Associate Professor
Department of Mathematical Sciences
E-mail: (my first name) dot math at gmail
Current research interest: lattice problems and related topics in number theory, homogeneous dynamics, cryptography.
CV is here.
Papers and preprints, in the order of completion:
A truncated inner product formula in the geometry of numbers (with S. Jin), preprint.
On counterexamples to the Mertens conjecture (with P. Q. Nguyen), ANTS XVI.
Souce files for experiments 1
Bounds on the gaps in the fractional parts of a linear form, PAMS, to appear.
A new upper bound on the smallest counterexample to the Mertens conjecture (with J. Rozmarynowycz), Exp. Math., to appear.
Source files for experiments 1
Adelic Rogers integral formula, JLMS, 109:e12830.
Higher-rank pointwise discrepancy bounds and logarithm laws for generic lattices (with M. Skenderi), Acta Arith., 205 (2022), 227-249.
A physical study of the LLL algorithm (with J. Ding, T. Takagi, Y. Wang, B. Yang), JNT, 244 (2023)
Source files for experiments 1 2
This is an augmented version of the 'LLL and stochastic sandpile models' below.
Mean value formulas on sublattices and flags of the random lattice, JNT, 241 (2022), 330-351.
Counting rational points on a Grassmannian, Mh. Math., (2023) 201: 825-864.
A stochastic variant of the abelian sandpile model (with Y. Wang), J. Stat. Phys., 178(3), 711-724.
LLL and stochastic sandpile models (with J. Ding, T. Takagi, Y. Wang), preprint.
LLL via the Lenstra graph (with J. Kim and M. Kim), preprint.
Random lattice vectors in a set of size O(n), IMRN, 2020(5):1385–1416, 04 2018.
The behavior of random reduced bases (with A. Venkatesh), IMRN, 2018(20):6442–6480, 2018.
On the distribution of lengths of short vectors in a random lattice, Math. Z., 282(3), 1117-1126.
Other stuff:
Vatsal seminar notes from Fall 2017 seminar at KIAS
Bachelor thesis (where I give an ``easy'' proof of the Roth's theorem on 3-progressions)