Articles: Weil’s Conjecture for Function Fields I (PDF), 2018
ArXiv(17): The prismatization of p-adic formal schemes, 2022
Homepage (IAS) (Kerodon) (MacArthur) (nlab)
YouTube: Lie Algebras and Homotopy Theory, 2019
The Classification of Extended Topological Field Theories, April 2022
Most recent and third email: 8 July 2022 at 12:24 Noon
Dear Prof. Dr. Jacob Lurie:
Aristotle didn’t observe a five-tetrahedral gap and laid the foundations to taint geometry with an error that was replicated by many for over 1800 years. Are scholars today missing the five-octahedral gap? I am not finding any specific references to it. Perhaps it goes by another name. It is the same 7.35610+ degree gap created by five tetrahedrons.
The AMS recognized the Lagarias-Zong article (PDF) that appears to be the most recent scholarly analysis of the five-tetrahedral gap. Taken together, I believe those gaps are as significant as they are attractive! Here is my best image of the gaps to date!
Of course, the twenty-tetrahedral icosahedron also has significant gaps yet any five tetrahedrons of the twenty fit nicely on top of the five-octahedral gap. It is a very different gap, yet makes for a most-fascinating stack and a bit of complexity. I just took a picture of it; it is a bit odd.
Currently, I envision this tetrahedral-octahedral generation as part of the dynamics of the first ten base-2 notations (within the 202 that encapsulate the universe — everything-everywhere-for-all-time). Perhaps here may be a hypergeometric and hypogeometric series and a very different start of automorphic forms. All conjectures, more conjectures, and simple geometries. Thanks.
PS. Yes, I am back reading from your collected works noted here: https://www.math.ias.edu/~lurie/index.html
Second email: 15 April 2021 at 6:30 PM
Dear Prof. Dr. Jacob Lurie:
We are back studying your ArXiv collection and I recently updated our own reference page about your work — https://81018.com/lurie/ — which gives us confidence that we are not on the wrong path.
Does anyone have a good starting point for a theory of the beginnings that necessarily defines space-time, mass-charge, electromagnetism-gravity in a way that our high school kids can say, “There’s an inherent logic to it all. I want to study these aspects of it…”? If we hold onto to big bang cosmology, all our math has to create too much heat for comfort.
We’ve decided that Hawking’s big bang cosmology’s infinitely hot start is a bit of silliness and Lemaitre’s first idea in 1927 of a cold start is a better idea. We forced our base-2 chart to be cold and decided to deal with Planck Temperature in other ways. Yes, we realize that we are idiosyncratic… for sure. Such is life. Notwithstanding, we wish you well with your infinity categories, derived algebraic geometry, and higher topos theory. Thank you.
First email: Tuesday, April 25, 2017, 4:25 PM
Dear Prof. Dr. Jacob Lurie –
Congratulations on all you have done to date! Most impressive.
In December 2011 in a New Orleans high school we began developing a base-2 chart from the Planck units to the Age of the Universe. There are 202+ notations to encapsulate the universe. But… is it at all meaningful? Most people think not. The first second within the life of this universe takes us up to just over Notartion-143 of those 202 notations. The first 67 notations are within length scales much smaller than the work done at CERN so some imagination is a key to visualizing the initial blocks of notations.
Because we are simple, we see it simply. Also, we use the epochs defined by the big bang theory as a level set and guide. We quickly picked up on close-packing of equal spheres and rather casually assumed Wolfram’s computer automaton, Langlands programs, Mandelbrot sets, expressions of topos theory… (and all other well-defined disciplines like M-Theory that have no current place on the grid), all compete for vertices (within those first 64-to-67 notations).
Has there been any attempt to visualize the dimensionless or “pointfree” geometries vis-a-vis Alfred North Whitehead and topos theory? Do you “see” anything?
Bruce E. Camber