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 (polytopes, graphs, matroids)
Preprints
Arnal, Charles, Renaudineau, Arthur, and Shaw, Kristin, Lefschetz section theorems for tropical geometry, 2019.
https://arxiv.org/abs/1907.06420
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
Stockholm University Dec 9-13, 2019
Tropical geometry and mirror symmetry
Matrix Institute, Creswick Dec 9-20, 2019
CIRM, Marseille, April 20-24, 2019
Facets of real algebraic geometry
CIRM, Marseille, April 27-May1, 2019.
ASGARD 2020, May
Past Events
Tropical methods in real algebraic geometry
Casa Matemática Oaxaca, Mexico, Sep 08 - Sep 13, 2019
Universidad Complutense de Madrid, June 17-21, 2019
Berlin Mathematical School Friday Colloquium
Urania Loft, June 7, 2019
Network games, Tropical Geometry and Quantum Computing
ZIB, Berlin June 3-7, 2019
University of Oslo, Norway May 14-16, 2019
Tropical Geometry: New directions
Mathematisches Forschungsinstitut Oberwolfach, 28 April - 4 May 2019
Einstein Workshop on Geometric and Topological Combinatorics
Freie Universität Berlin, Oct 29-31, 2018.
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 the Trond Mohn Foundation.