Research Interests
My research is in probability and combinatorics. A lot of my work involves using complex- and Fourier-analytic techniques in discrete settings; often, the problems I work on have origins in statistical physics or theoretical computer science.
Publications and Preprints
- 29. On random polynomials with an intermediate number of real roots
preprint, submitted
with Sean O'Rourke
- 28. Almost sure behavior of the zeros of iterated derivatives of random polynomials
preprint, submitted
with Xuan-Truong Vu
- 27. Fluctuations in the logarithmic energy for zeros of random polynomials on the sphere
preprint, submitted
with Oren Yakir
- 26. Zeros of a growing number of derivatives of random polynomials with independent roots
preprint, under revision
with Xuan-Truong Vu
- 25. Sums of random polynomials with differing degrees
preprint, under revision
with Isabelle Kraus and Sean O'Rourke
- 24. Potential-weighted connective constants and uniqueness of Gibbs measures
preprint, submitted
with Will Perkins
- 23. Random polynomials: the closest roots to the unit circle
preprint, submitted
with Julian Sahasrabudhe
- 22. The frog model on Galton-Watson trees
preprint, under revision
with Josh Rosenberg
- 21. Central limit theorems and the geometry of polynomials
preprint, submitted
with Julian Sahasrabudhe
- 20. The singularity probability of a random symmetric matrix is exponentially small
Accepted, Journal of the American Mathematical Society
with Marcelo Campos, Matthew Jenssen, and Julian Sahasrabudhe
- 19. The least singular value of a random symmetric matrix
Accepted, Forum of Mathematics, Pi
with Marcelo Campos, Matthew Jenssen, and Julian Sahasrabudhe
- 18. Optimal mixing of the down-up walk on independent sets of a given size
Accepted, 64th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2023)
with Vishesh Jain, Huy Tuan Pham and Thuy-Duong Vuong
- 17. Quasipolynomial-time algorithms for Gibbs point processes (2023)
Combinatorics, Probability and Computing
with Matthew Jenssen and Mohan Ravichandran
- 16. Maximum entropy and integer partitions (2023)
Combinatorial Theory
with Gweneth McKinley and Will Perkins
- 15. Analyticity for classical gasses via recursion (2022)
Communications in Mathematical Physics
with Will Perkins
- 14. Strong spatial mixing for repulsive point processes (2022)
Journal of Statistical Physics
with Will Perkins
- 13. Direct design of biquad filter cascades with deep learning by sampling random polynomials (2022)
The International Conference on Acoustics, Speech, & Signal Processing 2022
Joseph T. Colonel, Christian J. Steinmetz, Marcus Michelen, Joshua D. Reiss
- 12. Anti-concentration of random variables from zero-free regions (2022)
Discrete Analysis.
with Julian Sahasrabudhe
- 11. Singularity of random symmetric matrices revisited (2022)
Proceedings of the American Mathematical Society.
with Marcelo Campos, Matthew Jenssen, and Julian Sahasrabudhe
- 10. Success probability for selectively neutral invading species in the line model with a random fitness landscape (2021)
Studies in Applied Mathematics.
with with Suzan Farhang-Sardroodi, Natalia L. Komarova, and Robin Pemantle
- 9. Real roots near the unit circle of random polynomials (2021)
Transactions of the American Mathematical Society
- 8. A characterization of polynomials whose high powers have non-negative coefficients (2020)
Discrete Analysis
with Julian Sahasrabudhe
- 7. Asymptotic bounds on graphical partitions and partition comparability (2020)
International Mathematics Research Notices
with Stephen Melczer and Somabha Mukherjee
- 6. Quenched Survival of Bernoulli Percolation on Galton-Watson Trees (2020)
Journal of Statistical Physics
with Robin Pemantle and Josh Rosenberg
- 5. The frog model on non-amenable trees (2020)
Electronic Journal of Probability
with Josh Rosenberg
- 4. A Short Note on the Average Maximal Number of Balls in a Bin (2020)
Journal of Integer Sequences
- 3. Central limit theorems from the roots of probability generating functions (2019)
Advances in Mathematics
with Julian Sahasrabudhe
- 2. Critical Percolation and the Incipient Infinite Cluster on Galton-Watson Trees (2019)
Electronic Communications in Probability
- 1. Invasion Percolation on Galton-Watson Trees (2019)
Electronic Journal of Probability
with Robin Pemantle and Josh Rosenberg
Other publications and preprints
- Automatic Origami Crease Pattern Generation from k-uniform Tilings
Bridges 2023 Conference Proceedings, to appear
David Goncharov, Marcus Michelen, Uyen Nguyen
- Folding Functions: Origami Corrugations from Equations
Bridges 2019 Conference Proceedings
Uyen Nguyen, Be Fritzson, Marcus Michelen