**Tropical Geometry**

**VL: 326.133**

**Summer semester 2021**

**DI. Dr. Sebastian Falkensteiner**

Time and location: |
Thu 15:30 – 17:00 (two-week), | S3 047 (or via Zoom) |

First meeting: |
11 March |

__Lecture:__ A theoretical introduction into the area of Tropical Geometry will be presented. Tropical Geometry can be understand as a piecewise linear version of Algebraic Geometry. The applications reach to well-known problems in Algebra, Geometry, Combinatorics and Differential Algebra.

Video records will be of about 1 hour length and should be watched in advance to the corresponding meeting. The questions related to the content will be discussed in the meeting. For a (positive) grade these questions have to be worked out and submitted.

The course will mainly follow

D. Maclagan, B. Sturmfels: *Introduction to Tropical Geometry*,

American Mathematical Society, 2015.

Participants are expected to be acquainted with the basic notions in Computer Algebra (Commutative Algebra and Algebra are beneficial but not necessary).

**Video recordings:**

11.03. Tropical Semiring |

11.03. Tropical Polynomials |

25.03. Valuations |

22.04. Algebraic Varieties |

22.04. Tropical Varieties |

06.05. Convex Geometry |

20.05. Initials and Gröbner Bases |

Initials and Groebner Bases.png |

10.06. Tropical Linear Algebra |

Linear Algebra.png |

24.06. Graph Theory in Tropical Linear Algebra |

Graph Theory in Tropical Linear Algebra.png |

**Questions which will be discussed:**

TropicalSemiring.pdf |

TropicalPolynomials.pdf |

Valuations.pdf |

Varieties.pdf |

ConvexGeometry.pdf |

InitialsAndGroebnerBases.pdf |

LinearAlgebra.pdf |

LinearAlgebra2.pdf |

**Website:** `www.risc.jku.at/education/courses/ss2021/tropical`