Tropical Scheme Theory - Fall 2017
This course will be an introduction to tropical scheme theory.
Course info
- Lectures: TTh 1 - 2:15 pm
- Classroom: LOM 205
- Office: 406 DL
Syllabus
You can find the syllabus here.Lecture notes
The lecture notes for the class are available online here.Schedule
| Lecture # | Date | Topic |
|---|---|---|
| 1 | 09/05 | Semirings, ideals, homomorphisms (Sam Payne) |
| 2 | 09/07 | Prime and maximal ideals in semirings (Kalina Mincheva) |
| 3 | 09/12 | Introduction to matroids I (Max Kutler) |
| 4 | 09/14 | Matroids over Hyperfields (Matt Baker) |
| 5 | 09/19 | Introduction to matroids II (Max Kutler) |
| 6 | 09/21 | Factor objects in semirings; congruences (Kalina Mincheva) |
| 7 | 09/26 | More congruences (Kalina Mincheva) / Valuations and set theoretic tropicalization (Dave Jensen) |
| 8 | 09/28 | Bend relations and congruences (Dave Jensen) |
| 9 | 10/03 | Tropical Schemes (Kalina Mincheva) |
| 10 | 10/10 | Dimension of a tropical scheme (Kalina Mincheva) |
| 11 | 10/12 | Universal Tropicalization (Noah Giansiracusa) |
| 12 | 10/17 | Relation between tropical schemes, tropicalized ideals and valuated matroids (Kalina Mincheva) |
| 13 | 10/24 | Tropical Hilbert-Chow (Kalina Mincheva) |
| 14 | 10/26 | Tropical ideals (Felipe Rincón) |
| 15 | 10/31 | Tropical Nullstellensatz I - for tropical ideals (Sam Payne) |
| 16 | 11/2 | Tropical Nullstellensatz II - the dual Nullstellensatz (Kalina Mincheva) |
| 17 | 11/7 | The semiring of finitely generated ideals (Nati Friedenberg) |
| 18 | 11/9 | Tropical Nullstellensatz III - for congruences (Kalina Mincheva) |
| 19 | 11/14 | Geometry over the tropical dual numbers (Louis Brown) |
| 20 | 11/16 | Focus-focus singularity and its equation(Yuto Yamamoto) |
| 21 | 11/28 | Towards tropical (co)homology I (Kalina Mincheva) |
| 23 | 12/5 | Towards tropical (co)homology II (Kalina Mincheva) |
| 24 | 12/7 | Towards tropical (co)homology III (Kalina Mincheva) |