i feel like if you have to normalize your function by THIS you need to just go find a new function
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i always think it's funny when someone learns i'm a math phd student and they say "oh i hate math" like dude no one hates math more than me
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learning abt monster group as a mathematician: do you know what a group is? we know every finite simple group. the monster is a special one of those! isn't this lovely <3
monster group as a physicist: CONSIDER C = 24 VERTEX OPERATOR ALGEBRA OR MEROMORPHIC CONFORMAL FIELD THEORY-
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just accepted my PhD offer at UNC-Chapel Hill! can't believe that i actually convinced someone to pay me to do math.
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Classes that SHOULD be mandatory in high school:
- Nutrition
- Money Management
- Lie Groups and Lie Algebras
- How to build and keep good credit
- Establishing a job/career
- Self defense
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mathematicians really wake up in the morning like "i think im going to invent another homology theory today"
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I gave an intro (very intro, like first/second year grad student) talk on Kahler geometry and Hodge theory and the notes are online if anyone wants to read! I'd appreciate any comments or questions on these.
tarheels.live/rlance/notes/
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prof at the start of semester on which textbooks would be good to read for the class (paraphrased): "frankly i don't know which books are good or bad because i never read them. if i need to understand something i just call up the authors and ask them to explain it to me"
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i solved one of my big research questions today which i am very happy about. this problem is 1/2 of an upcoming paper (other half not finished yet). i know everyone says this, but the answer is so blindingly obvious in hindsight. what was i even doing for the last 6 months?
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it must be the lucrative salary and excellent work-life balance that being a phd student entails
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"we share a philosophy about linear algebra: we think basis-free, we write basis-free, but when the chips are down we close the office door and compute with matrices like fury"
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everyone who advertises functional analysis as "just linear algebra and topology" should be prosecuted by the federal trade commission for deceptive marketing tactics
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everything i know how to do is trivial and everything i don't know how to do is impossible
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the applied category theory people scare me. i feel like any day they're going to say something like "ordering a pizza is a functor"
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learning math makes me want to do math. watching movies makes me want to make movies. reading makes me want to write
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STOP talking shit about different mathematical fields
CATEGORY THEORY is BEAUTIFUL
DIFFERENTIAL GEOMETRY is ELEGANT
ALGEBRAIC TOPOLOGY is INSPIRING
analysis
MATHEMATICAL PHYSICS is INSIGHTFUL
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why are there so many sub 20 year old computer science nerds on twitter who know 10x more math than me
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since there seemed to be some interest, i wrote up a full, painstaking proof of this lemma here (at the very bottom):
tarheels.live/rlance/wp-cont…
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i have posted my first math overflow question and im absolutely terrified of getting roasted/downvoted/banned/you are stupid/your question is trivial/off topic/homework/etc
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apparently i'm taking on the "how much algebraic geometry and representation theory can i do without really knowing what a stack is" challenge
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the annoying part about most math exams is the timed aspect. The fun in doing math is letting things marinate over long periods of time and allowing your subconscious to work on problems in the background, then every once in a while your brain serves you up a good idea.
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in a reading course in supersymmetry a couple years ago, i asked my mentor why a particle was considered as an irreducible representation of the poincare group, and received "well, that's the definition of a particle" followed by several minutes of silence
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you know measure theory is an absolutely degenerate subject when it takes almost 5 pages for terrence tao to derive the formula for the volume of a box
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its kind of crazy to know that math professors exist. i've been doing math seriously for about 3 years and if all goes according to plan, one day that number will be like 20 or 30 ..... wtf
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a major academic (long term) goal i have is to understand witten's paper on the connection between geometric langlands and qft
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i will make friends in grad school i will make friends in grad school i will make friends in grad school i will make friends in grad school i will make friends in grad school i will make friends in grad school i will make friends in grad school i will make friends in grad school
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found a mistake in the recorded lecture but i can't tell the professor about it otherwise they will know how behind i am in watching the lectures
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i'm trying to fit in with category theory twitter by declaring everything to be "just a functor"
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like tell me you dont talk to mathematicians without telling me you dont talk to mathematicians
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the proof of maximum modulus principle should be presented by a magician who deploys a smoke screen at the end and vanishes
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okay i'm done taking quals this semester, who can explain to me what a double affine hecke algebra is and why they're cool
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just because you are vaccinated does NOT mean you can live out of your suitcase and travel from collaborator to collaborators house, living on their couch long enough to solve a problem, then promptly move on to the next one, while subsisting off of guest lecture money.
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what makes equivalence of categories a more useful notion than isomorphism of categories? i.e. are there some things which are preserved by iso but not equivalence that we don't want to preserve? or do they preserve the same properties but iso is harder to prove than equiv
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unbelievable as in: i don't actually believe any of this is true. the proofs are way too easy/slick
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Q: Which spheres are parallelizable? i.e., which spheres have trivial tangent bundle, or equivalently, admit n linearly independent vector fields?
A: S^1, S^3, and S^7 (only, but we won't show that).
Proof (using mostly linear algebra!!): Read thread 🧵
1/N
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ben shapiro voice: what if hypothetically, for the sake of argument, i skip my analysis class
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for the first time in my life (ie 3 years of grad school) i heard someone besides my advisor give a talk about exactly what I do. it was a very affirming experience. i'm jealous of people who work in such a popular/broad field where this is a regular occurrence
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oh god i just marked a bunch of people's homeworks wrong bc i didn't realize the textbook they use has 0 as a natural number
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my dentist was like "you're showing signs of grinding/clenching your teeth a lot is there anything stressful going on in your life?"
my brother in christ im in grad school
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the tangent space to the graph of a function is the graph of the differential! this generalizes the thesis of calculus, and when phrased in this way it implies things like the graph of a diffeomorphism is Lagrangian iff the diffeomorphism is a symplectomorphism
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this is pretty cool: you can realize the (geometric) braid group on k strands as the fundamental group of the configuration space of k unordered points in R^2
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on my immediate horizon: learn more complex geometry (kahler, CY, K3), and learn more geometric rep theory (quantum algebra, hecke algebra, perverse sheaves)
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fun fact I discovered while grading linear algebra exams: the n x n matrix A consisting of all 1's satisfies the relation A^k = n^(k-1)A, for example:
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cauchy integral formula -> gauss mean value theorem -> maximum modulus principle -> fundamental theorem of algebra
is one of my favorite sequences of results
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i cant wait to make the most stereotypically minimalistic math website in grad school. it will be a complete wasteland. im going to stick "<br>" around in random places too. everything left justified, especially the picture of me standing in front of a chalkboard
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~ thread ~ on computing the oriented cobordism group in degree 4! idk if this is how ppl normally do it, and some of these steps are my own, so i hope there aren't any mistakes 😁
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i forgot to mention this earlier, but i'm tex'ing notes for my course on algebraic geometry and seminar on categorical rep theory this semester. if ppl want to read them, i'd appreciate extra eyes on these docs for questions and comments:
tarheels.live/rlance/notes
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broke: a space is a set with a topology
woke: a space is a functor from CommRng -> Set
bespoke: a space is a presheaf on the category of affine schemes
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