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Algebraic and topological cycles in tropical and complex geometry

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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.

Vacancies

There will be one phd position available in the group starting January 2023. Stayed tuned for more information!

Upcoming Events 

Organized

ASGARD annual conference, University of Oslo,

May 2022

GEMS of combinatorics

Participation

Kris Shaw speaker in "Conference in enumerative, real and birational geometry", Le Croisic, France,

June 6-10, 2022

Norfjordeid Real Algebraic Geometry Summer school,

(projected) 2022

Past Events

Organized

GEMS of combinatorics (Gender Equity in the Mathematical Study of Combinatorics) first meeting, September 2-3, 2021, ZOOM. Co-organized by Kris Shaw.

ASGARD Math 2019

University of Oslo, Norway May 14-16, 2019. Organized by Corey Harris, Felipe Rincón, Kris Shaw.

ASGARD Math 2018: Real algebraic geometry and tropical mathematics

University of Oslo, Norway May 2 - 4, 2018. Co-organized by Felipe Rincón, and Kris Shaw.

Participation

BIRS Oaxaca digital workshop "Real polynomials : counting and stability", October 2021. Cédric Le Texier speaker.

ICERM workshop "Algebraic Geometry and Polyhedra, April 2021. Kris Shaw speaker.

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

MEGA Madrid

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

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

Tropical Geometry in Europe

Institut de Mathématiques de Toulouse, July 4-5, 2018.

Combinatorics and Hodge Theory

Nordfjordeid, Norway, June 18-22, 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.

 

Selected publications

Accepted papers

Bounding the Betti numbers of real patchworked hypersurfaces by Hodge numbers. Arthur Renaudineau and Kris Shaw. Accepted for publication in Annales de L'École Normale Supérieure.

https://arxiv.org/abs/1805.02030

Lefschetz section theorems for tropical hypersurfaces. Charles Arnal, Arthur Renaudineau, and Kris Shaw. The Annales Henri Lebesgue.Vol 4, 1347-1387, 2021.

https://doi.org/10.5802/ahl.104

Real algebraic curves on real del Pezzo surfaces. Matilde Manzaroli. International Mathematics Research Notices. rnaa169, 2020

https://doi.org/10.1093/imrn/rnaa169

Real algebraic curves of bidegree (5,5) on the quadric ellipsoid. Matilde Manzaroli. Algebra I Analiz, 32-2, St. Petersburg Mathematical Journal, 2020.

Segra class computations and practical application. Martin Helmer and Corey Harris. Mathematics of computation Volume 89, Number 321, 2020.

https://doi.org/10.1090/mcom/3448

Chern-Schwartz-MacPherson cycles of matroids. Lucia Lopéz de Medrano, Felipe Rincon, Kristin Shaw. Proc. Of the London Math. Soc. VOl 120, Issue 1, 1-27, 2019.

https://doi.org/10.1112/plms.12278

Toric degenerations of Grassmannians from matching fields. Fatemeh Mohammadi and Kristin Shaw. Algebraic Combinatorics Vol 2, Issue 6, 1109-1124, 2019.

https://doi.org/10.5802/alco.77

Lefschetz (1,1) theorem in tropical geometry. Philipp Jell, Johannes Rau, Kristin Shaw, EPIGA, Volume 2, 2018.

https://epiga.episciences.org/4981

Preprints

Aksnes, Edvard, Tropical Poincaré duality spaces, 2021.

https://arxiv.org/abs/2112.03680

Le Texier, Cédric, Topology of real algebraic curves near the non-singular tropical limit, 2021.

https://arxiv.org/abs/2111.08607

Le Texier, Cédric, Hyperbolic plane curves near the non-singular tropical limit, 2021.

https://arxiv.org/abs/2109.14961

Rau, Johannes, Renaudineau, Arthur, and Shaw, Kris, Real phase structures on matroid fans and matroid orientations, 2021.
https://arxiv.org/abs/2106.08728

Kummer, Mario, Le Texier, Cédric, and Manzaroli, Matilde, Real-fibered morphisms of del Pezzo surfaces and conic bundles, 2021.

https://arxiv.org/abs/2101.08703

Kastner, Lars, Shaw, Kris, and Winz, Anna-Lena, Tropical compactifications via Ganter's algorithm, 2020.

https://arxiv.org/abs/2012.12161

Tags: Mathematics, Algebra and algebraic geometry
Published Mar. 2, 2018 1:17 PM - Last modified Mar. 4, 2022 11:34 AM

Participants

Detailed list of participants