# 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 2020. Stayed tuned for more information!

## Upcoming Events

CIRM, Marseille, April 20-24, 2020.

Facets of real algebraic geometry

CIRM, Marseille, April 27-May 1, 2020.

**ASGARD 2020**, May 13-15, 2020

Quelques aspects réels et effectifs de la géométrie algébrique - CIMPA school

Ziguinchor, Senegal June 29 - July 7, 2020

## Past Events

Tropical geometry and mirror symmetry

Matrix Institute, Creswick Dec 9-20, 2019

Lucia Geometrica

Stockholm University Dec 9-13, 2019

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.