Thesis works.
Book reviews.
Some classwork.
Back to my front
page.
Thesis works
-
My PhD dissertation at UC Berkeley, entitled Dependent
percolation, critical exponents, anchored isoperimetry and random walks. The point of this not very elegant title, listing four different objects, DP, CE, AI, RW, is that Chapter 1 has DP, CE, RW in it, Chapter 2 has P, E, AI, RW, while Chapter 3 has DP and AI.
My previous degrees (kind of Masters) are from the Bolyai Institute, University
of Szeged, Hungary,
and from the University of Cambridge, UK (this was the so-called Part III).
- An improved version of my
essay written in Cambridge:
Morse theory.
(50 pages.) The original aim was to understand Edward Witten's supersymmetric approach to Morse theory and
Killing vector fields. Then it grew into a somewhat heroic attempt to give
a detailed introduction to modern geometry from the point of view of this
beautiful and deep theory. From Gauss-Bonnet through Hodge decomposition
to supersymmetry and Yang-Mills.
- My thesis for diploma at the
Bolyai Institute, József Attila University, Szeged: Disease
processes and bootstrap percolation, Contents,
Introduction, References, Deterministic
disease on the k-dimensional board, Random disease and
bootstrap percolation, Addenda and errata.
(30 pages.) This is based on my papers in Polygon (Szeged) 1997, and in Random Structures and Algorithms 1998, with
József Balogh. For the latest news and nice pictures about
bootstrap percolation on Z^2, go to Ander Holroyd's webpage.
Book reviews for Acta Math. Sci. (Szeged)
H. Bass - A. Lubotzky: Tree lattices.
B.
Bollobás:
Random
graphs, 2nd edition. G. Davidoff - P. Sarnak - A. Valette: Elementary number theory, group theory, and
Ramanujan graphs. G. Grimmett: Percolation,
2nd edition. E.Kleinert: Units in skew
fields.
W. Woess: Random walks on infinite graphs
and
groups.
Some classwork 
- Random walks on truncated
hypercubes.
With
Sam Riesenfeld, for Markov Chain Monte Carlo at UC Berkeley, course by
Alistair
Sinclair.
- Glauber dynamics on trees.
With
Manjunath
Krishnapur,
for Markov Chain Monte Carlo at UC Berkeley, course by Alistair
Sinclair.
- Introduction to the Ising model.
For
Spin
Systems
at UC Berkeley, course by Fabio Martinelli.
- Lagrange inversion and
strange giants in random forests. For Combinatorial Stochastic
Processes at UC Berkeley, course by Jim Pitman.
- Birkhoff's and Maximal Ergodic
Theorems,
and the Shannon-McMillan-Breiman Thm. For Probability 205B at UC
Berkeley, course by Yuval Peres.
- Maximal tori of compact Lie
groups.
For Kac-Moody Algebras at the Univ. of Cambridge, course by Anthony
Wassermann.
- Introduction to quasicrystals. At the
Univ. of
Szeged, course by Tibor Ódor.