| Instructor | Yassine El Maazouz |
|---|---|
| Course Webpage | http://www.yelmaazouz.org/Ma191B-2026/index.html |
| Course Code | Ma/ACM/IDS 191 abc |
| Lectures | Tu-Th 13:00–14:25, 187 Linde Hall |
| E-Mail: | maazouz [at] caltech [dot] edu |
| Office Hours | Th 14:00–15:00 Excluding holidays. Please email me if you cannot make any of these times. |
| Prerequisites | A foundation in commutative algebra and algebraic geometry is strongly recommended. Familiarity with polyhedral geometry is not necessary but will be helpful. |
| Required Text | There is no required text for this course. However, you may consult the following references:
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| Course Description |
Tropical geometry is the study of certain combinatorial shadows of algebraic varieties. It is based on tropical min-plus algebra, where the sum of two numbers is replaced with their minimum and the product with their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These combinatorial structures retain a surprising amount of information about their classical counterparts. This course will introduce and survey some topics in tropical geometry, including Puiseux series and valuations, Gröbner complexes, tropical varieties, the fundamental and structure theorems, hyperplane arrangements and matroids, complete intersections and tropicalization of toric varieties. If time permits we shall also discuss Bernstein’s theorem, Viro’s patchworking, and combinatorial Hodge theory. The schedule of the course will announced below and continuously updated as the course develops. |
| Homework |
There will be biweekly problem sets. Collaboration (between students) on homework is encouraged.
It is important to make sure you understand the solutions yourself, so you are required to write your own solutions separately.
I also strongly recommend that you spend some time attempting the problems yourself first before discussing with someone else.
You are required to name all your collaborators. You can use any result discussed in the lectures.
DO NOT PLAGIARIZE! The use of AI chatbots on problem sets is completely forbidden. Please write clear and legible solutions. It is strongly recomemded to write your solutions in TeX. Homework is due on Fridays at 23:59 PST and is to be submitted on Gradescope. Late homework submissions will not be accepted. |
| Final Exam | In the last week of the quarter, each student will give a 45min presentation on a topic of their choice related to tropical geometry. A list of suggested topics will be made available. You will be required to deliver your presentation without any notes. |
| Grading | The final grade will be based 60% on the problem sets and 40% on the presentation. The lowest homework grade will be dropped. |