I am a PhD student in the Department of Mathematics at MIT. I am excited by problems in extremal graph theory, discrete probability, and convex optimization. I am fortunate to be advised by Pablo Parrilo and Yufei Zhao.

See Google Scholar or the arXiv for an updated/more complete listing.

- Maximum gaps in one-dimensional hard-core models

*with Dingding Dong*

[ arXiv ]

- From algorithms to connectivity and back: finding a giant component in random $k\textsf{-SAT}$

*with Zongchen Chen, Ankur Moitra*

[ arXiv ] [ SODA '23 ]

- Nearly all $k\textsf{-SAT}$ functions are unate

*with József Balogh, Dingding Dong, Bernard Lidicky, Yufei Zhao*

[ arXiv ] [ blog ]

- On the number of error correcting codes

*with Dingding Dong, Yufei Zhao*

[ arXiv ]

- Enumerating $k\textsf{-SAT}$ functions

*with Dingding Dong, Yufei Zhao*

[ arXiv ] [ SODA '22 ] [ blog ] [ talk ]

- A note on directed analogues of the Sidorenko and forcing conjectures

*with Jacob Fox, Zoe Himwich, Yunkun Zhou*

[ arXiv ]

- Turán problems for mixed graphs

*with Edward Yu*

[ arXiv ]

- A fourth moment phenomenon for asymptotic normality of monochromatic subgraphs

*with Sayan Das, Zoe Himwich*

[ arXiv ]

- Extremal results on feedback arc sets in digraphs

*with Jacob Fox, Zoe Himwich*

[ arXiv ]

- Making an $H$-free graph $k$-colorable

*with Jacob Fox, Zoe Himwich*

[ arXiv ] [ Journal of Graph Theory ]

- Lower bounds on $\textsf{Max-Cut}$ in $H$-free graphs via semidefinite programming

*with Charles Carlson, Alexandra Kolla, Ray Li, Benny Sudakov and Luca Trevisan*

[ arXiv ] [ SIAM J. Discrete Math ] [ LATIN '20 ]

- Diophantine tuples over $\mathbb{Z}_p$

*with Simon Rubinstein-Salzedo*

[ arXiv ] [ Acta Arithmetica ] - Shifted convolution $L$-series values for elliptic curves

*with Asra Ali*

[ arXiv ] [ Archiv der Mathematik ]

- Infinite product exponents for modular forms

*with Asra Ali*

[ arXiv ] [ Research in Number Theory ]

Email: nmani@mit.edu