**Ulrike Tillmann**

Cambridge Isaac Newton Institute for Mathematical Sciences (INI)

Oxford Mathematical Institute

Oxford and Cambridge, England

• Articles: Next INI Director

• ArXiv(23): Point-pushing actions for manifolds with boundary (2020)

• Homepages: Oxford, Cambridge Isaac Newton Institute, Royal Society, Oxford Topology

• Video – YouTube: Minicourse Video at Centro di Ricerca Matematica Ennio De Giorgi, 2015

… The Shape of Data, Alan Turing Institute, 2018

• Wikipedia

Second email: 12 April, 2022 @ 10:53 AM

Dear Prof. Dr. Ulrike Tillmann:

In 1961 when first studying geometry 101 (just 14 years old), I questioned the completeness of the definitions of points and vertices. What ties those endpoints together? Is there anything inside a point and/or a vertex?

In 2011 my nephew asked if I would teach his high school classes about Plato’s solids. I had my own special models. By then, having spent time with folks like David Bohm and John Conway, I was still asking odd questions. We followed a Zeno-like path deeper and deeper inside the tetrahedron. Net-net, there were 202 base-2 notations from the first moment of time, Planck Time, to this very moment, right Now. The first 64 notations, below the thresholds of measurement (and perhaps below quantum fluctuations), were a mystery. Each notation had length, time, mass and charge. They also had all the mathematics that defined each Planck base unit. And, I believe they have the qualities of an infinitesimal sphere and the Fourier Transform. I concluded that these notations were not very good point particles and they were not even very good vertices… unless, of course, these were all part of a redefinition of points and vertices.

What a strange place to find oneself.

Might you advise me?

Have you ever studied this infinitesimal scale down to the Planck base units?

Thank you.

Warmest regards,

Bruce

Embedded links:

Tetrahedron: https://81018.com/tot/

Notations: https://81018.com/chart/

Fourier: https://81018.com/gravity/

Point particles: https://81018.com/point-particle/

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Take a course with an Oxford-Cambridge scholar:

ArXiv Abstract. Homology of mapping class groups…

ArXiv PDF: Homology stability

The video comes from Italy!

2015 **Centro di Ricerca Matematica Ennio De Giorgi**: Homology of mapping class groups and diffeomorphism groups. It was a minicourse within the session, “Algebraic topology, geometric and combinatorial group theory.”