Robert P. Langlands
School of Mathematics
Institute for Advanced Study
1 Einstein Drive
Princeton, New Jersey 08540 USA
Article: Canadian Who Reinvented Mathematics by Sandro Contenta
ArXiv: About Langlands Program, Trace Formulas, and their Geometrization by Edward Frenkel
YouTube: A short, but well-done introduction by Sandro Contenta
. . . . . . . . Langlands visit at Oxford, July 5, 2014
. . . . . . . . Edward Frankel did a series of video introductions to the Langlands programs
Other pages on this site that struggle to understand Langlands programs:
Langlands I, II, II III, IV
Email: Wed, Apr 26, 2017 at 10:58 AM
Dear Prof. Dr. Langlands:
We may be taking the data from our base-2 chart (starting with the Planck units and going to the Age of the Universe) to create a “spaceapp” this weekend for NASA’s Space App Challenge. Of course, we want to use all 202+ notations within that chart beginning with the so-called singularity at notation #1.
The first second within the life of this universe takes us to just over 143rd notation. Along the Planck Length continuum, the first 67 notations are smaller than the work done at CERN labs so imagination will be a key to creating a visualization of those initial notations.
The epochs defined by the big bang theory should be an excellent guide and level set for this work.
In my simple way, close-packing of equal spheres using the Feigenbaum constant, Wolfram’s computer automaton, and possibly some representation of the Langlands program should “compete” for pointfree vertices. I wonder if perhaps the visual manifestations of the pentagon and the heptagon could represent the Langlands programs.
I have dropped Stephen Wolfram and Mitchell Feignebaum a note to see if they have suggestions. Would I be correct to believe that this project would be the first time dimensionless or pointfree geometries vis-a-vis Alfred North Whitehead and topos theory would actually have been visualized?
This morning I have been listening to The Practice of Mathematics (October 26, 1999).
First email: Mon, Jan 18, 2016 at 4:58 PM
Dear Prof. Dr. Langlands,
In 2011 our high school geometry class divided by 2 the tetrahedron (and octahedron within it) about 105 times until we were at Planck Length & Time, then multiplied by 2 until we were out to the Observable Universe and the Age of the Universe. With just over 201 base-2 exponential notations, we unwittingly created a shortcut to everything, everywhere for all time. Hardly a theory, it was just simple math and great fun.
Then we could only find Kees Boeke’s 1957 work using base-10. Base-2 had been ignored. Yet, base-10 had no boundaries, no Planck base units, and no simple geometry.
It has taken us four years to begin to believe we actually may have something special here. Of course, it is idiosyncratic to fault. Bring in a quiet expansion of the universe where space and time are finite, discrete, quantized and derivative. I can hear Sir Isaac protesting, “That’s crazy enough.”
The first 67 notations, of course, are the magic. It is here I would wildly guess that the Langlands programs provide the interstitial mathematics and geometries between that which is defined as physical and that which gives rise to the physical.
I have begun playing with the earliest numbers. Might you have a little look? Could we be onto something? Thank you.