Research

Research Interests

My research interests are Mathematical Logic and its connections with Combinatorics and Ramsey Theory. In particular, the

• Partition regularity of polynomial equations.
• Nonstandard models of arithmetics and their applications to Ramsey Theory.
• Čech–Stone compactification of semigroups and its algebraic and combinatorial properties.

Publications

1. P. H. Arruda and L. Luperi Baglini, Note on Rado Functionals, Australasian Journal of Combinatorics (2024), to appear.
2. P. H. Arruda and L. Luperi Baglini, A limiting result for the Ramsey theory of functional equations, Fundamenta Mathematicae 264 (2024), 55-68. DOI: 10.4064/fm230621-5-10.
3. L. Luperi Baglini and P. H. Arruda, Rado equations solved by linear combinations of idempotent ultrafilters, Topology and its Applications 305 (2022), 107897. DOI: 10.1016/j.topol.2021.107897.

Presentations

1. A Limiting Result for the Partition Regularity of Functional Equations, Logic Seminar of the University of Pisa, Pisa, Italy, 2023.
2. Partition Regularity of Affine Plane Curves, UltraMath: Ultrafilters and Ultraproducts Across Mathematics, and Related Topics, Pisa, Italy, 2022