These have been my research and academic interests in the years.
Model theory
(present/future)
I have recently become interested in model theory.
This is the field that studies the combinatorial properties
of (first-order) definability.
I am writing a
textbook
on the subject.
I am also beginning with the supervision of a PhD project on applications of model theory
to fields such as extremal/probabilistic combinatorics, additive combinatorics, pseudorandomness, etc.
(recent results hint at deep connections).
Computability and randomness
(past)
Can we explain randomness -a very elusive notion- with (un)computability?
Kolmogorov made the first attempt to answer this question.
Building on it, Schnorr and Martin-Löf had the first important results.
I made a
seminal contribution
to the field (unpublished but highly cited because of two questions:
the first answered by
A.Kucera and S.A.Terwijn,
the second by
A.Nies).
I have also written a
paper
in collaboration with S.A.Terwijn.
Provability Logic
(past)
This field studies the algebraic properties of the provability predicate
(i.e. of Gödel's formalized provability formula). I
contributed
to the field with a couple of papers during my PhD in Amsterdam.
Complexity theory and formal systems
(past)
In particular, Bounded Arithmetic. My most
relevant contribution
to the field has been to establish a relation between
the finite axiomatizability of Bounded Arithmetic and
the collapse of the Polynomial Time Hierarchy. Cfr.
Stephen Cook's review
of this and related results.
This work was also part of my (heterogenous) PhD thesis.
Teaching
(present/future)
I enjoy teaching probability and statistics to molecular biologists.
I am coordinating a project that applies
Jupyter Notebooks
in teaching/presentation, laboratory classes,
homework assignments, exams, etc.
In this way the students
-though attending a standard introductory course of statistics-
will have the opportunity to familiarize with a cutting edge technology
that has applications ranging from
data exploration
to publication of
reproducible research.