Paulo Soto - Personal Website

About me

I am an Attaché Temporaire d'Enseignement et Recherche at the UFR Mathématiques of Université Paris Cité. I obtained my PhD at Université Paris Cité and the Institut de Mathématiques de Jussieu-Paris Rive Gauche under the supervision of Sylvy Anscombe. My main interests lie in the intersection between Model Theory and Algebra, namely in the Model Theory of Valued Fields and their classification theoretical properties (eg. NIP, NTP₂ and their variants).

During my PhD I was supported by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 945332.

**Applying for postdocs to begin after september 2027**

You can find me at paulo(dot)soto(at)imj-prg(dot)fr.

Here's a CV (Last updated: July 2026).

Preprints

Paulo Andrés Soto Moreno. On some NIP Fragments of Fields, Manuscript, 2026. To be submitted.

Abstract: In this note we study sets of NIP formulas in some theories of fields and valued fields, with a special focus on the sets of quantifier-free and existential formulas. First, we give a new proof of the fact that Separably Closed Valued Fields of any characteristic and any imperfection degree are NIP, and use this result to fill some gaps of a proof of the so-called NIP Transfer Theorem for henselian valued fields of equal characteristic. Second, we prove a variant of a theorem of Johnson: every positive characteristic valued field whose existential formulas are NIP is henselian. Finally, we set the ground for the finer question of transfer of NIP formulas of valued fields with bounded quantifier rank. Namely, we prove that for any henselian equicharacteristic valued field, any formula of quantifier rank at most $n\geq 1$ is NIP if and only if the same is true for the residue field and the value group, provided that the valued field is separably defectless Kaplansky and conditional on a multi-variable generalization of a well known statement about indiscernible sequences of singletons in ac-valued fields.

Paulo Andrés Soto Moreno. Fields of dp-Rank 2 and their W₂-Topologies: The Characteristic 2 Case, Manuscript, 2025. Submitted.

Abstract: In this note we reproduce Johnson's analysis of W₂-topologies on fields of characteristic 2, which was originally stated for fields of characteristic different than 2. Following his framework, we prove that the canonical topology of an unstable field of characteristic 2 and dp-rank at most 2 is a V-topology. Additionally, we show that any W₂-topology on a field of characteristic 2 is either induced by a the intersection of two valuation rings or it is induced by dense pre-diffeo-valuation data, completing the picture for all positive characteristic fields.

Paulo Andrés Soto Moreno. Relative Quantifier Elimination for Separable-Algebraically Maximal Kaplansky Fields, Manuscript, 2025. Submitted.

Abstract: Let C be the class of separable-algebraically maximal equi-characteristic Kaplansky fields of a given imperfection degree, admitting an angular component map. We prove that the common theory of the class C resplendently eliminates quantifiers down to the residue field and the value group, in a three sorted language of valued fields with a symbol for an angular component map and symbols for the parameterized lambda-functions. As a consequence, we obtain that equi-characteristic NIP and NIPn henselian fields with an angular component map resplendently eliminate field quantifiers in this language. We also prove that this elimination reduces existential formulas to existential formulas without quantifiers from the home sort. Finally, we draw several conclusions following the AKE philosophy for elements of the class C, including the usual AKE principles for ≡, ≡∃, ⪯, ⪯∃ and for relative decidability.

Work in Progress

Paulo Andrés Soto Moreno. Indiscernible sequences in ac-valued fields, 2026.

Abstract: In this work, we study a multivariable generalization of a well-known statement about indiscernible sequences of singletons in valued fields with an angular component, which makes it possible to extract indiscernible sequences in the residue field and in the value group from an indiscernible sequence in the valued field, evaluated in a given polynomial. We use this result to obtain a finer transfer of sets of NIP formulas from the residue field and the value group to the valued field, in the case of separably algebraically maximal Kaplansky valued fields. During this research, we will use tools from valuation theory and ramification theory, as well as tools from tropical geometry, which make it possible to describe the interaction of the variety defined by the given polynomial with the sets of valuations and angular components of its rational points.

Teaching Experience

In French, at Université Paris Cité, Paris, France. I taught the following courses:

Spring 2027: Formes bilinéaires et suites de fonctions, L2 MATH, Travaux Dirigés.
Fall 2026: Logique et Suites, L1 MATH, Cours Magistral et Travaux Dirigés.
Fall 2026: Tutorat de Mathématiques.
Spring 2026: Analyse et Algèbre Linéaire, L2 CUPGE, Tavaux Dirigés.
Fall 2025: Logique et Suites, L1 MATH, Cours Magistral et Travaux Dirigés.
Fall 2025: Algèbre et Analyse 3, L2 MIASHS, Travaux Dirigés.
Spring 2025: Analyse et Algèbre Linéaire, Travaux Dirigés.
Spring 2025: Outils Bureautiques et Informatiques, Travaux Pratiques.
Fall 2023: Analyse et Algèbre Linéaire, Travaux Dirigés.
Fall 2023: Tutorat de Mathématiques.

In Spanish, at Universidad de los Andes, Bogotá D.C., Colombia. I was a Teaching Assistant of the following courses:

Spring 2021: Vector Calculus.
Fall 2020: Vector Calculus.
Spring 2020: Vector Calculus
Fall 2019: Differential Calculus, Precalculus.
Spring 2019: Topology.
Fall 2018: Mathematical Logic, Linear Algebra.
Spring 2018: Differential Calculus.
Spring 2017: Mathematical Logic.
Fall 2016: Differential Calculus.

I was also a Social Work Practice Educator at Universidad de los Andes, Bogotá D.C., during the Fall of 2017. I was in charge of organizing and teaching high-school contents to a group of students of Bogotá's school network in order to enhance their academic aptitudes and increase their chances to pursue a university degree.

Conferences

Here are some conferences I have attended:

Arithmetic of Fields: Model Theory, Valuations and Geometry - April 2026 - CIRM - Marseille (France)
Logique à Paris - February 2026 - Université Paris Cité - Paris (France). I was a co-organizer of this year's edition.
Model Theoretic Methods in Non-Archimedean Geometry - January 2025 - Münster (Germany)
Model Theory of Valued Fields and Applications - February 2024 - Lille (France)
GEOMOD Final Conference - November 2023 - Freibourg (Germany)
Model Theory of Valued Fields - May 2023 - CIRM - Marseille (France)

Paulo Andrés Soto Moreno

About me

Preprints

Work in Progress

Education

Teaching Experience

Selected Talks

Conferences