Christian Gorski's Homepage

Research Interests

I am broadly interested in probability and statistical physics, and especially its interactions with other areas such as (geometric) group theory, coarse geometry, ergodic theory, and combinatorics. My current research is in first passage percolation and percolation on exotic graphs, particularly graphs of polynomial growth. Click here for a brief summary of my research so far (last updated 17 Dec 2023).

Actually, my interests are much broader, although the above is my current research focus. As a general rule, I am most excited when different areas of math interact. Some subjects that I am interested in in themselves include mathematical biology, condensed matter physics, many-player game theory, generally emergent behavior and phase transitions in complex systems; computer science, complexity theory, combinatorial optimization; group theory, additive combinatorics; rigidity phenomena, stability and testability (i.e. suppose that an object "almost" has some mathematical structure; is it "close" to an object that genuinely has that structure?). I am especially interested in applying the tools of probability theory, dynamics, metric geometry, coarse geometry and topology, combinatorics, analysis, representation theory, and operator algebras to the above areas. I certainly cannot claim expertise in all of the areas mentioned above, but I can claim enthusiasm (and many of the above areas I have done a fair amount of reading into)---I am always very open to conversations about ideas in any of these arenas!

Publications

Gorski, C. Strict monotonicity for first passage percolation on graphs of polynomial growth and quasi-trees, 2022. arXiv:2208.13922. To appear in Annals of Probability. arXiv 

Auffinger, A. and Gorski, C. Asymptotic shapes for stationary first passage percolation on virtually nilpotent groups. Probability Theory and Related Fields 186, 285-326 (2023). arXiv 

Recorded talks

I gave a mini-course on some classical results in percolation in the Randomness and Geometry Seminar at the Fields Insititute's Thematic Program on Randomness and Geometry. The course starts from very basics and goes through the proof of the Burton-Keane theorem (uniqueness of the infinite cluster for amenable graphs) and Duminil-Copin and Tassion's proof of sharpness of the phase transition.

Lecture 1: Definitions, weak existence of phase transition.

Lecture 2: Proof of the Burton-Keane theorem (uniqueness of the infinite cluster for amenable graphs).

Lecture 3: More on (non)uniqueness, and some tools---FKG and BK inequalities and Russo's formula.

Lecture 4: Duminil-Copin and Tassion's proof of sharpness of the phase transition.