TO: Ngô Bảo Châu, University of Chicago
FM: Bruce E. Camber
RE: Your extensive articles — https://math.uchicago.edu/~ngo/takagi.pdf — especially found in ArXiv:. I found the article, The 80-year development of Vietnam mathematical research (2020) very helpful. Also the ArXiv article, Invariant theory for the commuting scheme of symplectic Lie algebras; Algebraic Geometry (math.AG) (February 2021) and this comment within https://arxiv.org/abs/0801.0446: “We propose a proof for conjectures of Langlands, Shelstad and Waldspurger known as the fundamental lemma for Lie algebras and the non-standard fundamental lemma. The proof is based on a study of the decomposition of the l-adic cohomology of the Hitchin fibration into direct sum of simple perverse sheaves.”
Research and Relate: (1) Hitchin fibrations — purely geometric objects, (2) Galois groups in algebraic number theory to automorphic forms and representation theory of algebraic groups over local fields and adeles, (3) the automorphic L-function, L (s, π, ρ), as Langlands discovered, depended not only on the automorphic representation π, but also on an auxiliary finite dimensional representation ρ of a canonically associated dual group or L-group. Also , helpful are his homepages at Clay, Chicago, Google Scholar, IAS, VIASM (About), Semantic Scholar, Wikipedia, and Video: Orbital Integrals (July 20, 2022).
References with this website: This page: https://81018.com/2021/11/18/chau/
Fourth email: 28 November 2026
Dear Prof. Dr. Ngô Bảo Châu:
My last note to Robert Langlands! I thought you would appreciate it.
Bruce
From: camber 81018.com <camber@81018.com>
Sent: Wednesday, January 28, 2026 4:22 PM
To: rpl@ias.edu
Subject: Still at it — https://81018.com/langlands-correspondences/
Dear Prof. Dr. Robert Langlands:
I celebrate your insights and innovations and take them a simple logical step: https://81018.com/langlands-correspondences/
May you go gently into your days knowing you served us well.
Thank you.
Warmly,
Bruce
Third email: 17 August 2024
Dear Prof. Dr. Ngô Bảo Châu:
Of course, Robert Langlands assumed when he started that the mathematics was not conditional of infinity, of space-time, nor of the advent of dimensionless constants or infinitesimal spheres. If infinity is continuity- symmetry-harmony as given by the facets of pi, I would argue that, even if Langlands programs were to exist on a bridge between the finite-and-infinite, the perfections of continuity-symmetry-harmony would apply. I have discussed it in the current homepage — https://81018.com — which after this homepage cycle will be: https://81018.com/identity/
Thank you.
Warmly,
Bruce
P.S. My page about your work is https://81018.com/2021/11/18/chau/. — BEc
Second email: 21 February 2024
RE: The functoriality principle (or conjecture) of Langlands does not just exist on paper or as an abstraction in our mind…
Dear Prof. Dr. Ngô Bảo Châu:
As a general organizational scheme for all automorphic representations, the functoriality conjecture of Langlands exists in the universe. Not in a multiverse about which we can only speculate, it exists in a universe that is known by space, time, mass, and charge. If one were to comment that this statement is not fundamental enough, may we ask, “What is between Automorphic Representations or Forms (ARF) and spacetime, between the ARF and finite-infinite, or between the ARF and the perfect and imperfect?”
I find von Neumann’s attitude to be limiting when he said, “In mathematics you don’t understand things. You just get used to them.” What if the universe starts most simply with pi (π) and the Planck base units? What if the continuity-symmetry-harmony of pi (π) is built into the very fabric of our being, including automorphic representations? What if these qualitative faces of pi (π) define the infinite and “global” fields and settings truncate vision. And, if so, the nonstandard Fourier transform would become a standard.
Our definition of the universe begins with the Planck base units where we apply base-2 notation whereby an infinitesimal sphere begins spacetime, mass and charge whereby you and your people could tell us how automorphic forms define the first group of notations that further precondition spacetime?
Are these automorphic forms within spacetime? Do they define spacetime? Or, do they define a bridge between the finite and infinite? Or, is it all just nonsense?
Thank you.
Warmly,
Bruce
PS. Reference to this email is within today’s homepage: https://81018.com/reformat/#Chau and our page to follow your work (and a copy of our email): https://81018.com/2021/11/18/chau/. Thanks. -BEC
First email: 4 December 2021 at 4 PM
Dear Prof. Dr. Ngô Bảo Châu:
I spent a few days in Hanoi and Saigon about ten years ago. My very first interactions with Hanoi were in 1969 and 1970. That’s a long story.
In 2014 I picked up Ed Frenkel’s book, Love & Math, and was introduced to Robert Langlands, of course, and to others like Drinfeld and Gelfand. It is a very steep learning curve; and like most, I have barely scratched the surface.
Your work quickly came to my attention and it has taken until today to humble myself and confess that I will probably die before even grasping the essentials… even after spending time on the IAS papers of so many of the primary program authors like yourself.
My working summary page about your work is here: https://81018.com/2021/11/18/chau/ (this page).
May I ask you a few questions? It will be in light of my current work to follow-up this page: https://81018.com/almost/ The next article will open with comments about the Langlands programs understanding of place and role of infinity, pi, and infinitesimal spheres. Thank you.
Most sincerely,
Bruce
Bruce E. Camber
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