:
On the generating function and algebraicity of Eisenstein-Kronecker numbers
On the generating function and algebraicity of Eisenstein-Kronecker numbers
I had the chance in my Master thesis, to study the algebraic properties of the Eisenstein-Kronecker numbers, an elliptic analogue of the generalised Bernoulli numbers, in the case of an imaginary quadratic field. They are, in this sense, related to the special values of Hecke L-series on imaginary quadratic fields. The idea was to follow Bannai and Kobayashi’s paper [BK+10] and show that the two-variable generating function of these numbers (which is the elliptic analogue of the cotangent function for the Bernoulli numbers) belongs to a canonical class of theta functions, called the reduced theta functions.
elliptic functions
Mumford's algebraic Theta functions
Hecke L-functions
Hecke L-series
Imaginary quadratic fields