Aukosh S. Jagannath

Current Research Interests

• Probability Theory and Analysis
• Applications to Statistical Physics, Combinatorics, Math of data science, and High-dimenisonal Statistics

Publications

1. Statistical Thresholds for Tensor PCA,

   with P. Lopatto and L. Miolane arXiv

2. Algorithmic Thresholds for Tensor PCA,

   with G. Ben Arous and R. Gheissari ArXiv

3. Bounding flows for spherical spin glass dynamics,

   with G. Ben Arous and R. Gheissari ArXiv

4. On the unbalanced cut problem and the generalized Sherrington-Kirkpatrick model,

   with S. Sen, ArXiv

5. Thouless-Anderson-Palmer equations for generic p-spin glasses,

   with A. Auffinger, Ann. Probab. 47 (2019), no. 4, 2230--2256

6. On the Spectral Gap of Spherical Spin Glass Dynamics,

   with R. Gheissari, Ann. Inst. H. Poincare Probab. Statist., Vol. 55, No. 2 (2019) 756-776

7. On spin distributions for generic p-spin models,

   with A. Auffinger, J Stat Phys (2019) 174: 316

8. Spectral Gap Estimates in Mean Field Spin Glasses,

   with G. Ben Arous, Commun. Math. Phys. 361 (1), 1-52 (2018)

9. MAX \kappa-CUT and the inhomogeneous Potts spin glass,

   with J. Ko and S. Sen, Ann. Appl. Probab. (2018), Vol. 28, No. 3, 1536–1572

10. Bounding the Complexity of Replica Symmetry Breaking for Spherical Spin Glasses,

    with I. Tobasco, Proc. Amer. Math. Soc. 146 (2018), 3127-3142

11. Random Matricies and the New York City Subway System,

    with T. Trogdon, Phys. Rev. E 96, 030101(R) (2017)

12. Low Temperature Asymptotics of Spherical Mean Field Spin Glasses,

    with I. Tobasco, Commun. Math. Phys. 352 (3), 979-1017 (2017)

13. Some Properties of the Phase Diagram for Mixed p-Spin Glasses,

    with I. Tobasco, Probab. Theory Relat. Fields (2017) 167:615-672 (slides)

14. Approximate Ultrametricity for Random Measures with Applications to Spin Glasses,

    Comm. on Pure and Appl. Math 70 (2017), 611–664. (video)

15. A Dynamic Programming Approach to the Parisi Functional,

    with I. Tobasco, Proc. Amer. Math. Soc. 144 (2016), 3135-3150

16. On the Overlap Distribution of Branching Random Walks,

    Electron. J. Probab., 21 (2016), no. 50, 16 pp.

17. Solution of the Propeller Conjecture in R³,

    with S. Heilman and A. Naor, Disc. & Comput. Geom. (2013) 50: 263 (code)

    An extended abstract appeared at STOC 2012.

18. Charged Particle Motion in Electromagnetic Fields Varying Moderately Slowly in Space,

    with H. Weitzner, Physics of Plasmas 18, 104510 (2011)

Pages Concerning Research Projects

A rigorous, computational solution of the Propeller Conjecture in R^3