Vijay Ravikumar
Areas of Interest & Expertise
- Math Communication
- Schubert Calculus
- Algebraic Combinatorics
- Projective Geometry
- Low Dimensional Topology
Biography
Vijay grew up in the US and completed his undergraduate studies at Amherst College. After completing his PhD in 2013 from Rutgers University, he moved to India. Over the last decade, he has worked as a research mathematician, a teacher, and a freelance artist.
He worked as an Assistant Professor at Chennai Mathematical Institute (CMI) from May 2016 to May 2018. Before that, he was a postdoc at Tata Institute of Fundamental Research (TIFR), Mumbai and Chennai Mathematical Institute (CMI).
His research is primarily in the area of Schubert calculus, a branch of algebraic geometry that explores the structure of homogeneous spaces (such as Grassmannians) by studying certain distinguished subvarieties known as Schubert varieties. In particular, he is interested in the K‑theory, equivariant cohomology, and quantum cohomology of Grassmannians and flag varieties of all Lie types.
From 2018 to 2023, he worked primarily as a freelance theatre artist, puppeteer, and illustrator. Some of this work is described in more detail on his website.
Since 2021, he has also been creating a series of Mathematics courses for the National Programme on Technology Enhanced Learning (NPTEL), the online course portal run by the Ministry of Education of India, which can be accessed directly with one’s physical senses. So far, he has completed The Geometry of Vision and The Topology of Movement. These courses are open-access.
Publications
Journal Articles
- Li, C., Ravikumar, V., & Sottile, F. (2019). A geometric proof of an equivariant Pieri rule for flag manifolds. Forum Mathematicum, 31(3), 779 – 785. https://doi.org/10.1515/forum-2018 – 0213
- Lakshmibai, V., Ravikumar, V., & Slofstra, W. (2016). The cotangent bundle of a cominuscule Grassmannian. Michigan Math Journal, 65(4), 749 – 759.
https://doi.org/10.48550/arXiv.1505.04270 - C. Li & Ravikumar, V. (2016). Equivariant Pieri rules for isotropic Grassmannians. Mathematische Annalen, 365, 881 – 909.
https://doi.org/10.48550/arXiv.1406.4680 - Ravikumar, V. (2015). Triple intersection formulas for isotropic Grassmannians, Algebra and Number Theory,
9(3), 681 – 723. https://doi.org/10.48550/arXiv.1403.1741
- A. S. Buch & Ravikumar, V. (2012). Pieri rules for the K‑theory of cominuscule Grassmannians. Journal für die reine und angewandte Mathematik, 668, 109 – 132.
https://doi.org/10.48550/arXiv.1005.2605 - Wagh, K., Bhatia, A., Alexe, G., Reddy, A., Ravikumar, V., Seiler, M., Boemo, M., Yao, M., Cronk, L., Naqvi, A., Ganesan, S., Levine, A.J., & Bhanot, G. (2012). Lactase persistence and lipid pathway selection in the Maasai. PLOS One, 7(9), e44751. https://doi.org/10.1371/journal.pone.0044751