Sep 8 - Sep 11, 2025 at University of Warwick, UK
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The space of real numbers, although arguably a familiar space for people thinking mathematically, plays host to scary and intuition-defying objects such as the Cantor set and the Weierstrass function. O-minimal geometry provides a framework for studying sets and functions with tame topological and geometric properties, generalizing semi-algebraic and subanalytic geometry, while retaining key finiteness conditions. Over the years, o-minimality has had interactions with a wide range of areas such as diophantine geometry, Hodge theory, theoretical computer science, combinatorics, dynamical systems, physics, and machine learning, where it has been essential to go beyond just algebraic sets while at the same time having control over complexity and structure.
This conference will explore recent advances in o-minimal geometry and its interactions with other areas. Talks will cover both foundational aspects and emerging directions, highlighting new perspectives and open problems. Please register below and join us!
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Classification of types in o-minimal expansions of ordered abelian groups and real closed fields
We give a classification of 1-variable types in extensions of o-minimal expansions of ordered abelian groups and real closed fields. This is achieved by a valuation theoretic analysis of types, leading to the trichotomy: (i) immediate transcendental (ii) value transcendental (iii) residue transcendental. As application, we give necessary and sufficient conditions for a power bounded o-minimal expansion of a real closed field (in a language of arbitrary cardinality) to be $\kappa$-saturated. The conditions are in terms of the value group, residue field, and $\kappa$- bounded pseudo-Cauchy sequences of the natural valuation on the real closed field. A further application is a characterization of recursively saturated models. This provides a construction method for saturated and recursively saturated models, using fields of generalized power series. This is based on joint work with P. D'Aquino and K. Lange.
Nash Groups
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The homeomorphism type of semi-algebraic sets is elementary
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Bézout's bounds for rational and lacunary complex algebraic plane curves
I will explain which Bézout's bounds one can obtain in the complex case for rational plane curves and lacunary algebraic curves. More precisely, I will give lower and upper fewnomial bounds on the number of intersection points in a ball of the complex plane, between a rational curve $P(\CC)$ and a lacunary algebraic curve $Q=0$. These bounds depend only on the initial terms of $P$ and on the support of $Q$. This question is related to deep questions in algebraic complexity, such as the Valiant version of P vs NP. This is a joint work with Sébatien Tavenas.
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Fields with(out) Generic Derivations
We investigate the existence of generic derivations in expansions of fields. Specifically, we provide examples of field expansions that admit a generic derivation and study their model-theoretic properties. Furthermore, we show that exponential fields, in the absence of compatibility conditions between the derivation and the exponentiation, do not admit a generic derivation.
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A list of registered participants will be available closer to the conference dates.
Full schedule will be available closer to the conference dates.
The conference will be held in room B3.03 of the Zeeman building (Coventry CV4 7EZ) of the University of Warwick, UK
The nearest airport to the university is Birmingham International (BHX). To get to the University of Warwick from BHX, taxis are available, as is Uber; should take mildly upwards of 20 minutes to get to campus. Also, trains go from BHX to Coventry station. You can also fly into one of the London airports. If you fly into Heathrow, you can take a train to Watford Junction (Railair), and you can take another train from Watford Junction to Coventry station. From Coventry, several bus lines go to campus regularly, for example 11 or 12X, see the map and the timetables.
You can take long distance buses instead of trains; there is a direct one from Heathrow to Coventry.
It is a 10 minute walk from the University Interchange bus station to the Zeeman Building, which is not necessarily the closest bus station, but the easiest.
For any inquiries, please contact us at omigawd2025[hopefully at]gmail[on the dot]com.
The conference is organized by Abhiram Natarajan and the administrative staff of the Warwick Mathematics Institute, and Martin Lotz, Harry Schmidt.
Abhiram Natarajan gratefully acknowledges financial support for this event from his EPSRC Grant EP/V003542/1. Banner image made using InsMind with image taken from here.