Nitya Mani

I am a PhD student in the Department of Mathematics at MIT. I am excited by problems in probabilistic combinatorics, number theory, and convex optimization.

Selected publications

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

Approximate sampling + statistical physics

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

Asymptotic enumeration

• 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 ]
  

Probabilistic graph theory

• 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 ]
  

Algebraic number theory

• 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 ]
  

Contact

Email: nmani@mit.edu

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