Post by Department of Mathematical Sciences, Gothenburg

Congratulations to Rolf A., who successfully defended his PhD thesis on 11 June 2026 🎉 Rolf’s thesis explores connections between algebraic geometry, arithmetic, and statistical mechanics through a previously undeveloped idea. One theme of the thesis is the use of canonical Kähler–Einstein metrics to define so-called heights, a measure of the arithmetic complexity of arithmetic objects. “In geometry, one is always looking for natural or canonical choices. But one challenge with canonical metrics is that they are typically highly non-explicit, and if a height is defined in terms of them, it too becomes hopelessly non-explicit. So how can we study it? This is where a statistical-mechanical perspective becomes useful. This contribution from physics is a major development in the field that my supervisor Robert Berman has pioneered.” Rolf first became interested in doctoral studies after taking a PhD-level course on fractals during his undergraduate education. His master's thesis was supervised by Robert Berman, and Rolf looked forward to working in mathematical physics. “But I never imagined I would end up working on something as abstract as heights. I was almost shocked when Robert suggested it as a PhD project! My background is fairly concrete – I come from an engineering perspective, even though I had already begun moving toward more abstract mathematics.” Read the full interview with Rolf on our website (in Swedish): https://lnkd.in/eXqaeQdE Title of the thesis: Partition functions in algebraic geometry: with applications to Arakelov geometry, Coulomb gases, Kähler–Einstein metrics and Gibbs stability Main supervisor: Robert Berman Examiner: Håkan Samuelsson Kalm Assistant supervisors: Jakob Hultgren and Klas Modin Opponent: José Ignacio Burgos Gil, Instituto de Ciencias Matemáticas (ICMAT), Spain #PhD #PhDDefence #Mathematics #AlgebraicGeometry #Arithmetic #StatisticalMechanics