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.
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.
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
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
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