What is tropical geometry?

I wrote my PhD thesis about tropical geometry! This is a new, exciting, and rapidly developing area of math. In this video, I will teach you a bit of tropical geometry through examples.

If you enjoyed this video and would like to see something more in depth, you can follow up with my practice talk for ICERM:

[johnrickert]

I think a lot of people who say that they hate math have no idea that this is the sort of thing mathematicians do. Mathematics is an adventure for the curious. Thank you for your video.

[heathermac]

You are one of the best maths teachers on the internet. You seem as if you really prioritize making every single thing understandable (to a broad audience, including non-mathematicians) ... whereas often online maths teachers/presenters/lecturers seem more as if they are summarizing their topic for themselves! ... or, at best, for people who already know the topic.

[DaMonster]

I love this video! So well made. I wish more PhD students took the time to explain their research and its significance to the public. Best of luck!

[samuel-louisgardiner]

Thank you for making some tropical geometry content, it's great to see other people doing tropical stuff!

[phenixorbitall]

That was sooo nice!
It's a very underrated channel

[firevavanced]

You're awesome! I could understand easily those advanced abstract concepts from a math area I haven't studied before just by watching a single video. Thanks and keep it up!

[randalllionelkharkrang]

You're amazing at explaining complex things. I'm doing my masters in machine learning, and Ive been hearing tropical geometry being applied . Immediately subscribed.

[peabrane]

I learned about tropical geometry when I was looking at tensor networks for representing Ising spin glass models in statistical physics. It really is a fascinating topic of research

[harleychesney]

This is my first time seeing a description of this topic. Now I want to know everything. Great example too!

[tracyh]

I study toric varieties, and I've always felt that tropical geometry and toric varieties as kind of sister topics. Having a connection to discrete is fun!

[LucPatry]

Beautiful, please keep your work available to as many people as possible. ❤️

[kamilziemian]

Very good video. Now, I want to know a little bit more about tropical geometry.

[TheAAZSD]

I thoroughly enjoyed this video! Thank you for such a clear exposition on this subject!

[anonimmors]

Nice idea and amazing presentation of the topic

[ndmath]

These videos are much appreciated. Thanks for making this.

[lexinwonderland]

Hey, I just fell into this field from a #SoME3 video about generalizing the log semiring -- I would be FASCINATED to read your work, and I'm very curious how algebraic varieties in the log "softmax" semiring relate to algebraic varieties in the tropical semiring if you have any sources. This was a great explainer btw, thank you so much for posting and I look forward to your future work!!

[listsforthecurious]

I picked up a small book a while back by the Russian mathematician Arnold, which dealt briefly with tropical geometry on finite fields. It looked very interesting.

[hugoviloriagonzales]

Hahah!!!! Los recursos de las Matemáticas, son variados, para feeding the mind. Éste vídeo me clarifica lo que quería yo saber, Gracias.

[twistedcubic]

Nice video! May I ask how you made these animations?

[_faraz]

What are some introductory texts on tropical geometry. I am familar with AG upto hartshorne.