Publications and Preprints

Publications

• Fermat’s polygonal number theorem for repeated generalised polygonal numbers, with Soumyarup Banerjee, Ben Kane, Muratzhan Kyranbay, Dayoon Park, Sagnik Saha, Hiu Chun So, and Piyush Varyani, Journal of Number Theory, 2020. [doi] [arxiv]
• The arithmetic rank of the residual intersections of a complete intersection ideal, with Kesavan Mohana Sundaram, Taylor Murray, and Vaibhav Pandey, to appear in International Mathematics Research Notices. [arxiv]

Preprints

• Elimination templates in Macaulay2, with Cheng Chen, Anna Natalie Chlopecki, Timothy Duff, William Huang, Aolong Li, and Wanchun Shen. [pdf][https://manav77.github.io/assets/pdf/m2eliminationtemplates.pdf]
• Vanishing of local cohomology in unramified mixed characteristic. [arxiv]
• Syzygies of associated graded modules, with Hariharan Ananthnarayan and Omkar Javadekar. [arxiv]