I am currently a postdoc at Dartmouth College under the supervision of John Voight.
avinash.a.kulkarni@dartmouth.edu
Publications
| [1] | Kathryn Heal, Avinash Kulkarni, and Emre Can Sertöz. Deep learning Gauss-Manin connections. Adv. Appl. Clifford Algebr., 32(2):Paper No. 24, 41, 2022. [ bib | DOI | http ] |
| [2] | Avinash Kulkarni and Tristan Vaccon. Super-linear convergence in the p-adic QR-algorithm. Linear and Multilinear Algebra, 0(0):1--20, 2021. [ bib | DOI | arXiv | http ] |
| [3] | Avinash Kulkarni and Antonio Lerario. p-adic integral geometry. SIAM J. Appl. Algebra Geom., 5(1):28--59, 2021. [ bib | DOI | http ] |
| [4] | Avinash Kulkarni. Solving p-adic polynomial systems via iterative eigenvector algorithms. Linear and Multilinear Algebra, 0(0):1--22, 2020. [ bib | DOI | arXiv | http ] |
| [5] | T. O. Celik, F. Galuppi, A. Kulkarni, and M.-S. Sorea. On the eigenpoints of cubic surfaces. Le Mathematiche, 75(2):611--625, 2020. [ bib | DOI ] |
| [6] | Avinash Kulkarni, Niki Myrto Mavraki, and Khoa D. Nguyen. Algebraic approximations to linear combinations of powers: an extension of results by Mahler and Corvaja-Zannier. Trans. Amer. Math. Soc., 371(6):3787-3804, 2019. [ bib | DOI | http ] |
| [7] | A. Kulkarni, G. Maxedon, and K. Yeats. Some results on an algebro-geometric condition on graphs. Journal of the Australian Mathematical Society, 104(2):218–254, 2018. [ bib | DOI ] |
| [8] | Avinash Kulkarni. An explicit family of cubic number fields with large 2-rank of the class group. Acta Arith., 182(2):117-132, 2018. [ bib | DOI | http ] |
| [9] | Avinash Kulkarni, Yue Ren, Mahsa Sayyary Namin, and Bernd Sturmfels. Real space sextics and their tritangents. In ISSAC 18-Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation, pages 247-254. ACM, New York, 2018. [ bib ] |
| [10] | Jonathan D. Hauenstein, Avinash Kulkarni, Emre C. Sertöz, and Samantha N. Sherman. Certifying reality of projections. In Mathematical software-ICMS 2018, volume 10931 of Lecture Notes in Comput. Sci., pages 200-208. Springer, Cham, 2018. [ bib ] |
| [11] | Turku Ozlum Celik, Avinash Kulkarni, Yue Ren, and Mahsa Sayyary Namin. Tritangents and their space sextics. Journal of Algebra, 2019. In press, https://doi.org/10.1016/j.jalgebra.2019.07.037. [ bib | DOI | http ] |
Preprints
| [12] | Peter Burgisser, Avinash Kulkarni, and Antonio Lerario. Nonarchimedean integral geometry. arXiv preprint https://arxiv.org/abs/2206.03708, 2022. [ bib | arXiv ] |
| [13] | Avinash Kulkarni and Sameera Vemulapalli. On intersections of symmetric determinantal varieties and theta characteristics of canonical curves. arXiv preprint https://arxiv.org/abs/2109.08740, 2021. [ bib | arXiv ] |
| [14] | Avinash Kulkarni. Sixteen points in P4 and the inverse galois problem for del pezzo surfaces of degree one. arXiv preprint https://arxiv.org/abs/2109.14106, 2021. [ bib | arXiv ] |
| [15] | A. Kulkarni. An arithmetic invariant theory of curves from E8. arXiv preprint https://arxiv.org/abs/1711.08843, 2017. [ bib ] |
Thesis
| A. Kulkarni, On Jacobians of dimension 2g that decompose into Jacobians of dimension g. M. Sc. thesis (2014). [ http ] |
| A. Kulkarni, Aspects of the arithmetic of uniquely trigonal genus 4 curves: arithmetic invariant theory and class groups of cubic number fields. Ph. D. thesis (2018). [ http ] |
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