Algebraic and topological cycles in tropical and complex geometry
About the project
This project focuses on the connections between geometry and combinatorics, provided specifically by tropical geometry. Tropical geometry is a relatively new field with powerful applications to other areas of mathematics and beyond. Perhaps most well known are the applications to algebraic, symplectic, enumerative, and discrete geometries. Additionally there are connections to number theory, statistical models, optimisation, thermodynamics, computer science, mathematical physics and mathematical biology.
Sub-projects
- topology of real algebraic varieties
- algebraic geometry of discrete structures (matroids and combinatorial designs)
Preprints
Mohammadi, Fatemeh and Shaw, Kristin, Toric degenerations of Grassmannians from matching fields, submitted, 2018.
https://arxiv.org/abs/1809.01026
Renaudineau, Arthur and Shaw, Kristin, Bounding Betti numbers of real hypersurfaces near the tropical limit, 2018.
https://arxiv.org/abs/1805.02030
Vacancies
There will be one phd position available in the group starting fall of 2019. Stayed tuned for more information!
Upcoming Events
Einstein Workshop on Geometric and Topological Combinatorics
Freie Universität Berlin, Oct 29-31, 2018.
Tropical Geometry: New directions
Mathematisches Forschungsinstitut Oberwolfach, 28 April - 4 May 2019
Non-Archimedean Geometry and Applications
Mathematisches Forschungsinstitut Oberwolfach, 24 Feb- 2 Mar 2019
University of Oslo, Norway May 14-16, 2019
Tropical Methods in Real Algebraic Geometry
Casa Matemática Oaxaca (CMO), Mexico, Sep 08 - Sep 13, 2019
Past Events
Tropical Geometry and Moduli Spaces
ICM Satellite conference, Cabo Frio, Brazil, August 13-17, 2018
Institut de Mathématiques de Toulouse, July 4-5, 2018.
Combinatorics and Hodge Theory
Nordfjordeid, Norway, June 18-22, 2018
ASGARD Math 2018: Real algebraic geometry and tropical mathematics
University of Oslo, Norway May 2 - 4, 2018
Tropical Geometry, Amoebas, and Polytopes
Institut Mittag-Leffler, Sweden Jan 15th - April 30, 2018
Financing
This project is funded by Bergen Research Foundation.