Christina Grossack

hallasurvivor@sunny.garden

math/music. she/they.I'm a PhD student interested in the intersection of algebra, geometry and logic. An intersection often made clearer with the language of category theory.Leftist

Posts

Post #2272187
In case you haven&#39;t seen it, here&#39;s a SUPER cool video where someone builds puzzles based on sporadic groups. In particular, the M12 puzzle looks VERY clean! I&#39;m sure lots of people would find this interesting, but I think that @henryseg in particular would be REALLY interested! There&#39;s one based on M24 as well, which I&#39;ll leave as a surprise for those who watch the video 👀 https://www.youtube.com/watch?v=xwQ5dx4dE9g
Post #2142406
Hmmm... Wondering if I should try and learn some condensed matter physics, lol
Post #2060191
Just learned that the theory of generating functions can be seen as harmonic analysis on Z?? Then the usual way we use generating functions to solve recurrence relations is a special case of Fourier transforms turning translation into multiplication, which turns the recurrence relation into an algebraic equation! If you haven&#39;t seen this before, it&#39;s really fun to work out for yourself ^_^. Whether or not you&#39;ve seen this before, post your thoughts here! If you alread...
Post #1815131
It&#39;s kind of funny, I remember learning algebraic geometry and wondering why people would care about the derived pushforward R*f. I don&#39;t think I ever got an answer to that specific question -- I just learned so many reasons to care about derived functors broadly that now R*f seems inevitable... BUT ☝️ I finally have a 𝑟𝑒𝑎𝑙𝑙𝑦 good reason that I think would have satisfied younger me! If you&#39;re interested in sheaves then you&#39;re interested in their global sections, a...
Post #1655826
It&#39;s finally done! Have a 3 part series on the topological topos First, let&#39;s talk about some fundamentals. How do we think of objects in the topos? How do we compute with them? How do they relate to objects in &quot;the real world&quot;? https://grossack.site/2024/07/03/life-in-johnstones-topological-topos Then, since post 1 is loooong, a little palate cleanser. It&#39;s a short post about how we can use the topological topos to more effectively study algebraic s...
Post #1487037
I have a friend visiting me from out of town and he gave me this fun puzzle which COMPLETELY broke my brain! The quaternions are a &quot;skew-field&quot; in the sense that they satisfy all the axioms of a field, except they&#39;re not commutative. In the quaternions, we have a crazy fact: x²+1 has uncountably many roots! Puzzle 1: Can you find uncountably many roots of x²+1 in the quaternions? Puzzle 2: This means that in the proof of &quot;a polynomial of degree n has at mo...
Post #1487034
Just said &quot;the situation is worse in the absence of inequality&quot; in a meeting, lol. I was talking about the theory of an object vs the theory of a 𝑑𝑒𝑐𝑖𝑑𝑎𝑏𝑙𝑒 object, but I had to chuckle at how that sounds out of context, haha