Very excited to finally have this paper out! Elliott Gesteau, Matilde Marcolli, and I repurposed ideas from perturbative renormalization to study the Factorization Paradox, and found a symmetry group controlling topology change arxiv.org/abs/2407.20324
These two new papers arxiv.org/abs/2303.13585 and arxiv.org/abs/2303.14203 paint an absolutely amazing picture: all the stringy T and S dualities between 10d supergravities are derived from the bottom-up using Swampland principles!
One of the strangest coincidences in physics is the fact that Newtonian fluid dynamics in three dimensions is exactly equivalent to a scalar field theory in FOUR dimensions, with a Lorentzian signature metric. I know of no intuitive reason for this to be true, but it is.
i asked ChatGPT to generate what a scientist would tweet and it wrote:
"by age 40 you should have realized life is meaningless and that the only knowledge that matters is mathematics"
The typical proof of Van Kampen's theorem, computing the fundamental group of a union or pushout of spaces, involves a choice of basepoint and the group theoretic construction of the amalgamated free product. With groupoids, it is merely a result - the structure of the product...
“Genius has an important role in developing [insert a topic], but actually the knowledge itself is the result of the activity of a community. It’s the real goal of knowledge to become the knowledge of the community, not the knowledge of one or two persons.”
André Joyal
Audrey-has-covid math thread for you all. Not actually about my thesis directly, yet, and a little more musing/philosophical than my other 4-manifolds threads I've done: Embedded Surfaces and 4-Dimensional Exotic Behavior as a Local Phenomenon 🧵1/n
Check out my latest video on @DeepMind’s recent “AI for Mathematics” breakthrough that enabled mathematicians to establish new and significant theorems. I cover the knot theory background, machine learning basics, and the Nature paper youtube.com/watch?v=UPCI1-…
Cool picture I just learned from arxiv.org/abs/hep-th/991…, which identifies non-commutative instantons with blow-ups of spacetime. The (center of mass) moduli space of two U(1) instantons on non-commutative C^2 is T^* S^2. There's a nice intuition behind this! (1/3)
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