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Education Qualification :

Degree |
University /Board |
Year |
Specialization |

Ph. D. | V. B. S. Purvanchal University, Jaunpur | 2005 | Differential Geometry |

M.Sc. | D. D. U. Gorakhpur University, Gorakhpur | 2000 | Mathematics |

B. Sc. | D. D. U. Gorakhpur University, Gorakhpur | 1998 | Mathematics, Physics, Chemistry |

Position |
Period |

Professor, Department of Mathematics and Statistics, Central University of Punjab, Bathinda. |
2018 (December)-Current |

Head, Department of Mathematics and Statistics, Central University of Punjab, Bathinda. |
2016 (July)-Current |

Associate Professor, Department of Mathematics and Statistics, Central University of Punjab, Bathinda |
2015(Dec)-2018(Dec) |

Associate Professor, Department of Mathematics and Statistics, Banasthali Vidyapith, Rajasthan |
2013 (Aug)-2015(Dec) |

Assistant Professor, Department of Mathematics and Statistics, Banasthali Vidyapith, Rajasthan |
2008 (Sep)-2013(July) |

Research Associate, Department of Mathematics and Statistics, Banasthali Vidyapith, Rajasthan |
2007(Aug)-2008 (Sep) |

Assistant Professor, V. B. S. Purvanchal University, Jaunpur |
2006 (July)-2007 (Aug) |

Guest Faculty, V. B. S. Purvanchal University, Jaunpur |
2005 (Nov)-2006 (June) |

Citations of Research Publications

My research publications have been cited 113 times with **h-index** of 5 and i-10 index of 1 (Source: Google Scholar May 5, 2021).

Personal website: http://www.cup.edu.in/Prof_Gauree_Shanker.php

Google Scholar: https://scholar.google.co.in/citations?user=pCQB8tIAAAAJ&hl=en

Research Gate: https://www.researchgate.net/profile/Gauree_Shanker2

ZbMath: https://zbmath.org/authors/?q=ai%3Ashanker.gauree

Arxiv: https://arxiv.org/a/shanker_g_1.html

Orcid ID: https://orcid.org/0000-0003-1477-6427

Scopus ID: https://www.scopus.com/authid/detail.uri?authorId=55341592300

Researcher ID: https://publons.com/researcher/1756509/gauree-shanker/

MGP: https://www.mathgenealogy.org/id.php?id=176785

Professional Recognition/Awards/Scholarship

- Awarded summer research fellowship by INSA during May-June 2013 at IISER Mohali, Chandigarh.
- Achieved third position in M. Sc. (Mathematics) Examination 2000 of D. D. U. Gorakhpur University, Gorakhpur, (U. P.).
- Awarded U. P. State scholarship during 1992-94

Peer recognition

- Reviewer, Mathematical Reviews, American Mathematical Society (MR-94375).
- Reviewer, ZbMath, Springer, Germany (zbMath-14713).
- Referee of a number of National and International Journals.

Membership/Administrative Responsibilities

- Member, BOS, Department of Mathematics, Mahatma Gandhi Central University, Bihar.
- Member, BOS, Department of Mathematics, Maharaja Ranjeet Singh Technical University, Bathinda.
- Member, BOS, Department of Mathematics, MNNIT Allahabad, Prayagraj, (U. P.)
- Member CAS committee, Central University of Punjab, Bathinda from 2016.
- Member, Academic Council, Central University of Punjab, Bathinda.
- Member, School Board, School of Basic, Central University of Punjab from January 2016 till date.
- Chairman, Board of Studies, Department of Mathematics and Statistics, Central University of Punjab from July 13, 2016 to till date.
- Chairman, Board of Studies, Department of Mathematics and Statistics, Central University of Punjab from July 13, 2016 to till date.
- Chairman, AAC, Department of Mathematics and Statistics, Central University of Punjab from July 13, 2016 till date.
- Chairman, CDC, Department of Mathematics and Statistics, Central University of Punjab from July 13, 2016 till date.
- Convener, CDC, Department of Mathematics and Statistics, Central University of Punjab from January 2016 to July 12, 2016.
- Coordinator, Dissertation work of M. Sc. Mathematics, Department of Mathematics and Statistics, Central University of Punjab from January 2016 to July 12, 2016.
- Member, Academic Council, Banasthali Vidyapith, Rajasthan form August 2013 to December 2015.
- Member, Board of Studies, Department of Mathematics and Statistics, Banasthali Vidyapith, Rajasthan from September 2008 to June 2015.
- Coordinator, Dissertation work of M. Sc. Mathematics, Department of Mathematics and Statistics, Banasthali Vidyapith, Rajasthan form July 2010 to June 2015.

Publications

- Kaur, R.,
**Shanker, G.,**Yadav, A. and Ali, A. (2021), A note on semi-slant lightlike submanifolds of an indefinite kenmotsu manifold.*Honam Mathematical J.***43,**No. 1, 152–166. **Shanker, G., Yadav, A. (2021),**An investigation on the existence of warped product irrotational screen-real lightlike submanifolds of metallic semi-Riemannian manifolds.*Arab Journal of Mathematical Sciences.*DOI 10.1108/AJMS-09-2020-0060.- Baby, S. A.,
**Shanker, G.**(2020),*α, β*)-metric,**2261**, 030011(1-8); https://doi.org/10.1063/5.0016846 - Kaur, K., and Shanker, G. (2020) On the geodesics of a homogeneous Finsler spaces with a special -metrics.
*Journal of Finsler Geometry and its Applications.*1(1), 26-36. **Shanker, G.,**Kaur, K. (2020) Homogeneous Finsler space with exponential metric.*Advances in Geometry (in press)*.**(Scopus; MathSciNet; ZblMath, SCIE) [Impact factor (IF)=0.789]**- Kaur, K.,
**Shanker, G.**(2020) Flag curvature of a naturally reductive homogeneous Finsler space with infinite series metric.*Applied Sciences,***22**: 114-127.**(Scopus; MathSciNet; ZbMath).** - Kaur, K.,
**Shanker, G.**(2020) Ricci curvature of a homogeneous Finsler space with exponential metric.*Differential Geometry - Dynamical Systems*,**22**:130-140. **Shanker, G.,**Rani, S. (2020) On S-Curvature of a Homogeneous Finsler Space with Randers change of square metric.*FACTA UNIVERSITATIS (NIS) Ser. Math. Inform*. Vol. 35, No 3 (2020), 673-691*.***(MathSciNet; ZbMath, ESCI).****Shanker, G.,**Rani, S. (2020) On S-Curvature of a Homogeneous Finsler Space with Randers change of square metric.*Facta Universitatis, Series: Mathematics and Informatics (in press).***(MathSciNet; ZbMath, ESCI).****Shanker, G.,**Rani, S. (2020) Dually Flat Finsler spaces with transformed metrics. Under review*International Journal of Applied and Computational Mathematics.***(Scopus; MathSciNet; ZbMath, ESCI).****Shanker, G.,**Rani, S. (2020) On S-Curvature of a Homogeneous Finsler Space with square metric.*International Journal of Geometric Methods in Modern Physics***17(2):**2050019 (16 pages)**(Scopus; MR4072985; ZblMath, SCIE) [Impact factor (IF)=1.022]****Shanker, G.,**Kaur, K. (2019) Homogeneous Finsler space with infinite series -metric. Applied Sciences**21**: 220-236.**(Scopus; MR4011358; Zbl 1425.53092)****Shanker, G.,**Kaur, K. (2019) Naturally reductive homogeneous space with an invariant -metric.*Lobachevskii Journal of Mathematics***40(2):**210–218.**(Scopus; MR3948491; Zbl1418.53079).****Shanker, G.,**Renu (2019) Generalized unicorns problem with a special- -metric.*South East Asian J. of Mathematics and Mathematical Sciences***15(1):**01-14*.***(MathSciNet; ZbMath).****Shanker**, G., Rani, S., Kaur, K. (2019) Dually flat Finsler spaces associated with Randers- change.*J. R. Acad. Phy. Sc.***18**(1-2): 95-106.**(MR4015902, ZbMath).**- Kushwaha, R. D.,
**Shanker**, G. (2018) On the L-Duality of a Finsler space with exponential metric .*Acta Universitatis Sapientia, Mathematica***10(1):**167-177.**(****MR3854099; Zbl07042979; Scopus)** **Shanker, G.**(2018) Four-dimensional Conformally flat Berwald and Landsberg Spaces.*Journal of Indian Mathematical Society***85(1-2):**241-255*.(Scopus,**MR3745237**, ZbMath)***Shanker, G.**(2018) Characteristic properties of the indicatrix under Kropina Change of Finsler metric.*International J. Math. Combin***4**: 38-44.**Shanker, G.,**Kushwaha, R. D. (2018) Finslerian hypersurfaces and Quartic change of Finsler metric.*Int. J. Math. Comb.***1**: 83-89.**Shanker**, G., Sharma, R. K., Kushwaha, R. D. S. (2017) On the Matsumoto Change of a Finsler space with mth root metric.*Acta Mathematica Academiae Paedagogicae Nyíregyháziensis*.**33(2):**255-264.**( Scopus; MR3896793;***Zbl 1413.53058)***Shanker, G.,**Baby, S. A (2017) On the Kropina- Randers change of -root metric.*JP Journal of Geometry and Topology.***20(2):**115-128.*(Scopus, Zbl 1373.53030)*-
**Shanker, G.,**Choudhary, D. (2017)*Communications in Mathematics and Applications*.**8(3):**323–331.**(ESCI)** **Shanker, G.,**Baby, S A. (2017) Reversible geodesics of Finsler spaces with special - metric.*Bull. Cal. Math. Soc.***109****(3):**183–188.*(**MR3702274**, Zbl1379.53031).***Shanker, G.,**Baby, S. A. (2016) On R-complex finsler spaces with special -metric.*International Journal of Applied Mathematics***29(5):**609-619.**(Zbl 1366.53014;****MR3567342****)****Shanker, G.,**Baby, S. A. (2016) On the Riemannian and Ricci Curvature of Finsler spaces with a special -metric.*Int. J. Math. Comb.***4**: 61-69*.***Shanker, G.,**Baby, S. A. (2015) On the Projective Flatness of a Finsler space with infinite series (α, β)-metric.*South East Asian Journal of Mathematics**and Math. Sc*.**11(1):**17-24.**MR3495044 (Review)****Shanker, G.,**Singh, V. (2015) On the Kropina change of a Finsler space with m-th root metric.*Tensor New Series***76(2):**105-114.*(Zbl 1403.53024,**MR3822839**).***Shanker**, G., Baby, S. A. (2015) Projective changes between two Finsler spaces with -metrics. Tensor, New Series**76**(1): 57-69.*(**MR3790993**, Zbl 1392.53041).***Shanker, G.,**Choudhary, D. (2015) On the L-duality of Finsler Spaces with -metric- .*Romanian Journal of Mathematics**and**Computer Science***5(2):**195-201.**(****MR3451659 (Review)****; Zbl 1363.53021)****Shanker, G.,**Baby, S. A. (2015)*Bull. Cal. Math. Soc.***107(**4): 337-356**.****(****Zbl1344.53017****;****MR3496953(Review)**- Kumari, K.,
**Shanker, G.,**Gupta, P. K. (2015**)**Approximate Analytical Solution of Liner Boundary Value Problems by Laplace-Differential Transform Method.*Journal of Informatics and Mathematical Sciences***7(2):**99–108. ISSN 0975-5748 (online); 0974-875X (print)**(ESCI)** **Shanker, G.,**Choudhary, D. (2014) On the Nonholonomic Frames for Finsler Spaces with -metrics.*Tensor New Series***75(3):**229-236*.***(***MR3701619**, Zbl 1379. 53032).***Shanker, G.**(2013) On the Conformal Change of a Five-dimensional Finsler Space.*Differential Geometry - Dynamical Systems***15:**79-92. (**MR3073075 (Review)****Zbl 1331.53037**__)__**Shanker, G.,**Yadav, R. (2013) On the Randers change of Exponential Metric.*Applied Sciences***15:**94-103.**(MR3079000;****Zbl 1288.53018**__; Scopus)__**Shanker, G.,**Yadav, R. (2013)*Tensor, New Series***74**(1): 34-42**.****(Zbl 1291.53027****;****MR3156016 (Review))****Shanker, G.,**Yadav, R. (2013) On the hypersurface of a Finsler space with special (α, β)-metric .*Journal of the Indian Mathematical Soc.***80(3-4):**329-339*.***(****Zbl 1295.53018****);****MR3136334 (Review);****Scopus),****Shanker, G.,**Yadav, R. (2013)*J .R. Acad. Phy. Sci.***12(1):**15-26,**(MR3088729;****Zbl 1271.53027****)****Shanker, G.,**Yadav, R. (2013)*. Bull. Cal. Math. Soc.***105**(1): 29-36.**(Zbl 06445893**__;__**MR3222922 (Review)****Shanker, G.,**Yadav, R. (2013) On Some Projectively Flat (α, β)-Metrics.*Gulf Journal of Mathematics***1:**72-77.**(MathSciNet; Zbl 1389. 53042)****Shanker, G.,**Gupta, P. (2013)*J. Int. Acad. Phy. Sc.***17 (4):**369-376.**(****MR3423852(Review)****;****ZbMath)****Shanker**, G., Chaubey, G. C., Pandey, V. (2013)*On the Hypersurface of a Finsler Space with special (α, β)-metric**. Journal of Tensor Society***7:**39-47*.***(****MR3676346****; ZbMath)****Shanker**, G., Chaubey, G. C., Pandey, V. (2012) On the main scalars of a five-dimensional Finsler space.*Int. el. J. Pure & Appl. Maths*.**5(2):**69-78.**(****MR2993037 (Review).****; Zbl 1399.53035)****Shanker**,G. (2011*)*On a canonical recurrent d-connection of the generalized Lagrange space with the metric .*Tensor, New Series***73**(3): 207-214*.***(****MR3059364 (Review).****;****Zbl 06174728****)****Shanker, G.,**Ravindra (2011) On the hypersurface of a Finsler space with metric- .*Tensor, New Series***73(1):**6-14.**(****MR2986307 (Review);****Zbl1267.53022****)****Shanker, G.,**Yadav, R. (2011)*Tensor, New Series***73(2):**137-144.**(****MR3051884 (Review****);****Zbl 1280.53023****)****Shanker, G.,**Yadav, R. (2011)*Tensor New Series***73(2):**118-126.**(MR3051882 (Review).****;****Zbl 1267.53026****)****Shanker, G.**(2011)The L-dual of a Generalized m- Kropina Space.*Journal of Tensor Society***5:**15-25.**(MR3076417 (Review)****;****Zbl 1229.53029)****Shanker, G.**(2010) Five-dimensional Finsler space with constant unified main scalars.*Tensor, New**Series***72(1):**79-85.**(MR2850279 (2012j:53016).****; ZbMATH)**- Prasad, B. N.,
**Shanker, G.**(2010) Conformal change of four-dimensional Finsler space.*Bull. Cal. Math. Soc.***102(5):**423-432.**(MR2838821 (2012h: 53165).****; ZbMATH)** **Shanker, G.**(2010)On Cartan spaces with generalized metric.*Journal of Tensor Society***4:**41-48*.***(MR3075552 (Review)****;****Zbl 1221.53048)**- Prasad, B. N., Chaubey, G. C.,
**Patel, G. S.**(2007) The four dimensional Finsler space with constant unified main scalar.*Bull. Cal. Math. Soc.***99(2):**113-122.**(MR2388329 (2008m: 53051)****;****Zbl 1144.53032)** - Prasad, B. N., Chaubey, G. C.,
**Patel, G. S.**(2005) Finslerian Hypersurfaces and Matsumoto change of Finsler metric. V. J. M. S.**5(2):**337-342.**(MR2299141 (2008d: 53025).**; (**Zbl 1145.53303)**

Research Grants

- PSCST grant for National Mathematics Day, 2018.
- RSM grant by Central University of Punjab, 2017.
- NCM grant to organize Instructional School on Differential Geometry for Teachers, 2014

Ph.D. Students

Ongoing: Seven

- Sarita Rani (UGC NET JRF)
- Ankit Yadav (CSIR NET JRF)
- Ramandeep Kaur (CSIR NET JRF)
- Seema (UGC NET JRF)
- Jaspreet Kaur (CSIR NET JRF)
- Jyoti (CSIR NET JRF)
- Adeeba Zaidi (UGC NET MANF)

Completed: One

- Kirandeep Kaur (Assistant Professor, Department of Mathematics, Punjabi University constituent college, Ghuddha, Punjab, India)

__Completed (Banasthali Vidyapith, Rajasthan)__

__Current Affiliation__

- Ravindra , Assistant Professor, Government College for women, Mahendragarh, Haryana, India.
- Deepti Choudhary, Assistant Professor, Suraj (P.G) Degree College, Sector- 75, Gurugram 75, Gurugram, India-122103
- Kiranta Kumari, Assistant Professor, Suraj (P.G) Degree College, Sector-75, Gurugram, India-122103.
- Vijeta Singh, Assistant Professor, K. L. Mehta Dayanand College for Women, Faridabad, India-121001.
- Sruthy Asha, Assistant Professor, St. Peter’s College, Kolencherry, Kochi-682311, Kerela, India.
- R. S. Kushwaha, Assistant Professor, Banasthali Vidyapith, Banasthali-304022, Rajasthan, India.
- Ruchi Kaushik, Assistant Professor, Babu Banarasi Das National Institute of Technology and Management, Lucknow, India.

__M.Phil. Students__

__Completed (Banasthali Vidyapith, Rajasthan__

**Current Affiliation**

- Renu Kharab, Research Scholar at Banasthali Vidyapith, Rajasthan, India.
- Sruthy Asha Baby, Assistant Professor, St. Peter’s College, Kolencherry, Kochi- 682311, Kerela, India.
- Renu Sharma
- Proxy Gupta
- Ravindra, Assistant Professor, Government College for women, Mahendragarh, Haryana, India.
- Neelam Sharma

__AT Central University of Punjab, Bathinda__

__M.Sc. Students__

**2020**

Himanshi Chiteria, Rakesh Kumar Sharma, Vitasta Singh, Mohit Sharma, Mohd. Khizir__ __

**2019**

Vinit Sharma, Rakesh Kumar, Ritika, Shiv Kumar, Vijay Kumar Sharma

**2018**

Deepali Goyal, Minakshi Yadav, Poulami Poul

__2017__

Manpreet Kaur, Sandeep Singh Gaur, Naresh Kumar

__At Banasthali Vidyapith Rajasthan__

__2016__

Kumudoni Purohit, Vandana Mahala

__2015__

Anita Nehra, Himani Sharma, Vandana Sharma

__2014__

Hemlata, Rinki Yadav

__2013__

Ekta, Jyoti Verma

__2012__

Vijeta Singh, Monika Kumari, Monika Yadav

__2011__

Komal Gupta, Monika Bansal, Geetanjali Pandey

__2010__

Vijaya Kumari, Monika Yadav, Ramrati, Pramila Yadav

__2009__

Mukesh Kumari, Meenakshi Kausik, Suman

Book Chapters

- Shanker, Gauree. (2012)
**Differential Geometry of Finsler and Lagrange Spaces**, LAP LAMBERT Academic Publishing Germany. - Chandel, R. S., Singh, S. K., Shanker, Gauree (2005)
**A Text Book of Algebra and Trigonometry**, Ram Prasad & Sons Agra. - Singh, S. K., Shahi, J. P., Shanker, G. (2007)
**A Text Book of Real and Complex Analysis**, Ram Prasad & Sons Agra.

Conference Talks/Presentations

__Gauree Shanker__. Invited talk “**An Introduction to Curves in Plane and Space’**in Refresher course in Mathematical Sciences, jointly organized by UGC-HRDC and Department of Mathematics and Statistics,**D.D.U.Gorakhpur University Gorakhpur**during December 29, 2020 to January 11, 2021.__Gauree Shanker__. Invited talk “**Curves in Plane and Space”**in Refresher course in Mathematical Sciences, jointly organized by UGC-HRDC and Department of Mathematics,**Punjabi University Patiala**during November 16-28, 2020.__Gauree Shanker.__Invited talk “**Applications of Differential Geometry**” in National Seminar on Mathematical Applications in Science and Technology on the occasion of**National Mathematics Day**, organized by Department of Mathematics,**Chaudhary Bansi Lal University Bhiwani, Haryana**on December 22, 2020.__Gauree Shanker.__Invited talk “**Recent Advances on Homogeneous Finsler Sapces”**in the 26th International e-Conference of International Academy of Physical Sciences (CONIAPS XXVI) on "Advances in Relativistic Astrophysics & Cosmology" organized by Department of Mathematics, Sant Longowal Institute of Engineering and Technology during 18-20 December 2020.__Gauree Shanker.__Invited talk**“Modern view of Curves in Plane and Space”**in the One week Faculty Development Programme On Mathematical Tools and Recent Advances in Mathematics(MTAM-2020) organized by Department of Mathematics and Scientific Computing, Madan Mohan Malaviya University of Technology, Gorakhpur during September 21-25, 2020.__Gauree Shanker.__Invited talk “Importance and Applications of Mathematics in Engineering” in the Webinar on “Importance and Applications of Mathematics in Engineering” held on June 14, 2020 at**Babu Banarasi Das Institute of Technology and Managemant, Lucknow**.__Gauree Shanker__. Invited talk “Geometry of Manifolds with First Approximate Matsumoto Metric" in the**85th Annual Conference of Indian Mathematical Society}, An International Meet**, held at**IIT Kharagpur**during November 22-25, 2019.__Gauree Shanker__. Invited talk “Geometry of Surfaces with Constant Negative Curvature" in the**Int. Con. Diff. Geom. and Relativity**, held at**D.D.U.Gorakhpur University Gorakhpur**during November 08-10, 2019.__Gauree Shanker__. Invited talk**“**Geometry of some Important Surfaces**”**in the DST INSPIRE Internship Camp-2019 on September 27, 2019 at**Guru Nanak College for Girls at Muktsar**.__Gauree Shanker__. Invited talk “Orientable and Non-orientable Surfaces” in the National Conference on Recent Trends in Mathematical Sciences organized by Department of Mathematics and Statistics,**D. D. U. Gorakhpur University, Gorakhpur**during November 24-25, 2018.__Gauree Shanker__. Invited talk “Lie Groups and Lie Algebra” in the National Conference on, organized by Department of Mathematics*“Fractional Calculus, Special Functions and their Applications in Computer Science”***T. D. P.G. College, Jaunpur**in collaboration with Ramanujan Society of Mathematics and Mathematical Sciences during November 10-12, 2018.__Gauree Shanker__. Invited talk “The Geometry of the Gauss map” in the National Workshop onorganized by Department of Mathematics*“Science fare creating awareness, interest, motivation in Science and Mathematics for school students and teachers”,***T.D.P.G. College, Jaunpur**in collaboration with Ramanujan Society of Mathematics and Mathematical Sciences during November 10-13, 2018.__Gauree Shanker__. Invited talk “An Introduction to Surface Theory” on 08/10/2018 to the faculty and students of Department of Mathematics at**Baba Farid College Bathinda.**__Gauree Shanker__. Invited talk “Global Bahavior of Geodesics” in the 23rd International Conference of International Academy of Physical Sciences held at**Dr. R. M. L. Avadh University Faizabad**during April 13-15, 2018.__Gauree Shanker__. Invited talk “Metric structures associated with Finsler metrics” in the**International Conference on Mathematics and Applications**held at**Guru Ghasidas Viswavidyalaya, Bilaspur, Chhatishgarh**February 23-25, 2018.__Gauree Shanker__. Invited talk “Surgery on Manifolds” in the National Conference on Ramanujan: A Goddess Gifted Mathematician held at**T. D. P. G. College Jaunpur**during October 30-31, 2017.__Gauree Shanker__. Invited talk “Fundamentals of Surgery Theory” in the National Conference on Discrete Mathematics, Theoretical Computer Science, Computer Engineering and Applications held at**T. D. P. G. College Jaunpur**during October 28-29, 2017.__Gauree Shanker__. Invited talk “Sphere and its properties” on 20/09/2017 to the faculty and students of UG Department of Mathematics at**Baba Farid College Bathinda.**__Gauree Shanker__. Series of lectures in Mathematical Sciences**Refresher course at Punjabi University Patiala**during June 26-28, 2017.__Gauree Shanker__. Invited talk “Reversible geodesics for Finsler spaces with special (α, β) metrics" in the International Conference of**TIMC and American Mathematical Society**, held at**BHU Varanasi**during December 14-17, 2016.__Gauree Shanker__. Invited talk “Hyperbolic Geometry” in the National Workshop on "Treasures of great Indian Mathematician Srinivasa Ramanujan” organized by Ramanujan Society of Mathematics and Mathematical Sciences in collaboration with the Department of Mathematics,**T. D. P. G. College Jaunpur**during November 03-07, 2016, sponsored by DST Gov. of India.__Gauree Shanker__. Invited talk “Osculating Sphere” on 20/10/2016 to the faculty and students of PG Department of Mathematics at**Baba Farid College Bathinda.**__Gauree Shanker__. Invited talk "On the Nonholonomic Frames in Finsler Geometry" in the International Conference on Emerging Areas of Mathematics for Science and Technology held in the Department of Mathematics**Punjabi University, Patiala**during January 30-February 1, 2015.__Gauree Shanker__.Course associate in the**Instructional School for Lecturers on Differential Geometry**held at**Banasthali Vidyapith, Rajasthan**during December 8-20, 2014, supported by NCM, A Joint Centre of IIT Bombay and TIFR, Mumbai.__Gauree Shanker.__Invited talk “Stop Teaching Calculating, Start Teaching Math” in National Workshop on "Thoughts on Mathematics Education" held at**T. D. P. G. College Jaunpur**during November 02-06, 2014, sponsored by DST Gov. of India.__Gauree Shanker__. Invited "On the Conditions for a Four dimensional Conformally flat Landsberg space to be a Berwald space" in the symposium on Riemann-Finsler geometry organized in the**Annual meeting of Ramanujan Mathematical Society****held at IISER Pune**during 23-27 June 2014.

Special Training Programs / Workshops Attended

- Discussion Meeting on Zero Mean Curvature Surfaces (online) held at
**International Centre for Theoretical Sciences (ICTS), TIFR Bangalore**during July 07-15, 2020. - CIMPA School on Finsler Geometry and Applications held at
**DST-CIMS, BHU Varanasi**during December 05-15, 2019. - Instructional school for Lecturers on Geometric Topology held at
**DST-CIMS, BHU Varanasi**during July 07-19, 2014 supported by NBHM. - Instructional school for Lecturers on Topology and Geometry held at
**HRI Allahabad**during December 16-28, 2013 supported by NBHM. - National Workshop on Differential Geometry held at
**Banasthali Vidyapith, Rajasthan**during October 23-27, 2013, sponsored by DST Gov. of India. - National Workshop on Recent Trends in Biomathematics & Statistics held at
**Banasthali Vidyapith, Rajasthan**during Nov. 02-05, 2012, sponsored by DST Gov. of India. - Instructional school for Lecturers in Differential Geometry held at
**Kumaun University Almora**during May 21 to June 09, 2012 supported by NBHM. - National Workshop on Cryptography and Number Theory held at
**Banasthali Vidyapith, Rajasthan**during May 03-06, 2012, sponsored by DST Gov. of India. - Discussion Meeting on Analysis and Geometry held at
**HRI Allahabad**during March 12-16, 2012, sponsored by NBHM. - Workshop on Lie groups and Lie Algebra, organized by
**HRI, Allahabad**during August 22-27, 2011, sponsored by NBHM. - National Workshop on Inventory Modeling, organized by Center for Mathematical Sciences,
**Banasthali Vidyapith, Rajasthan**, India during March 04-07, 2011. - National Workshop on Block Designs and Their Applications, organized by Center for Mathematical Sciences,
**Banasthali Vidyapith, Rajasthan**, during February 05-08, 2011. - Workshop on Latex and other open source Software, organized by Center for Mathematical Sciences,
**Banasthali Vidyapith, Rajasthan**, during March 25-27, 2010. - National Workshop on Discrete Mathematics, organized by Center for Mathematical Sciences,
**Banasthali Vidyapith, Rajasthan**during May 01-05, 2010. - Mini MTTS Program on Number Theory and Algebra, organized by
**Banasthali Vidyapith, Rajasthan**during December 18-24, 2010 supported by NBHM. - Advanced Training In Algebra and Number Theory, organized by
**Panjab University, Chandigarh**during December 15-31, 2009, sponsored by NBHM. - Pre-Conference Workshop on Discrete Mathematics, organized by Center for Mathematical Sciences,
**Banasthali Vidyapith, Rajasthan**during January 06-10, 2009. - Training Program on Optimization Techniques, organized by Center for Mathematical Sciences,
**Banasthali Vidyapith, Rajasthan**during December 24-29, 2008.

Training programs / Workshops/Conferences Organized

- Organized
**One day seminar and quiz competition**on**National Mathematics Day**, December 22, 2018 sponsored by Punjab State Council for Science and Technology, at**Central University of Punjab, Bathinda** - Organized special lectures by Prof. Valeriey Bardakov Russia and Prof. K. Gongopaphyay, IISER Mohali on October 25, 2016 in Centre for Mathematics and Statistics,
**Central University of Punjab, Bathinda.** - Convener, Instructional School for Lecturers on Differential geometry held at
**Banasthali Vidyapith, Rajasthan**during December 08-20, 2014, sponsored by NCM. - Co-coordinator, National Workshop on Differential Geometry held at
**Banasthali Vidyapith, Rajasthan**during October 23-27, 2013, sponsored by DST Gov. of India. - Member organizing committee, National Workshop on Recent Trends in Biomathematics & Statistics held at
**Banasthali Vidyapith, Rajasthan**during Nov. 02-05, 2012, sponsored by DST Gov. of India. - Member organizing committee, National Workshop on Cryptography and Number Theory held at
**Banasthali Vidyapith, Rajasthan**during May 03-06, 2012, sponsored by DST Gov. of India. - Member organizing committee, National Workshop on Linear and Non-linear systems, organized by
**Banasthali Vidyapith, Rajasthan**during December 15-19, 2011, supported by DST Gov. of India. - Member organizing committee, National Workshop on Block Designs and Their Applications, organized by Center for Mathematical Sciences,
**Banasthali Vidyapith, Rajasthan,**India during February 05-08, 2011. - Member organizing committee, Workshop on Latex and other open source Software, organized by Center for Mathematical Sciences,
**Banasthali Vidyapith, Rajasthan**during March 25-27, 2010. - Member organizing committee, National Workshop on Discrete Mathematics, organized by Center for Mathematical Sciences,
**Banasthali Vidyapith, Rajasthan**during May 01-05, 2010. - Member organizing committee, Mini MTTS Program in Number Theory and Algebra, organized by
**Banasthali Vidyapith, Rajasthan**during December 18-24, 2010 supported by NBHM. - Member organizing committee, Pre-Conference Workshop on Discrete Mathematics, organized by Center for Mathematical Sciences,
**Banasthali Vidyapith, Rajasthan**during January 06-10, 2009.

Member/Life member of Learned Bodies

- Associate member, American Mathematical Society, USA.
- Annual member, Tensor Society, Japan. (Membership code: G-22).
- Life member, Tensor Society, India. (Membership code: LS-43).
- Life member, Indian Mathematical Society. (Membership code: S-10-330).
- Life member, Ramanujan Mathematical Society (1002).
- Life member, Indian Society of Mathematics and Mathematical Sciences. (Membership code: LM-327).
- Associate member, International Academy of Physical Sciences, Allahabad. (A21365)

Research Areas

- Geometry and Topology: Riemann-Finsler Geometry, Homogeneous and Symmetric Finsler Spaces, Submanifold Theory.

Overview of Research work

The study of Differential geometry makes us aware of the potential applications of exploring non-linear aspects and non-trivial symmetries arising in various models of gravity, classical and quantum field theory and geometric mechanics. Finsler geometry has its roots in various problems of Differential Equations, Calculus of Variations, Mechanics and Theoretical Physics. The basic idea of Finsler space came from the groundbreaking "habilitation" lecture of Riemann: Uber die Hypothesen, Welch der Geometric zugrnde liegen (On the Hypothesis, which lie at the Foundations of Geometry). During the last thirty years, Finsler geometry has gone under remarkable developments. Specially, a lot of results from Riemannian manifolds have been extended for Finsler manifolds by the researchers from all over the world. Presently, Finsler geometry has found an abundance of applications in both Physics and its applications. Such applications include not only the traditional area of general Relativity, but also the theory of Yang-Mills fields, non-linear sigma models, superstring theory, and other types of non-linear field systems that feature in modern elementary particle theory and quantum gravity and Biology. In Biology, there are a lot of Finsler metrics which are suitable to describe biological models like Protein structure, coral reef ecology, etc.

The applications of Finsler geometry in various fields of science and its pure impact on real life problems motivate researchers to do research in this beautiful area of mathematics. We are particularly interested to work in Riemann- Finsler geometry. We have worked on several interesting and important topics of Finsler Geometry like Conformal transformation of Finsler spaces, Projective change and Projective flatness of Finsler spaces, Hypersurface of Finsler spaces with (α,β) metric, Finsler-Cartan duality in which we have obtained L-duals of Finsler spaces with (α,β)-metrics, Main scalars of Finsler spaces, Non-holonomic frames in Finsler geometry, existence of reversible geodesics in Finsler spaces, locally duallly flatness of Finsler spaces and Unicorn problems. Currently, we are working on Homogeneous Finsler spaces, Symmetric Finsler spaces Geometry of Finsler spaces with some special (α,β)-metrics, and some more interesting current topics. Further, we have also started some work on submanifolds theory.

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