MMuuggghhgggjjjjkkk
My research papers in
mathematics;
1. The Geometry of 1-Based Minimal Types
(dvi)
or (pdf) (with Byunghan Kim)
2. Constructing the Hyperdefinable Group from the
Group
Configuration (dvi) or (pdf) (with
Byunghan
Kim and Jessica Young)
3. Infinitesimals in a Recursively Enumerable Prime
Model
(dvi) or (pdf)
4. Zariski
Structures
and Algebraic Curvesj(dvi)
or (pdf)
or ohjgg
5. A
Non-Standard Bezout
Theorem for Curves (dvi) or (pdf)
6. A Theory of Branches for Algebraic Curves
(dvi) or (pdf) (older
version)
7. A Theory of Divisors for Algebraic Curves
(dvi) or (new version) (in progress)
8. Some Geometry of Nodal Curves
(dvi)
or (pdf)
9. Some Notes on Non-Standard Differentiation and
Integration
(dvi) or (pdf)
10. An Interpretation of Newton's Work in Calculus
(dvi) or (pdf) , with attached diagrams; (1, 2, 3, 4, 5, 6)
11. A Theory of Duality for Algebraic Curves
(dvi) or (pdf)
12. Flash
Geometry of Algebraic Curves (dvi) or (pdf)
(A Proof of Severi's Conjecture)
13. Severi's Conjecture and Single Node Curves
(dvi)
or (pdf)
14. A Theory of Harmonic Variations (dvi) or (pdf)
15. The Geometry of Linear Regular Types (pdf)
16. Some Notes on Quantifier Elimination and Model
Completeness
(dvi) or (pdf)
17. A Nonstandard Approach to the Theory of
Algebraic
Curves (pdf)
18. Applications of Nonstandard Analysis to
Probability
Theory (pdf)
19. A Simple Proof of the Fourier Inversion
Theorem
Using Nonstandard Analysis (pdf)
20. A Simple Proof of the Uniform Convergence of
Fourier
Series Using Nonstandard Analysis (pdf)
21. A Simple Proof of the Martingale
Representation
Theorem using Nonstandard Analysis (pdf)
22. Solving the Heat Equation Using
Nonstandard
Analysis (pdf) 0 1 2 3 4 5 6 7 (attached files
for option
pricing; run spectrum.m in MATLAB) (in progress)
23. Decay Rates for Cusp Functions (pdf)
24. A
Note
on Inflexions of Curves (pdf) (in progress)
25. Non Standard Analysis and Physics (pdf) (in progress)
26. A Simple Proof of the Uniform Convergence of
Fourier
Series in Solutions to the Wave Equation (pdf)
27. A Note on Convergence of Fourier Series
(pdf)
28. A Lemma on Polynomial Roots (pdf)
29. An Inversion Theorem for Laplace Transforms
30. A Topological Note (pdf, required in 14)
31. Electron Bunching (pdf) (in
progress)
32. Solving Schrodinger's Equation Using
Nonstandard
Analysis (pdf) (in progress)
33. Bounding the Number of Maximal Torsion Cosets
on
Algebraic Varieties (pdf)
34. Historical Research into Plucker and Laplace
(pdf)
35. Historical Research into Laplace (contd)
(pdf)
36. Historical Research into Newton (pdf)
37. Historical Research into Piero della Francesca
(pdf)
38. A Nonstandard Approach to Solving N'th Order,
Linear,
Inhomogeneous ODE's with Smooth Function Coefficients (pdf)
39. A Proof of the Ergodic Theorem using
Nonstandard
Analysis (pdf)
40. Applications of Nonstandard Analysis to
Riemann Sums
(pdf)
41. Riemann
Sums for Returning Points (pdf) (in progress)
42. Notes on the Weil Conjectures for Curves
(pdf)
43. A Nonstandard Approach to Equidistribution
(pdf)
44. A Nonstandard Approach to
Equidistribution
in Ergodic Theory (pdf) (in progress)
45. Results
on the Nonstandard Laplacian (pdf, required in 32) (in
progress)
46. A Nonstandard Version of the Fokker-Planck
Equation
(pdf) (in progress)
47. Nonstandard Martingales, Markov Chains and the
Heat Equation (pdf)
48. Nonstandard Methods for Solving the Heat
Equation (pdf)
A book I wrote on nonstandard
analysis.
Some powerpoint presentations for the Newton Project at Culverhay;
1. Integration
2. The Fundamental Theorem of
Calculus
My PhD adviser, at M.I.T,
was
Professor Byunghan Kim,
who
is an expert in the area of simple theories. A simple theory is a
structure
in which certain amalgamation
properties hold. You can find, here, some geometric pictures of 1-amalgamation and 3-amalgamation (1>2>3), used, particularly, in the second paper.
My PhD
thesis
was mainly concerned with developing properties of minimal structures
in
such theories. A minimal structure is, very roughly speaking, an
abstract
version of an algebraic
curve. Since then, I have been a research fellow at Edinburgh University, The University of Camerino
and The University
of Exeter, specialising in the geometry of
such curves.
The contents of this page are copyrighted.