TOYKAMP is a pure math playgroup that meets weekly on Thursday afternoons. We do weaving (Fine Springer Fibres to make Higgs Bundles) and box building (black boxes to put the fibres and bundles in to make Modules). The participants are usually local, but we have some Commuting Operators who come in to run the black box modules and navigate Spectral Curves with them. Our systems are often Integrable into a larger mathematics department (if the bundle is sufficiently ample). Everyone is welcome.
| Ting Xue | Lecture Notes | 17 August 2017 |
| Omar Foda | Lecture Notes | 21 September 2017 |
| Yaping Yang | Lecture Notes | 10 August 2017 |
| Kari Vilonen | Lecture Notes | 7 September 2017 |
| Arun Ram | Lecture Notes | 31 August 2017 |
| Michael Wheeler | Lecture Notes | 28 September 2017 |
| Paul Norbury | Lecture Notes | 24 August 2017 |
From the Lecture notes:
| Ting Xue | Lecture Notes | 17 August 2017 |
| Omar Foda | Lecture Notes | 21 September 2017 |
| Yaping Yang | Lecture Notes | 10 August 2017 |
| Kari Vilonen | Lecture Notes | 7 September 2017 |
| Arun Ram | Lecture Notes | 31 August 2017 |
| Michael Wheeler | Lecture Notes | 28 September 2017 |
| Paul Norbury | Lecture Notes | 24 August 2017 |
The point is
that affine Springer fibres
are weaving together to form the
moduli space of Higgs bundles
which is gonna be
Pic of a spectral curve.
The
Cohomology is a Black Box
containing the affine Springer fibers
and making a DAHA module
and that DAHA module
has got commuting operators acting on it
and in important cases
it corresponds
to an integrable system.
That's an integrable system for which
the Energies
are eigenvalues of the
Macdonald polynomials
and it provides some kind of
Fourier analysis
imbedded in the
Langlands correspondence
This was the plan for a School Pure Mathematics Research presentation for the School Review 1 November 2017.