Robert J Budzyński
about me
I work at the Warsaw University Faculty of Physics as head of the Faculty's Computing Center.
my interests
- theoretical and mathematical physics
- programming (mainly Python and Javascript)
- Linux and Unix
education
- PhD in Physics (University of Warsaw, 1997)
- MSc in Physics (University of Warsaw, 1982)
some of my publications
old and older
- Robert J Budzynski, Witold Kondracki. Remarks on the L1 distance in statistical data analysis. Communications in Statistics - Theory and Methods, 46:19, 9355-9363, 2014.
- Robert J. Budzyński, Witold Kondracki, Andrzej Królak. On the geometry of the parameter space reduction with application to gravitational wave data analysis. Advances and Applications in Statistics, Volume 34, Issue 1, 2013.
- Robert J. Budzyński, Witold Kondracki, Andrzej Królak. Applications of distance between probability distributions to gravitational wave data analysis. Class. Quantum Grav. 25 (2008) 015005, 2007.
- R. J. Budzyński, W. Kondracki. Stability of Cauchy Horizons. International Journal of Theoretical Physics, Vol. 42, No. 7, 2003.
- Robert J. Budzyński, Witold Kondracki, Andrzej Królak. On the Differentiability of Compact Cauchy Horizons. Letters in Mathematical Physics 63: 1, 2003.
- W. Rudnicki, R. J. Budzynski, W. Kondracki. Generalized Strong Curvature Singularities and Cosmic Censorship. Mod.Phys.Lett. A17:387-397, 2002.
- R. Budzyński, S. Janeczko, W. Kondracki, A. F. Künzle, (eds.). Symplectic Singularities and Geometry of Gauge Fields. Banach Center Publications vol. 39, 1997.
- Robert J Budzynski. Remarks on tree-level topological string theories. Acta Phys.Polon. B28:2027-2037, 1997.
- Robert J. Budzynski, Michal A. Spalinski. On the chiral algebra of topological conformal field theory. Phys.Lett. B275:75-81, 1992.
- E. Leader, E. Predazzi; translated to Polish by RJ Budzyński. Wstęp do teorii oddziaływań kwarków i leptonów (orig. An Introduction to Gauge Theories and the "New Physics"). PWN Warszawa (ISBN 83-01-09699-3), 1990.
- Robert J. Budzynski, Michal A. Spalinski. Free energy of heterotic strings and covariant lattices. Int.J.Mod.Phys. A5:3053-3070, 1990.
- R.J. Budzynski, S. Klimek, P. Sadowski. The group of local biholomorphisms of C(1) and conformal field theory in the operator formalism. Commun.Math.Phys. 120:481-499, 1988.
teaching
Though teaching is currently not the #1 item in my job description, I continue to do some teaching as part of my work in the Physics Faculty.
In recent times this has been:
- Information Technology: actually a code name for an introduction to programming for beginners in Python
- Introduction to Databases: basics of processing of (mainly non-numeric) data, and an intro to relational databases and SQL, addressed to students of Neuroinformatics
In the more distant past I have taught practice classes in courses including undergraduate Math, Statistical Physics I, and Group Theory.
side projects
mostly finished
These projects are mostly feature complete. To appreciate them you probably need to be initiated in theoretical physics to some extent.
I deployed them to the surge.sh static site hosting service mostly because it's free and dead-easy to use, but they could equally well be hosted anywhere as the code runs purely in your browser and demands nothing from the server other than the capability to serve static files.
For those projects that leverage WebGPU, a relatively new technology, I made some effort to provide fallbacks using WebGL2—which is rather universally supported by browsers, unlike WebGPU—which to my knowledge is not fully supported on Linux by any browser. On the fallback, performance may be slightly degraded.
Nearly all the actual code was written by various LLM coding agents—mainly Google Gemini, versions 2.5 and 3. I played architect and project manager.
- Mathematical Billiards on a Variety of Figures: particles move on bounded planar regions, at constant velocity except for elastic bouncing off the edges. A demonstration of deterministic chaos. Implemented in pure Javascript and Canvas2d;
- Ising model on a two-dimensional lattice: a classic model of statistical physics, the simplest to display critical behavior; high-performance WebGPU-powered simulation on square lattices up to 1024x1024 nodes in size, implementing a variety of Monte Carlo algorithms;
- XY model on a two-dimensional lattice: in a similar vein as the above—a lattice of nearest-neighbor coupled planar rotators, anothe famous model of statistical physics;
- Vicsek model: a WebGPU-powered simulation of a seminal model of soft matter—self-propelled "particles" moving within a finite area, with a tendency to align their directions of motion (flocking), but subject to random "noise"; featuring interactive controls, measurement of order parameters, and high performance on consumer grade hardware.
- Topological Vicsek Model: a variant of the above, where each particle interacts not with its neighbors within a fixed distance, but with a fixed number of nearest neighbors irrespective of their distances. This model is computationally more challenging, and displays different behavior.
- Coupled Rotators: a simulation of two planar rotators minimally coupled as in the XY model (but dynamical), and with an external field. Numerically solved by Runge-Kutta and visualized in the browser.
prototypes, eye candy and old stuff
- made in collaboration with LLMs ("AI"), in an initial exploration of their coding capabilities:
- "polymers" on a lattice again (see below)
- Ising model, code by "AI" - nearly one-shot
- Vicsek model, not optimized (ie. canvas2d)
- a playground of various in-browser animations
- self-avoiding lattice polymers of sorts
- Ulam's spiral, a pattern on a plane created by prime numbers — which are computed on the fly in the browser
- a crude demo of a few interacting particles flying around in a rectangular box; while it's fun to watch for a while, it usually soon succumbs to numerical instability.
Among non-web projects, there's a yet not-quite-complete Python/OpenGL implementation of the Vicsek model, essentially identical to the web version mentioned above. UPDATE: not likely to be completed, since the in-browser implementations work so well.
contact
My private email is Robert@Budzynski.xyz. Use this to contact me about this page, my side projects, or other non-business matters.
You may also contact me:
I don't think anyone has ever contacted me via Signal or Twitter yet, still I'm keeping those options open 😏
Office:
ul. Ludwika Pasteura 5
02-093 Warszawa, Poland
phone: +48 22 5532 521
My work email is Robert.Budzynski@fuw.edu.pl.