Email: niezipei2124@gmail.com
Welcome to my homepage! I am a senior researcher in Lagrange Mathematics and Computing Research Center, Huawei. Before joining Huawei, I earned my Ph.D. from Princeton University in 2020 under the guidance of Zoltán Szabó. My academic journey began at MIT, where I earned my Bachelor of Science in Mathematics in 2015. Here is my CV.
My research interests span across various areas, including low dimensional topology, algorithms, combinatorics, and random matrix theory, among others. In particular, two specific research topics need continued, long-term study in the future:
(1) The L-space Conjecture: This is a conjectural equivalence for irreducible rational homology 3-spheres, among not being a Heegaard Floer L-space, admitting a taut foliation, and having a left orderable fundamental group. Together with the Heegaard Floer Poincaré conjecture, it yields the Poincaré conjecture as a corollary. One potential method for resolving this conjecture involves developing a cut-and-paste framework to describe L-spaces.
(2) Eigenvector/Eigenvalue Distribution for Random Matrices with Correlated Entries: Random matrices find diverse applications in theoretical computer science, physics, and telecommunications. While the spectral behavior of random matrices with i.i.d. entries is well-understood, many realistic random matrix models do not follow to the same laws as the Gaussian ensembles, and lack basic spectral analysis. Exploring these models is valuable for real-world applications.
All of my works are publicly accessible and can be found below.
Chainmail links and non-left-orderability [fields: low dimensional topology]
arXiv:2310.16830
Petal diagram from simple braids [fields: low dimensional topology]
arXiv:2310.09569
Automated reasoning for proving non-orderability of groups [fields: automated reasoning, low dimensional topology, group theory]
(Joint with Alexei Lisitsa and Alexei Vernitski)
arXiv:2310.05891
Simpler analyses of union-find [fields: data structrue]
(Joint with Zhiyi Huang, Chris Lambert, and Richard Peng)
arXiv:2308.09021
Euclidean capacitated vehicle routing in random setting: A 1.55-approximation algorithm. [fields: approxiamation algorithm]
(Joint with Hang Zhou)
arXiv:2304.11281
On a conjecture of Knuth about forward and back arcs [fields: data structure, combinatorics]
arXiv:2301.05704
The number of correct guesses with partial feedback [fields: combinatorics]
arXiv:2212.08113
Matrix anti-concentration inequalities with applications [fields: random matrix theory, algorithm]
In Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing (STOC), pages 568–581, 2022 arXiv:2111.05553
Non-left-orderability of cyclic branched covers of pretzel knots P(3, -3, -2k-1) [fields: low dimensional topology]
(Joint with Lin Li)
Proceedings of the Japan Academy, Series A: Mathematical Sciences, 98(10), 2022 arXiv:2106.15582
Improved online correlated selection [fields: online algorithm]
(Joint with Ruiquan Gao, Zhongtian He, Zhiyi Huang, Bijun Yuan, and Yan Zhong)
In 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS), pages 1265–1276. IEEE, 2022 arXiv:2106.04224
An explicit description of (1, 1) L-space knots, and non-left-orderable surgeries [fields: low dimensional topology]
Communications of Huawei Research, VOL-001:212–219, 2021 arXiv:2102.10891
On 1-bridge braids, satellite knots, the manifold v2503 and non-left-orderable surgeries and fillings [fields: low dimensional topology]
arXiv:2003.14296
Topologically slice (1, 1)-knots which are not smoothly slice [fields: low dimensional topology]
arXiv:1901.07774
Left-orderability for surgeries on (-2, 3, 2s+1)-pretzel knots [fields: low dimensional topology]
Topology and its Applications, 261:1–6, 2019 arXiv:1803.00076
Linear restrictions on cone polynomials [fields: combinatorics]
(Joint with Weibo Fu)
arXiv:1510.04630
On the minimum area of null homotopies of curves traced twice [fields: combinatorics, group theory]
arXiv:1412.0101
Hilbert functions and the finite degree Zariski closure in finite field combinatorial geometry [fields: combinatorics]
(Joint with Anthony Y Wang)
Journal of Combinatorial Theory, Series A, 134:196–220, 2015 arXiv:1402.3018
Points on lines in \mathbb{F}_q^3 [fields: combinatorics]
(Joint with Anthony Y Wang)
MIT SPUR Final Papers. 2013 pdf