# 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.