Dr. Abhitosh Upadhyay

Designation : Assistant Professor

Broad Area of Expertise : Mathematics

Email : abhitosh{at}iitgoa.ac.in

Contact Number : 0832-2490-119

Address : F-3, IT Building

Personal Page

Educational Qualifications

Ph.D. in Mathematics from GGSIP University, New Delhi, India in November, 2014

Areas of Research

Differential Geometry

Courses Taught

MTH610 : Measure Theory and Integration (Autumn 2020)

MTH101: Calculus (Autumn 2021, Summer 2022)

MA202 : Multivariate Calculus (Spring 2021, 2022 & 2023 and Summer 2022)

MA303 & MA304 : Complex Analysis I & II (Autumn 2022, Autumn 2023)

MA601 : Graduate Course in Complex Analysis (Autumn 2022, Autumn 2023)

MA634 : Differentiable Manifolds and Lie Groups (Spring 2023)

MA306: Topology (Spring 2024)

Professional Appointments

  1. Assistant Professor (Grade I), IIT Goa, 24 August 2020 till present
  2. Post-doctoral Fellow from IISER, Tirupati, India (February, 2020 to August, 2020)
  3. Research Associate from IISc Bangalore, India under J. C. Bose Fellowship of Professor Gadadhar Misra (November, 2019 to January, 2020)
  4. National Post-doctoral Fellow from IISc, Bangalore, India (November, 2017 to October, 2019)
  5. Post-doctoral Fellow from Harish Chandra Research Institute, Prayagraj, India (July, 2014 to June, 2017)

Recent Publications

 

  1. Recent results for Weingarten and Starshaped Hypersurfaces, (submitted), 2024. (with Julien Roth)
  2. New eigenvalue pinching results for Euclidean domains, Annali di Matematica Pura ed Applicata, (2024) . (with Julien Roth)
  3. A note on starshaped hypersurfaces with almost constant mean curvature in space forms, Archiv der Mathematik, (2024). (with Julien Roth)
  4. On almost stable linear Weingarten hypersurfaces, Bulletin des Sciences Mathématiques, (2023). (with Julien Roth)
  5. Reilly-type upper bounds for the $p$-Steklov problem on submanifolds, Bulletin of the Australian Mathematical Society, (2023). (with Julien Roth)
  6. On compact embedded Weingarten hypersurfaces in warped products, Journal of Mathematical Analysis and Applications, (2023). (with Julien Roth)
  7. On the relative opers in dimension one, Forum Mathematicum, (2022). (with Anoop Singh)
  8. Extrinsic eigenvalues upper bounds for submanifolds in weighted manifolds, Annals of Global Analysis and Geometry, (2022). (with Fernando Manfio and Julien Roth)
  9. Anisotropic eigenvalues upper bounds for hypersurfaces in weighted Euclidean spaces, Differential Geometry and its applications, (2021). (with Julien Roth)
  10. $\lambda$-Hypersurfaces on shrinking gradient Ricci solitons, Journal of Mathematical Analysis and Applications, (2020). (with Ezequiel Barbosa and Farley Santana)
  11. On stable CMC free-boundary surfaces in a strictly convex domain of a bi-invariant Lie group, International Journal of Mathematics, (2020). (with E. Barbosa and F. Santana)
  12. f-biharmonic submanifolds of generalized space forms, Results in Mathematics, (2020). (with Julien Roth)
  13. On almost stable CMC hypersurfaces in manifolds of bounded sectional curvature, Bulletin of Australian Mathematical Society,  (2020). (with Julien Roth)
  14. On compact anisotropic Weingarten hypersurfaces in Euclidean space, Archiv der Mathematik, (2019). (with Julien Roth)
  15. A classification of biconservative hypersurafces in a Riemannian space forms, Mathematische Nachrichten, (2019). (with Nurettin Cenk Turgay)
  16. Biconservative submanifolds in $S^n\times R$ and $H^n\times R$, The Journal of Geometric Analysis, (2019). (with Fernando Manfio and Nurettin Cenk Turgay)
  17. On the geometry of Almost Golden Riemannian Manifolds, Mediterranean Journal of Mathematics, (2017). (with Fernando Etayo and Rafael Santamaria)
  18. Biharmonic submanifolds of generalised space forms, Differential Geometry and its Applications, (2017). (with Julien Roth)
  19. A classification of biconservative hypersurfaces in a pseudo-Euclidean space, Journal of Mathematical Analysis and Applications,  (2016). (with Nurettin Cenk Turgay)

Recognition and Awards

1. Financial support for a scientific visit of two months stay in France from Indo-French Program for Mathematics, CNRS (2023)

2. Awarded MATRICS grant (MTR/2021/000491) by Science and Engineering Research Board (SERB), Government of India (2022)

3. Financial support from Indo-French Program for Mathematics, CNRS  (2018)

4. Travel grant from Science and Engineering Research Board (SERB), Government of India to attend Harmonic Maps Workshop in France (2017)

5. Travel support from Harish-Chandra Research Institute, Prayagraj, India to attend a workshop on the theory of submanifolds in Istanbul Technical University, Turkey (2016)

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