If you drop a ball into a rugged landscape and let it roll, it will eventually reach a minimum. What height will it arrive to? With experiments one can say for each specific landscape and initial condition, but with less work one can predict what happens on average. Such predictions are typical of dynamical mean field theory.

But what if you change the kind of ball, or replace the ball with a mouse or robot? One can treat each set of behavior in turn and produce a zoo of predictions. However, there are certain features of high dimensional random landscapes that constrain the height reached by a large variety of agents.

Very intelligent rollers will find themselves stuck at a height given by the
*overlap gap property*, which bounds the performance of reasonable algorithms
given reasonable time using geometric properties of configuration space.
However, most approaches to these problems are not very intelligent: they behave
more like the stupid ball. We try to predict or bound where such approaches will land.

The above is quite abstract, but such questions are important in the physics of glasses and spin glasses, in the statistics of large inference problems, and in machine learning. We work at the intersection of these fields.

**On the topology of solutions to random continuous constraint satisfaction problems**, JK-D, arXiv:2409.12781 (2024)**Conditioning the complexity of random landscapes on marginal optima**, JK-D, arXiv:2407.02082 (2024)**Arrangement of nearby minima and saddles in the mixed spherical energy landscapes**, JK-D, SciPost Physics**16**, 001 (2024)**When is the average number of saddle points typical?**, JK-D, Europhysics Letters**143**, 61003 (2023)**How to count in hierarchical landscapes: a full solution to mean-field complexity**, JK-D & Jorge Kurchan, Physical Review E**107**, 064111 (2023)

The renormalization group of Kadanoff and Wilson famously explained Widom’s scaling, and has found application in nearly every field of physics. Mostly it is used to justify the blind application of Widom scaling in diverse settings, where critical exponents are fit by eyeballing an appropriate scaling collapse.

However, the renormalization group does not predict exponents: rather, exponents are a trait of the most commonly encountered type of critical point. But the scaling functions that describe critical singularities can take more diverse and strange forms than simple power laws.

In addition, there is little besides experience to justify the renormalization group’s application in general nonequilibrium systems. What kinds of nasty surprises await in their singular structure and corrections to scaling?

**Normal forms, universal scaling functions, and extending the validity of the RG**, James P. Sethna, David Hathcock, JK-D & Archishman Raju, in*50 years of the Renormalization Group: Dedicated to the memory of Michael E Fisher*, edited by Amnon Aharony, Ora Entin-Wohlman, David A Huse & Leo Radzihovsky (August 2024)**Normal form for renormalization groups**, Archishman Raju, Colin B Clement, Lorien X Hayden, JK-D, Danilo B Liarte, D Zeb Rocklin & James P Sethna, Physical Review X**9**, 021014 (2019)**Smooth and global Ising universal scaling functions**, JK-D & James P Sethna, arXiv:1707.03791 (2021)**Cluster representations and the Wolff algorithm in arbitrary external fields**, JK-D & James P Sethna, Physical Review E**98**, 063306 (2018)

Other topics in statistical mechanics and physics more broadly interest us.

What trait do magnetic fluids and maximally correlated local hidden variable theories share? As it happens, a zoo of interesting morphological phases and an effective description in terms of a novel integral transformation.

Landau–Ginsburg theory sheds light on the possible electronic order of a mysterious phase transition in a heavy fermion material, and a deterministic cost function designed to find Hadamard matrices produces glassy behavior.

Surprises lurk in the correlation functions of Monet’s paintings…

**Origin of symmetry breaking in the grasshopper model**, David Llamas, JK-D, Kun Chen, Adrian Kent & Olga Goulko, Physical Review Research**6**, 023235 (2024)**Energy driven pattern formation in planar dipole-dipole systems in the presence of weak noise**, JK-D & Andrew J Bernoff, Physical Review E**91**, 032919 (2015)**Elastic properties of hidden order in URu**, JK-D, Michael Matty & Brad J Ramshaw, Physical Review B_{2}Si_{2}are reproduced by a staggered nematic**102**, 075129 (2020)**Glass phenomenology in the hard matrix model**, Junkai Dong, Veit Elser, Gaurav Gyawali, Kai Yen Jee, JK-D, Avinash Mandaiya, Megan Renz & Yubo Su, Journal of Statistical Mechanics: Theory and Experiment**2021**, 093302 (2021)**Log-correlated color in Monet’s paintings**, JK-D, arXiv:2209.01989 (2022)

(from my collaborator)