About Me | Research | Contact | Miscellaneous
I am an EPSRC postdoctoral fellow at the Mathematical Institute, University of Warwick, hosted by Prof. Martin Lotz. Previously, I was a postdoctoral fellow at the University of Colorado at Boulder working under the supervision of Prof. Joshua Grochow. I obtained a PhD in May 2020 from Purdue University supervised by Prof. Saugata Basu and Prof. Elena Grigorescu.
At a very high level, I would describe my research interests as algebraic methods (broadly interpreted), taking inspiration from mathematical applications. The questions often have a topological flavour. Currently, I am working on some questions in homological algebra and commutative algebra with potential applications in computational complexity theory. During my PhD, I worked on topological questions in semialgebraic and o-minimal geometry (both deterministic and random), with a view toward incidence combinatorics.
Earlier, I got a masters degree from Brown University, USA, and a bachelors degree from R. V. College of Engineering, Bangalore, India.
| Attn! I am teaching a TCC course titled "Algebraic Methods in Computational Complexity Theory". Webpage here. |
Abhiram Natarajan. Betti Numbers of Deterministic and Random Sets in Semi-Algebraic and O-minimal Geometry. PhD Thesis, Purdue University, 2020. Defense slides.
Saugata Basu, Antonio Lerario, and Abhiram Natarajan. Betti Numbers of Random Hypersurface Arrangements. Journal of the London Mathematical Society, 2022. doi: 10.1112/jlms.12658. arXiv:1911.13256. Slides. Poster. Talk at ICERM.
Saugata Basu, Antonio Lerario, and Abhiram Natarajan. Zeros of Polynomials on Definable Hypersurfaces: Pathologies exist, but they are rare. Quarterly Journal of Mathematics, 2019. doi: 10.1093/qmath/haz022. arXiv:1803.00539. Slides. Talk by Saugata Basu at IHP.
Ilias Diakonikolas, Elena Grigorescu, Jerry Li, Abhiram Natarajan, Krzysztof Onak, and Ludwig Schmidt. Communication-Efficient Distributed Learning of Discrete Probability Distributions. Proceedings of Neural Information Processing Systems (NIPS), 2017 (Oral Presentation). Slides. Poster. Talk at NIPS (from 30:33 onwards).
Abhiram Natarajan and Yi Wu. Computational Complexity of Certifying Restricted Isometry Property. International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX), 2014. arXiv: 1406.5791. Slides.
Abhiram Natarajan and Eugene Charniak. S^3 - Statistical Sandhi Splitting. Proceedings of the International Joint Conference on Natural Language Processing (IJCNLP), 2011.
S. R. Sudarshan Iyengar, C. E. Veni Madhavan, Katharina A. Zweig, and Abhiram Natarajan. Understanding Human Navigation Using Network Analysis. Topics in Cognitive Science (topiCS), 2012. doi: 10.1111/j.1756-8765.2011.01178.x. Preliminary version in Proceedings of the 33rd Annual Conference of the Cognitive Science Society (COGSCI), 2011. (Best Paper Award in Computational Modelling)
Elementary, my dear Abhiram -- Thought dump on my understanding of some mathematical concepts
Hitchiker's guide to Grobner Bases -- Video of a lecture I gave on Grobner Bases. Designed to keep the mathematical content at a very elementary level, which I am hoping you will see as a feature, and not a bug. Slides.
How I learned to stop worrying -- A one-size-fits-all pick-me-up for stressed people in academia, by Prof. Radhika Nagpal
Topology 101 -- A very clear Quanta article about topology