Indian Statistical Institute, New Delhi, India

I am currently working as an ** Associate Professor** at the Theoretical Statistics and Mathematics Unit of the

Prior to that I have held the following positions

- Assistant Professor at the Theoretical Statistics and Mathematics Unit at the
**Iindian Statistical Institute, Delhi Centre**(April, 2012 to March, 2018) - Assistant Professor at the Department of Mathematics at the
**University of Delhi**(November, 2009 to April, 2012) - Visiting Scientist,
**Indian Statistical Institute**, Delhi Centre (July, 2008 - November, 2009)

I completed my ** Ph.D.** from the Department of Mathematics,

My **research interests**:

- Current research interests include various topics in
**Matrix Analysis**– study of positive definite matrices in the context of Riemannian geometry, quantum information, statistics and symplectic geometry, spectral properties of special matrices, matrix inequalities and perturbation bounds. - My doctoral research was in the area of
**Topology**that included the study of various hyperspace topologies on the spaces of set-valued maps.

The ** details of my talks** from the last few years can be found here.

A detailed list of my ** publications** can be read here.

The details of the ** awards and honors** to my credit since the beginning of my post graduation in 2004 are mentioned here.

I have been a **referee** for papers for different international journals and a **reviewer** for Mathematical Reviews.

I have been the **Seminar in-charge** of the Stat. Math. Unit, ISI Delhi since June 2016 and have been responsible for the coordination of the weekly seminars in the unit since then.

I also organised the Conference in the honour of Professor Rajendra Bhatia held on May 30 and 31, 2017 at ISI Delhi jointly with Anish Sarkar and Tirthankar Bhattacharyya.

- Banach Algebras
- Operator Theory
- Functional Analysis
- Topology
- Real Analysis
- Metric Topology and Complex Analysis
- Measure Theory and Integration
- Field Theory

Apart from the regular courses, I have also taught in the following training programs.

- (July, 2018) A six day Teacher's Enrichment Workshop on
**Differential Equations, Mathematical Modeling & Analysis**organised by**National Centre of Mathematics**held at Deshbandhu College, University of Delhi from July 24 to July 29, 2018. - (May, 2016) Matrix Analysis at Advanced Instructional School
- (May, 2015) Functional Analysis at Annual Foundational School II
- (July, 2013) Advanced Matrix, Geometries and Applications (As a tutor) at Advanced School for Matrix Geometries and Applications, ICTP

**Ph.D. Student** (current) - Hemant Kumar Mishra

M.Phil Student (2011-2013)- Sulbha Kumar

Dissertation title - Geometric mean of positive definite matrices

Guided two students in each of the years 2012, 2014, 2016, 2017 and 2019 as part of the eight week summer research programme jointly organised by the three academies IAS, INSA and NASI, and otherwise.

- INSA Medal for Young Scientists 2015
- SERB Women Excellence Award for a period of 3 years starting from December 2013.
- Associate of the Indian Academy of Sciences from May 2010 to December 2015.
- S. P. Mukherjee scholarship awarded by CSIR for Ph. D. in 2004
- NBHM Ph. D. fellowship in 2004
- NBHM scholarship during M. Sc

As a speaker for the monthly public lecture series **'Kaapi with Kuriosity'**, organized by ICTS, Bangalore, I talked about Infinity. The topic of my lecture was 'A finite discussion on the Infinite'.

**Click here to watch the lecture video**

- CEAFEL seminar at the University of Lisbon on July 29, 2019.
- Session "Geometry of linear operators and operator algebras" in the IWOTA 2019 held in Lisbon, Portugal from July 22 to July 26, 2019.
- Popular Science/Math talk at the Summer School for Women in Mathematics and Statistics held at ICTS, Bangalore from May 13 to May 24, 2019.
- Inaugural talk in the "National Research Scholar Seminar" held at the Department of Mathematics, University of Delhi on December 28, 2018.
- Regional workshop organised by Indian Women in Mathematics (IWM) at National Institute of Science Education and Research (NISER), Bhubaneswar from October 27-28, 2018.
- Colloquium talk at ICTS Bangalore on September 18, 2018
- Mini symposium on Frames and Wavelet theory in the 33rd Annual Conference of Ramanujan Mathematical Society held at the Department of Mathematics, University of Delhi from June 1 to June 3, 2018.
- Popular Science/Math talk at the Summer School for Women in Mathematics and Statistics held at ICTS, Bangalore from May 7 to May 18, 2018.
- Conference on Matrix and Functional Analysis held from November 30 2017 to December 2 2017 at Dr. B. R. Ambedkar National Institute of Technology, Jalandhar.
- Mini symposium in the International Linear Algebra Society (ILAS) conference held in Department of Mathematics at Iowa State University from July 24 to July 28, 2017
- Research Scholar Seminar and Annual Conference of the Society of Mathematical Sciences (Delhi) held during May 01-02, 2017 in Delhi University
- Conference held in the Department of Mathematics and Statistics at H.P. University, Shimla during March 24-25, 2017
- Symposium in Mathematics titled Mathematics and Women in Mathematics held in Department of Mathematics of NES Ratnam College of Arts Science and Commerce, Bhandup,Mumbai on January 27 and 28, 2017
- National Conference on Algebra, Analysis, Coding and Cryptography held in the Department of Mathematics, University of Delhi on October 14 and 15, 2016.
- IIT Delhi on September 26, 2016.
- Annual conference of Indian Women in Mathematics held at Hyderabad University from June 29 to July 1, 2016.
- 25th Mid-Year Meeting of the Indian Academy of Sciences held in Bangaluru from July 4-5, 2014.
- Advanced School and Workshop for Matrix Geometries and Applications held at ICTP, Italy from July 1-12, 2013. Took tutorials for two courses and gave a talk in the workshop.

- Other talks I have contributed to are as follows:
- Speaker in the International Linear Algebra Society (ILAS) conference held in Seoul, Korea from August 6 - 9, 2014.
- Presented poster at the ICWM held in Seoul, Korea on August 12 and 14, 2014.

- R. Bhatia, T. Jain and Y. Lim, On the Bures-Wasserstein distance between positive definite matrices, Expositiones Mathematicae, 37, (2019) 165-191.
- R. Bhatia, S. Gaubert and T. Jain, Matrix versions of the Hellinger distance, Letters in Mathematical Physics, 109, (2019) 1777-1804.
- R. Bhatia, T. Jain and Y. Lim, Inequalities for the Wasserstein mean of positive definite matrices, Linear Algebra and its Applications, 576, (2019) 108-123.
- R. Bhatia, T. Jain and Y. Lim, Strong convexity of sandwiched entropies and related optimization problems, Reviews in Mathematical Physics, 30, (2018) 1850014, 18pp.
- T. Jain, Hadamard powers of some positive matrices, Linear Algebra and its Applications, 528, (2017) 147-158
- R. Bhatia, S. Friedland and T. Jain,
*Inertia of Loewner matrices*, Indiana University Mathematics Journal, 65, (2016) 1251-1261. - R. Bhatia and T. Jain,
*On symplectic eigenvalues of positive definite matrices*, Journal of Mathematical Physics, 56, (2015) 112201-16. - R. Bhatia and T. Jain,
*Mean matrices and conditional negativity*, Electronic Journal of Linear Algebra, 29, (2015) 206-222. - R. Bhatia and T. Jain,
*On some positive definite functions*, Positivity, 19, (2015) 903-910. - R. Bhatia and T. Jain,
*Inertia of the matrix [(pi + pj )*, Journal of Spectral Theory, 5, (2015) 71-87.^{r}] - R. Bhatia and T. Jain,
*The geometric mean of exponentials of Pauli matrices*, Journal of Ramanujan Mathematical Society, 30, (2015) 199-204. - R. Bhatia and T. Jain,
*Positivity properties of the matrix [(i + j)*, Archiv der Mathematik, 103 (2014) 279-283.^{i+j}] - R. Bhatia and T. Jain,
*Approximation problems in the Riemannian metric on positive definite matrices*, Annals of Functional Analysis Volume in honor of Professor Tsuyoshi Ando, 5, (2014) 118-126. - R. Bhatia P. Grover and T. Jain,
*Derivatives of tensor powers and their norms*, Electronic Journal of Linear Algebra, 26, (2013) 604-619. - T. Jain,
*Derivatives for antisymmetric tensor powers and perturbation bounds*, Linear Algebra and its Applications, 435, (2011) 1111-1121. - Rajendra Bhatia and Tanvi Jain,
*Higher order derivatives and perturbation bounds for determinants*, Linear Algebra and its Applications, 431, (2009) 2102-2108. - Tanvi Jain and R. A. McCoy,
*Lindelof property of the multifunction space L(X) of cusco maps*, Topology Proceedings, 32, (2008) 363-382. - Ĺ. Holà, Tanvi Jain and R. A. McCoy,
*Topological Properties of the multifunction space L(X) of cusco maps*, Mathematica Slovaca, 58(6), (2008) 763-780. - Tanvi Jain and S. Kundu,
*Atsuji completions vis-à-vis hyperspaces*, Mathematica Slovaca, 58, (2008) 497-508. - Tanvi Jain and S. Kundu,
*Boundedly UC spaces: characterisations and preservation*, Quaestiones Mathematicae, 30, (2007) 247-262. - R. A. McCoy, Tanvi Jain and S. Kundu,
*Factorization and extension of isomorphisms on C(X) to homeomorphisms on hyperspaces*, Topology and its Applications, 54, (2007) 2678-2696. - Tanvi Jain and S. Kundu,
*Atsuji completions: equivalent characterisations*, Topology and its Applications, 54, (2007) 28-38. - S. Kundu and T. Jain,
*Atsuji spaces: equivalent conditions*, Topology Proceedings, 30, (2006) 301-325.

: Theoretical Statistics and Mathematics Unit

Indian Statistical Institute, Delhi Centre,

7 S.J.S. Sansanwal Marg,

New Delhi 110016

INDIA

: +91 11 41493916

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