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.
There will be one phd position available in the group starting January 2023. Stayed tuned for more information!
ASGARD annual conference, University of Oslo,
GEMS of combinatorics
Kris Shaw speaker in "Conference in enumerative, real and birational geometry", Le Croisic, France,
June 6-10, 2022
Norfjordeid Real Algebraic Geometry Summer school,
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.
University of Oslo, Norway May 2 - 4, 2018. Co-organized by Felipe Rincón, and Kris Shaw.
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.
Matrix Institute, Creswick Dec 9-20, 2019
Stockholm University Dec 9-13, 2019
Casa Matemática Oaxaca, Mexico, Sep 08 - Sep 13, 2019
Universidad Complutense de Madrid, June 17-21, 2019
Urania Loft, June 7, 2019
ZIB, Berlin June 3-7, 2019
Mathematisches Forschungsinstitut Oberwolfach, 28 April - 4 May 2019
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.
Nordfjordeid, Norway, June 18-22, 2018
Institut Mittag-Leffler, Sweden Jan 15th - April 30, 2018
This project is funded by the Trond Mohn Foundation.
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.
Lefschetz section theorems for tropical hypersurfaces. Charles Arnal, Arthur Renaudineau, and Kris Shaw. The Annales Henri Lebesgue.Vol 4, 1347-1387, 2021.
Real algebraic curves on real del Pezzo surfaces. Matilde Manzaroli. International Mathematics Research Notices. rnaa169, 2020
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.
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.
Toric degenerations of Grassmannians from matching fields. Fatemeh Mohammadi and Kristin Shaw. Algebraic Combinatorics Vol 2, Issue 6, 1109-1124, 2019.
Lefschetz (1,1) theorem in tropical geometry. Philipp Jell, Johannes Rau, Kristin Shaw, EPIGA, Volume 2, 2018.
Aksnes, Edvard, Tropical Poincaré duality spaces, 2021.
Le Texier, Cédric, Topology of real algebraic curves near the non-singular tropical limit, 2021.
Le Texier, Cédric, Hyperbolic plane curves near the non-singular tropical limit, 2021.
Rau, Johannes, Renaudineau, Arthur, and Shaw, Kris, Real phase structures on matroid fans and matroid orientations, 2021.
Kummer, Mario, Le Texier, Cédric, and Manzaroli, Matilde, Real-fibered morphisms of del Pezzo surfaces and conic bundles, 2021.
Kastner, Lars, Shaw, Kris, and Winz, Anna-Lena, Tropical compactifications via Ganter's algorithm, 2020.