Current Research Interests
 Probability theory, Mathematics of data science, Mathematical physics
Publications and preprints

 Existence of the free energy for heavytailed spin glasses
 with P. Lopatto
arXiv

 Concentration of the exponential mechanism and differentially private multivariate medians
 with K. Ramsay and S. Chenouri arXiv

 Graph attention retrospective
 K. Fountoulakis, A. Levi, S. Yang, A. Baranwal and A.J. arXiv

 Hardness of random optimization problems for boolean circuits, lowdegree polynomials, and Langevin dynamics,
 with D. Gamarnik and A. S. Wein, arXiv

 Circuit lower bounds for the pspin optimization problem,
 with D. Gamarnik and A. S. Wein, Markov Proc. Relat. Fields (special issue for IRS 2022) (to appear)

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

 Shattering versus metastability in spin glasses,
 with G. Ben Arous, Comm. Pure Appl. Math (to appear)

 A simple construction of the dynamical Φ^{4}_{3} model,
 with
N. Perkowski, Trans. Amer. Math. Soc. Vol. 376, No. 3, pp 1507–1522 (2023)

 Highdimensional limit theorems for SGD: Effective dynamics and critical scaling
 with G. Ben Arous and R. Gheissari, Advances in Neural Information Processing Systems 36 (NeurIPS 2022), (Outstanding Paper Award) Full version: arXiv

 The overlap gap property in principal submatrix recovery,
 with D. Gamarnik and S. Sen, Probab. Theo. Relat. Fields 181, pp 757–814 (2021)

 Graph Convolution for SemiSupervised Classification: Improved Linear Separability and OutofDistribution Generalization,
 with A. Baranwal and K. Fountoulakis, ICML 2021, Proc. Mach. Learn. Res. Vol 139 684693, 2021

 Online stochastic gradient descent on nonconvex losses from highdimensional inference,
 with G. Ben Arous and R. Gheissari, J. Mach. Learn. Res., Vol 22, No.106,151(2021)

 On the unbalanced cut problem and the generalized SherringtonKirkpatrick model,
 with S. Sen, Ann. Inst. Henri Poincaré Comb. Phys. Interact. 8 (2021), 3588.

 The overlap gap property and approximate message passing algorithms for pspin models,
 with D. Gamarnik, Ann. Probab., Vol 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 pp. 131140.

 Statistical thresholds for tensor PCA,
 with P. Lopatto and L. Miolane, Ann. Appl. Probab. (2020), Vol. 30, No. 4, 19101933

 Algorithmic thresholds for tensor PCA,
 with G. Ben Arous and R. Gheissari, Ann. Probab. (2020), Vol. 48, No. 4, 20522087

 Bounding flows for spherical spin glass dynamics,
 with G. Ben Arous and R. Gheissari, Commun. Math. Phys. 373, 10111048 (2020)

 Dynamics of mean field spin glasses on short and long timescales,
 J. Math. Phys. 60, 083305 (2019)

 Thouless–Anderson–Palmer equations for generic pspin glasses,
 with A. Auffinger,
Ann. Probab. 47 (2019), no. 4, 22302256

 On the spectral gap of spherical spin glass dynamics,
 with R. Gheissari, Ann. Inst. H. Poincare Probab. Statist., Vol. 55, No. 2 (2019) 756776

 On spin distributions for generic pspin models,
 with A. Auffinger, J Stat Phys (2019) 174: 316

 Spectral gap estimates in mean field spin glasses,
 with G. Ben Arous, Commun. Math. Phys. 361 (1), 152 (2018)

 MAX \kappaCUT and the inhomogeneous Potts spin glass,
 with J. Ko and S. Sen, Ann. Appl. Probab. (2018), Vol. 28, No. 3, 1536–1572

 Bounding the complexity of replica symmetry breaking for spherical spin glasses,
 with I. Tobasco, Proc. Amer. Math. Soc. 146 (2018), 31273142

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

 Low temperature asymptotics of spherical mean field spin glasses,
 with I. Tobasco, Commun. Math. Phys. 352 (3), 9791017 (2017)

 Some properties of the phase diagram for mixed pspin glasses,
 with I. Tobasco,
Probab. Theory Relat. Fields (2017) 167:615672
(slides)

 Approximate ultrametricity for random measures with applications to spin glasses,
 Comm. Pure Appl. Math 70 (2017), 611–664. (video)

 A dynamic programming approach to the parisi functional,
 with I. Tobasco,
Proc. Amer. Math. Soc. 144 (2016), 31353150

 On the overlap distribution of branching random walks,
 Electron. J. Probab., 21 (2016), no. 50, 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,
Disc. & Comput. Geom. (2013) 50: 263 (code)
 An 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)