VL: Discrete Geometry III: Tropical Geometry (Summer 2024)

This is a BMS Advanced Course, which will thus be given in English. It is accompanied by a seminar, for those who are interested.

VL: Tuesday 10-12 MA 549
Thursday 10-12 MA 650

Contents

We will give an introduction to tropical geometry, assuming a solid background in polyhedral geometry (as taught in Discrete Geometry I+II). Knowing bits and pieces about topology and algebraic geometry does not hurt. Two topics will be discussed in greater detail: plane and abstract tropical curves, tropical linear spaces and their connection to matroid theory. My goal is to make the connection to research topics of recent interest. In particular, work of Chan, Galatius and Payne on the topology of moduli spaces of tropical curves, and of Adiprasito, Huh and Katz on combinatorial Hodge theory.

References

  1. Adiprasito, Huh and Katz: Hodge theory for combinatorial geometries, Ann. Math. 188 (2018).
  2. Brodsky, Morrison, Joswig and Sturmfels: Moduli of tropical plane curves. Res. Math. Sci. 2.4 (2015).
  3. Chan, Gelatius and Payne: Tropical curves, graph complexes, and top weight cohomology of Mg, J. Amer. Math. Soc. 34 (2021).
  4. Joswig: Essentials of tropical combinatorics. AMS 2021.
  5. Maclagan, Sturmfels: Introduction to tropical geometry. AMS 2015.
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Last modified: Tue Apr 30 08:06:08 UTC 2024 by joswig