Peter Scholze (left) and Dustin Clausen are undertaking an ambitious project to generate an entire new category of mathematical objects. Their work retains all of the best parts of topological spaces — without the drawbacks. www.quantamagazine.org/two-research...

You may find the comments by Melanie Matchett Wood on the discovery of a counter example to Erdős’ Unit Distance Conjecture as interesting as I did 👇🏼(see previous post for a link)

Jason Li, Stephen Muirhead: The maximum of a strongly correlated Gaussian process https://arxiv.org/abs/2605.20700 https://arxiv.org/pdf/2605.20700 https://arxiv.org/html/2605.20700

With this, let me share an important announcement - I am actively seeking highly motivated & mathematically inclined PhD students to work on problems at the intersection of TCS, probability & mathematical physics! If you are interested, and have a strong math background, get in touch!

Xiaodong Yang, Subhabrata Sen, Yue M. Lu: Sharp Spectral Thresholds for Multi-View Spiked Wigner Models https://arxiv.org/abs/2605.19894 https://arxiv.org/pdf/2605.19894 https://arxiv.org/html/2605.19894

Update: We fixed a small bug about the MLSI for our final Glauber sampler; we now use entropy-contraction of the polarized walk instead (since Glauber might not work). More exposition for theorem-5.1 also added. Many thanks to reviewers for a careful reading! 1/2

Yuichi Yoshida Tolerant Testing for Unique Games https://arxiv.org/abs/2605.17760

Lu\'is Daniel Abreu, Tomoyuki Shirai: Zero correlations and averaged fields of orthonormal Gaussian functions https://arxiv.org/abs/2605.17296 https://arxiv.org/pdf/2605.17296 https://arxiv.org/html/2605.17296

Bin Gui: Conformal Blocks: Vector bundle structures, Sewing, and Factorization https://arxiv.org/abs/2605.17020 https://arxiv.org/pdf/2605.17020 https://arxiv.org/html/2605.17020

Rafael Chiclana: Nonconcentration of hitting times for random walks on graphs https://arxiv.org/abs/2605.17513 https://arxiv.org/pdf/2605.17513 https://arxiv.org/html/2605.17513

Ron Nissim: Deconfinement For $\mathrm{SO}(3)$ Lattice Yang-Mills at Strong Coupling https://arxiv.org/abs/2605.16162 https://arxiv.org/pdf/2605.16162 https://arxiv.org/html/2605.16162

Alexey Sevostyanov: A tree-free approach to 3D Yang-Mills Langevin dynamic. Analytic estimates and the existence of a model for a regularity structure https://arxiv.org/abs/2605.14616 https://arxiv.org/pdf/2605.14616 https://arxiv.org/html/2605.14616

Nils Berglund: Topics in Gaussian Wiener chaos expansion https://arxiv.org/abs/2605.14630 https://arxiv.org/pdf/2605.14630 https://arxiv.org/html/2605.14630

Anouar Kouraich, Simone Warzel: Lower bound on the mixing time of $p$-spin glasses https://arxiv.org/abs/2605.14681 https://arxiv.org/pdf/2605.14681 https://arxiv.org/html/2605.14681

Stefan Tappe: Rough path theory and an introduction to rough partial differential equations https://arxiv.org/abs/2605.10150 https://arxiv.org/pdf/2605.10150 https://arxiv.org/html/2605.10150

Boaz Klartag: Poisson approximation of random lattices https://arxiv.org/abs/2605.10479 https://arxiv.org/pdf/2605.10479 https://arxiv.org/html/2605.10479

Christof F. Peter, Martin Slowik: Scaling limits for nonlinear functionals of the discrete Gaussian free field with degenerate random conductances https://arxiv.org/abs/2605.10884 https://arxiv.org/pdf/2605.10884 https://arxiv.org/html/2605.10884

Dongming Merrick Hua, Antoine Song, Stefan Tudose: On Talagrand's Convexity Conjecture https://arxiv.org/abs/2605.10908 https://arxiv.org/pdf/2605.10908 https://arxiv.org/html/2605.10908

Rui Okayasu: Geometric Means and Lebesgue-type Decomposition of Completely Positive Maps https://arxiv.org/abs/2605.06019 https://arxiv.org/pdf/2605.06019 https://arxiv.org/html/2605.06019

Jnaneshwar Baslingker, B\'alint Vir\'ag: The Efron-Stein inequality for identically distributed pairs https://arxiv.org/abs/2605.05388 https://arxiv.org/pdf/2605.05388 https://arxiv.org/html/2605.05388

Gerard Ben Arous, Pax Kivimae: Wandering Exponents and the Free Energy of the High-Dimensional Elastic Polymer https://arxiv.org/abs/2605.05631 https://arxiv.org/pdf/2605.05631 https://arxiv.org/html/2605.05631

Theodoros Assiotis, Zahra Sadat Mirsajjadi: $\mathsf{GL}_N(\mathbb{C})$ Brownian motion and stochastic PDE on entire functions https://arxiv.org/abs/2605.06429 https://arxiv.org/pdf/2605.06429 https://arxiv.org/html/2605.06429

UIUC Canvas has been hacked, as have many more universities. The hackers clearly know that finals are ongoing to maximize damage with this.

We just put out a 180-page paper on sampling from the SK model! One big surprise we ran into: the Hessian Ascent algorithms investigated for non-convex optimization have been diffusion models in disguise the whole time! arxiv.org/abs/2605.03718 @freegaussians.bsky.social @oldheneel.bsky.social

Rollo-Davidson prizes for this year have been announced!

With @oldheneel.bsky.social and @jnshi.bsky.social (+Ewan), we extend the PHA framework developed to optimize the SK model to become a negligible TVD-error sampler for beta < 1/2. 2 key conceptual observations: PHA implements ASL at high-temperature + Jarzynski's gives a way to rejection sample 1/2

David Gamarnik, Mikl\'os Z. R\'acz, Gabe Schoenbach Optimal Hardness of Online Algorithms for Large Common Induced Subgraphs https://arxiv.org/abs/2605.03893

Yi Han: Glauber dynamics for random field Ising models on bounded degree graphs and MLSI https://arxiv.org/abs/2605.02002 https://arxiv.org/pdf/2605.02002 https://arxiv.org/html/2605.02002

Octavio Arizmendi, Katsunori Fujie: An analytic approach to the finite R-transform https://arxiv.org/abs/2605.02093 https://arxiv.org/pdf/2605.02093 https://arxiv.org/html/2605.02093

Filippo Giovagnini, Sotirios Kotitsas, Marco Romito: Universality in Deep Neural Networks: An approach via the Lindeberg exchange principle https://arxiv.org/abs/2605.02771 https://arxiv.org/pdf/2605.02771 https://arxiv.org/html/2605.02771

Yichao Huang: Royen's proof of the Gaussian correlation inequality as a supersymmetric dimensional reduction https://arxiv.org/abs/2605.00533 https://arxiv.org/pdf/2605.00533 https://arxiv.org/html/2605.00533

Siu On Chan, Tommaso d'Orsi, Jeff Xu Strongly Refuting Random CSP without Literals https://arxiv.org/abs/2604.27336

Renjie Feng, Dong Yao: Smallest distances between zeros of Gaussian analytic functions https://arxiv.org/abs/2604.26316 https://arxiv.org/pdf/2604.26316 https://arxiv.org/html/2604.26316

Yihan Zhang: Sharp One-Dimensional Sub-Gaussian Comparison in Convex Order https://arxiv.org/abs/2604.26819 https://arxiv.org/pdf/2604.26819 https://arxiv.org/html/2604.26819

Manaka Okuyama, Masayuki Ohzeki Griffiths inequalities and Gibbs-Bogoliubov inequality for general gauge glasses with Gaussian disorder on Nishimori line https://arxiv.org/abs/2604.25697

Walid Hachem The SK model with a sparse variance profile: free energy and AMP algorithm for TAP equations at high temperature https://arxiv.org/abs/2604.25535

Luis A. Cede\~no-P\'erez, Alexis E. L\'opez-Vel\'azquez Invariant Measures in Hamiltonian Systems: The Analytical Foundations of Statistical Physics https://arxiv.org/abs/2604.25066

Markus Heydenreich, Christian Hirsch, Matthias L\"owe: A mathematical analysis of hierarchical Hopfield models https://arxiv.org/abs/2604.25470 https://arxiv.org/pdf/2604.25470 https://arxiv.org/html/2604.25470

Jason Miller, Yi Tian: The conformal dimension of the Brownian tree is one https://arxiv.org/abs/2604.25769 https://arxiv.org/pdf/2604.25769 https://arxiv.org/html/2604.25769

James Bona-Landry: Invariant measures for the open KPZ equation: the Gaussian case https://arxiv.org/abs/2604.23462 https://arxiv.org/pdf/2604.23462 https://arxiv.org/html/2604.23462

Nicolas Tokka: Local Limit of Random Regular Bipartite Planar Maps https://arxiv.org/abs/2604.24677 https://arxiv.org/pdf/2604.24677 https://arxiv.org/html/2604.24677

A. Mazel, I. Stuhl, Y. Suhov A Nearest-Neighbor Hard-Core Model on a Penrose Graph https://arxiv.org/abs/2604.21086

Melchior Wirth The KMS and GNS Spectral Gap of Quantum Markov Semigroups https://arxiv.org/abs/2604.21630

Phan Th\`anh Nam, Rongchan Zhu, Xiangchan Zhu Derivation of Gibbs measure from Gibbs state with the fractional Bessel interaction in Two Dimensions https://arxiv.org/abs/2604.21583

Reza Gheissari, Curtis Grant, Tianmin Yu: Mixing times of Langevin dynamics for spiked matrix models https://arxiv.org/abs/2604.20008 https://arxiv.org/pdf/2604.20008 https://arxiv.org/html/2604.20008

Jeanne Boursier: The Legendre structure of the TAP complexity for the Ising spin glass https://arxiv.org/abs/2604.20660 https://arxiv.org/pdf/2604.20660 https://arxiv.org/html/2604.20660

Antonio Blanca, Reza Gheissari, Heehyun Park, Xusheng Zhang: Uniqueness and Mixing in the Low-Temperature Random-Cluster Model on Trees and Random Graphs https://arxiv.org/abs/2604.20693 https://arxiv.org/pdf/2604.20693 https://arxiv.org/html/2604.20693

Avijit Mandal, Henry D. Pfister Quantum Message Passing for Factor Graphs over Finite Abelian Groups https://arxiv.org/abs/2604.12186

Absolutely wonderful work from @davidjekel.myatproto.social ! Following up on his previous work where he looked at information geometry for certain ensembles of random matrices!

This is a wonderful result. In a few days, I will push something to arXiv and then comment a bit more on this paper, in particular a lemma in this paper using a certain Ito computation to prove a bound. Anyway - Nice to have a proof that the RS regime extends all the way to the dAT line!