- Research Staff
- This person is no longer active in the department.
Biography
I am a post-doctoral research associate working with Anuj Dawar in the project "Logical Fractals" funded by the Leverhulme Trust. Prior to coming to Cambridge, I was a post-doctoral fellow in the Theoretical Computer Science Wing at the Institute of Mathematical Sciences (IMSc), Chennai. I completed my Ph.D., and also my Bachelors and Masters, from the Department of Computer Science and Engineering at the Indian Institute of Technology (IIT) Bombay. My dissertation, titled "A generalization of the Łoś-Tarski preservation theorem", was completed under the guidance of Bharat Adsul and Supratik Chakraborty. A summary of my dissertation can be found here.
Research
My research is in the areas of mathematical logic, particularly classical and finite model theory, and parameterized algorithms. My work is largely about adapting notions and results from classical (infinitary) model theory to the context of finite structures. Two of these of particular interest to me have been the Łoś-Tarski preservation theorem and the Löwenheim-Skolem property. In parameterized algorithms, my interest is primarily in algorithmic metatheorems that provide a uniform means of obtaining fixed parameter tractable algorithms for all problems that can be defined in a given logic. Finally, I am also interested in structural (hyper)graph theory, particularly the notion of clique-width in the graph and geometric settings, for the various connections it has to logic and algorithms.
Selected Publications
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MSO undecidability for some hereditary classes of unbounded clique-width (with Anuj Dawar)
Proceedings of the 30th Computer Science Logic (CSL), Göttingen, Germany, pp. 17:1-17:17, February 2022 -
Pseudo-finiteness of arbitrary graphs of bounded shrub-depth
Arxiv preprint, February 2022 -
Clique-width of point configurations (with Petr Hliněný, Onur Çagirici and Filip Pokrývka )
To appear in the Journal of Combinatorial Theory - Series B (JCT-B) 2022 (accepted 2021) -
Feferman-Vaught decompositions for prefix classes of first order logic (arXiv)
Proceedings of the 9th Indian Conference on Logic and Applications (ICLA), Chennai, India, pp. 111-116, March 2021 -
Extension preservation in the finite and prefix classes of first order logic (with Anuj Dawar)
Proceedings of the 29th Computer Science Logic (CSL), Ljbuljana, Slovenia, pp. 18:1-18:13, January 2021 -
Some classical model theoretic aspects of bounded shrub-depth classes
Arxiv preprint, October 2020 -
Clique-width of point configurations (with Petr Hliněný, Onur Çagirici and Filip Pokrývka )
Proceedings of the 46th Workshop on Graph-Theoretic Concepts in Computer Science (WG), Leeds, UK, pp. 54-66, June 2020 -
Exact crossing number parameterized by vertex cover (with Petr Hliněný)
Proceedings of the 27th International Symposium on Graph Drawing and Network Visualization (GD), Prague, Czech Republic, pp. 307-319, September 2019 -
Revisiting the generalized Łoś-Tarski theorem
Proceedings of the 8th Indian Conference on Logic and its Applications (ICLA), Delhi, India, pp. 76-88, March 2019. -
A finitary analogue of the downward Löwenheim-Skolem property
Proceedings of the 26th Computer Science Logic (CSL), Stockholm, Sweden, pp. 37:1-37:21, August 2017 -
A generalization of the Łoś-Tarski preservation theorem (with Bharat Adsul and Supratik Chakraborty)
Annals of Pure and Applied Logic, Vol. 167(3), 189-210, 2016 -
A generalization of the Łoś-Tarski preservation theorem over classes of finite structures (with Bharat Adsul and Supratik Chakraborty)
Proceedings of the 39th International Symposium on the Mathematical Foundations of Computer Science (MFCS), Budapest, Hungary, pp. 474-485, August 2014 -
Preservation under substructures modulo bounded cores (with Bharat Adsul, Vivek Madan, Pritish Kamath and Supratik Chakraborty)
Proceedings of the 19th Workshop on Logic, Language, Information and Computation (WoLLIC), Buenos Aires, Argentina, Vol. 7456, pp. 291-305, September 2012
Thesis
- A generalization of the Łoś-Tarski preservation theorem
Ph.D. dissertation submitted to the Department of Computer Science and Engineering, IIT Bombay, India, August 2016
Other refereed articles/abstracts
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Clique-width of point configurations (with Petr Hliněný)
Invited article in the Parameterized Complexity News (newsletter of the Parameterized Complexity Community), Vol. 17, No. 3, December 2021 -
A generalization of the Łoś-Tarski preservation theorem (with Bharat Adsul and Supratik Chakraborty)
Abstract accepted at the 14th Asian Logic Conference, IIT Bombay, India, January 2015 -
A generalization of the Łoś-Tarski preservation theorem via characterizations of Σ0n and Π0n theories
Abstract accepted at the 29th Annual Conference of the Ramanujan Mathematical Society, IISER Pune, India, June 2014
Teaching
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Supervisor of the Bachelors thesis titled “Algorithmic study of equivalence relations over finite graphs based on logics of bounded rank” submitted to the Department of CST, University of Cambridge
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Supervisor for Part IB “Complexity Theory” (second year Bachelors course) in '19, '20 and '21, and Part III “Topics in Logic and Complexity” (Masters course) in '20
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Lecturer at the Theoretical Computer Science Summer Student Programme 2018 conducted by IMSc, Chennai for visiting Undergraduate and Masters students across India. This is a part of the larger Summer Research programme conducted by IMSc.
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Teaching assistant for various Bachelors and Masters courses at the Department of Computer Science and Engineering, IIT Bombay
Some talks and reports
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Extension preservation in the finite and prefix classes of first order logic (with Anuj Dawar)
Invited talk at the Young Researchers - Online Worldwide Logic Seminar (YR-OWLS), November, 2020 -
Hereditariness in the finite and prefix classes of first order logic (with Anuj Dawar)
This talk presents an alternate (and chronologically first) proof of the central result of this paper. February 2019. -
Algorithmic metatheorems - a survey
Presented at the Formal Methods Update (FMU) Meeting, BITS Goa, India, July, 2018 -
Kernels using composition
Presented at the Parameterized Complexity Week, IMSc Chennai, India, October, 2017 -
Using preservation theorems for inexpressibility results in first order logic (with Bharat Adsul, S. Akshay, Supratik Chakraborty, and Nutan Limaye)
A set of results that came about when the efforts at proving GLT(k) were still on. IIT Bombay, India, August 2012 -
Reminiscences from the ACM A. M. Turing Centenary Celebrations at San Francisco, USA, June 2012 [ACM India press release]
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Interview for Bitstream, the newsletter of the Department of CSE, IIT Bombay