Nitya Mani

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.

Selected publications

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

Asymptotic enumeration

• Nearly all $k\textsf{-SAT}$ functions are unate
  with József Balogh, Dingding Dong, Bernard Lidicky, Yufei Zhao
  [ arXiv ] [ blog ] [ STOC '23 ]
  
  Enumerating $k\textsf{-SAT}$ functions
  with Dingding Dong, Yufei Zhao
  [ arXiv ] [ blog ] [ SODA '22 ] [ talk ]
  
• On sum-intersecting families of positive integers
  with Aaron Berger
  [ arXiv ]
  
• A fourth moment phenomenon for asymptotic normality of monochromatic subgraphs
  with Sayan Das, Zoe Himwich
  [ arXiv ] [ Random Structures Algorithms ]
  
• On the number of error correcting codes
  with Dingding Dong, Yufei Zhao
  [ arXiv ] [ Combin. Probab. Comput. ]
  

Sampling + statistical physics

• Strong spatial mixing for colorings on trees and its algorithmic applications
  with Zongchen Chen, Kuikui Liu, Ankur Moitra
  [ arXiv ] [ FOCS '23 ]
  

• From algorithms to connectivity and back: finding a giant component in random $k\textsf{-SAT}$
  with Zongchen Chen, Ankur Moitra
  [ arXiv ] [ SODA '23 ]
  

• Maximum gaps in one-dimensional hard-core models
  with Dingding Dong
  [ arXiv ]
  

Probabilistic graph theory

• 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 ]
  
• Extremal results on feedback arc sets in digraphs
  with Jacob Fox, Zoe Himwich
  [ arXiv ] [ Random Structures Algorithms ]
  
• Making an $H$-free graph $k$-colorable
  with Jacob Fox, Zoe Himwich
  [ arXiv ] [ J. 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 ]
  

Algebraic number theory

• Diophantine tuples over $\mathbb{Z}_p$
  with Simon Rubinstein-Salzedo
  [ arXiv ] [ Acta Arith. ]
• Shifted convolution $L$-series values for elliptic curves
  with Asra Ali
  [ arXiv ] [ Arch. Math. ]
  
• Infinite product exponents for modular forms
  with Asra Ali
  [ arXiv ] [ Res. Number Theory ]
  

Contact

Email: nmani@mit.edu

Accessibility