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Foundations and applications of tropical moduli theory

Objective

Tropical geometry is the geometry of the combinatorial objects associated to degenerations and compactifications of algebraic (or analytic) varieties. As in algebraic geometry, the tropical geometry of moduli spaces is one of the richest and most fundamental parts of this field, with many of the features of tropical geometry only being visible through the prism of moduli spaces.

The experienced researcher proposes to extend the foundations of tropical moduli theory, building on his prior work on tropical moduli stacks, and to explore new applications of these combinatorial techniques to classical problem in arithmetic and algebraic geometry.

During the fellowship the experienced researcher will focus on the
following three types of moduli spaces:

- The universal Picard variety, with applications to Brill-Noether theory (universally over the moduli space of curves), as well as to theta-characteristics, spin curves, and Prym varieties.

- Moduli of (higher) differentials, with applications to Eliashberg's problem on the compactification of the double ramification locus and the compactification of strata of abelian and quadratic differentials.

- Moduli of G-admissible covers with the goal of developing a tropical approach to the regular inverse Galois problem.

Fields of science (EuroSciVoc)

Keywords

Programme(s)

Topic(s)

Funding Scheme

MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)

See all projects funded under this funding scheme

Call for proposal

(opens in new window) H2020-MSCA-IF-2017

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Coordinator

UNIVERSITY OF WARWICK
Net EU contribution
€ 195 454,80
Address
KIRBY CORNER ROAD UNIVERSITY HOUSE
CV4 8UW COVENTRY
United Kingdom
Region
West Midlands (England) West Midlands Coventry
Activity type
Higher or Secondary Education Establishments
Links
Total cost
€ 195 454,80