Hugo!

I'm working on a blog platform with those features, it's in closed alpha right now. Drop me a line if you would like to be an early user, my email is in my profile. You'll keep the service for free now, and even after it goes public in exchange for feedback and bug reporting.

I am using Hugo since 2019. Prior to that Jekyll. Both will handle what you want! I am not sure about tex markup because I have not tried to use it since grad school but seems like a good idea to look into.

Making your own is fun, though.

I'm a happy Zola [0] user, which does everything you mentioned except LaTeX.

There are a few themes [1], though I ended up writing my own [2] (which supports MathJax [3] for mathematical notation).

[0]: https://www.getzola.org/

[1]: https://www.getzola.org/themes/

[2]: https://github.com/welpo/tabi

[3]: https://www.mathjax.org/

Are you open to do it with Node? I wrote a blog post[0] with a fairly easy setup. If you're using markdown and any markdown processor you should be good to go.

[0] https://www.itzami.com/blog/how-to-build-a-blog-with-nodejs

I've loved Astro [0] for my blog [1]. You get a lot for free and you can tinker as much or as little as you like.

It renders to static HTML/CSS (unless you _want_ JS) and it feels lightweight. You can start with a plain unthemed site today and slowly add features/polish when you feel like procrastinating on writing :)

[0]: https://docs.astro.build/en/tutorial/0-introduction/

[1]: https://github.com/shepherdjerred/sjer.red