Current Research Interests
 Probability theory, Mathematical foundations of data science, Mathematical physics
People
 Justin Ko (postdoc, current)
 Aseem Baranwal (PhD CS, current)
 Taj JonesMcCormick (PhD Stats, current)
 Varnan Sarangian (PhD Stats, current)
 Parsa Rangriz (MMath Stat, current)
 Lily Seebach (MMath Data Science, current)
 Yiming Xu (postdoc, now Asst. Prof. at U. Kentucky)
 Victor Issa (ENS M2 Intern, 2023, now PhD at ENS Lyons)
 Tingzhou Yu (MMath Stat, 2023, now PhD at U. Alberta)
 Philipp Schroeppel (MMath Stat, 2022, now PhD at Ulm U.)
 Anna Brandenberger (MSc, Perimeter Institute, 2022, now PhD at MIT)
Publications and preprints

 Finding planted cliques using Markov Chain Monte Carlo
 with R. Gheissari and Y. Xu,
 arXiv

 Shattering in the Ising pure pspin model
 with D. Gamarnik and E. Kizildag,
 arXiv

 Differentially private multivariate medians
 with K. Ramsay and S. Chenouri,
 arXiv

 Existence of the free energy for heavytailed spin glasses
 with P. Lopatto,
 Communications in Mathematical Physics 405 (2024) no. 226

 Circuit lower bounds for the pspin optimization problem,
 with D. Gamarnik and A. S. Wein,
 Markov Processes and Related Fields 30 no. 1 (2024) 8196 (special issue for IRS 2022)

 Highdimensional SGD aligns with emerging outlier eigenspaces
 with G. Ben Arous, R. Gheissari,
and J. Huang,
 International Conference on Learning Representations 12 (ICLR 2024) (spotlight)

 Hardness of random optimization problems for boolean circuits, lowdegree polynomials, and Langevin dynamics,
 with D. Gamarnik and A. S. Wein,
 SIAM Journal on Computing 53 no. 1 (2024) 146

 Highdimensional limit theorems for SGD: Effective dynamics and critical scaling
 with G. Ben Arous and R. Gheissari,
 Communications on Pure and Applied Mathematics 77 no. 3 (2024) 20302080
 Extended abstract appeared in NeurIPS 2022 (Outstanding Paper Award)

 Shattering versus metastability in spin glasses,
 with G. Ben Arous,
 Communications on Pure and Applied Mathematics 77 no. 1 (2024) 139176

 Optimality of MessagePassing Architectures for Sparse Graphs
 with A. Baranwal and K. Fountoulakis,
 Advances in Neural Information Processing Systems 37 (NeurIPS) 2023

 Graph attention retrospective
 K. Fountoulakis, A. Levi, S. Yang, A. Baranwal and A.J.,
 Journal of Machine Learning Research 24 no. 246 (2023) 152

 Effects of Graph Convolutions in MultiLayer Networks
 with A. Baranwal and K. Fountoulakis,
 International Conference on Learning Representations 11 (ICLR) 2023 (spotlight)

 A simple construction of the dynamical Φ^{4}_{3} model,
 with
N. Perkowski,
 Transactions of the American Mathematical Society 376 no. 3 (2023) 1507–1522

 The overlap gap property in principal submatrix recovery,
 with D. Gamarnik and S. Sen,
 Probability Theory and Related Fields 181 (2021) 757–814

 Graph Convolution for SemiSupervised Classification: Improved Linear Separability and OutofDistribution Generalization,
 with A. Baranwal and K. Fountoulakis,
 International Conference on Machine Learning 38 (ICML 2021) (spotlight)
 Proceedings of Machine Learning Research 139 (2021) 684693

 Online stochastic gradient descent on nonconvex losses from highdimensional inference,
 with G. Ben Arous and R. Gheissari,
 Journal of Machine Learning Research 22 no. 106 (2021) 151

 On the unbalanced cut problem and the generalized SherringtonKirkpatrick model,
 with S. Sen,
 Annales de l'Instut Henri Poincaré D Comb. Phys. Inter. 8 (2021) 3588.

 The overlap gap property and approximate message passing algorithms for pspin models,
 with D. Gamarnik,
 The Annals of Probability 49 no. 1 (2021) 180205

 Low degree hardness of random optimization problems,
 with D. Gamarnik and A. S. Wein
 Foundations of Computer Science (FOCS) (2020) 131140

 Statistical thresholds for tensor PCA,
 with P. Lopatto and L. Miolane,
 The Annals of Applied Probability 30 no. 4 (2020) 19101933

 Algorithmic thresholds for tensor PCA,
 with G. Ben Arous and R. Gheissari,
 The Annals of Probability 48 no. 4 (2020) 20522087

 Bounding flows for spherical spin glass dynamics,
 with G. Ben Arous and R. Gheissari,
 Communications in Mathematical Physics 373 (2020) 10111048

 Dynamics of mean field spin glasses on short and long timescales,
 Journal of Mathematical Physics 60, 083305 (2019)

 Thouless–Anderson–Palmer equations for generic pspin glasses,
 with A. Auffinger,
 The Annals of Probabability 47 no. 43 (2019) 22302256

 On the spectral gap of spherical spin glass dynamics,
 with R. Gheissari,
 Annales de l'Institut Henri Poincaré B Probab. et Stat. 55 no. 2 (2019) 756776

 On spin distributions for generic pspin models,
 with A. Auffinger,
 Journal of Statistical Physics (2019) 174316

 Spectral gap estimates in mean field spin glasses,
 with G. Ben Arous,
 Communications in Mathematical Physics 361 no. 1 (2018) 152

 MAX κCUT and the inhomogeneous Potts spin glass,
 with J. Ko and S. Sen,
 The Annals of Applied Probability 28 no. 3 (2018) 1536–1572

 Bounding the complexity of replica symmetry breaking for spherical spin glasses,
 with I. Tobasco,
 Proceedings of the American Mathematical Society 146 (2018) 31273142

 Random matrices and the New York City subway system,
 with T. Trogdon,
 Physical Review E 96, 030101(R) (2017)

 Low temperature asymptotics of spherical mean field spin glasses,
 with I. Tobasco,
 Communications in Mathematical Physics 352 no. 3 (2017) 9791017

 Some properties of the phase diagram for mixed pspin glasses,
 with I. Tobasco,

Probability Theory and Related Fields 167 (2017) 615672
(slides)

 Approximate ultrametricity for random measures with applications to spin glasses,
 Communications on Pure and Applied Mathematics 70 (2017) 611–664 (video)

 A dynamic programming approach to the Parisi functional,
 with I. Tobasco,
 Proceedings of the American Mathematical Society 144 (2016) 31353150

 On the overlap distribution of branching random walks,
 Electronic Journal of Probability 21 no. 50 (2016) 16 pp.

 Variational and Structural Methods in Mean Field Spin Glasses,
 Ph.D. Thesis, May 2016

 Solution of the propeller conjecture in R^{3},
 with S. Heilman and A. Naor
 Discrete & Compututational Geometry 50 (2013) 263305 (code)
 Extended abstract appeared at STOC 2012.

 Charged particle motion in electromagnetic fields varying moderately slowly in space,
 with H. Weitzner,

 Physics of Plasmas 18, 104510 (2011)