It is my space: Let's take a walk!!

Workplace & Home

Education

• 1994 Ph.D. BHU, Varanasi [Thesis Advisor: Prof. Nand Lal] "Polynomial Compactness of Operators and Induced Derivations" 

• 1986 M.Sc. A.P.S. University , Rewa (M.P.)

• 1983 B.Sc. Bhopal University,  Bhopal (M.P.)

Research Experience

• 1989-1991: Junior research fellow, Department of Mathematics, BHU

• 1991-1994: Senior research fellow, Department of Mathematics, BHU

• July,1995-October,1995: Research Associate (CSIR), Department of Mathematics,University of Delhi (DU)

• November,1995-July,1996: Post-doctoral Fellow (NBHM), Department of Mathematics,University of Delhi (DU) [PDF Mentor: Prof. Ajit Iqbal Singh]

Employment (Deen Dayal Upadhyaya College, University of Delhi)

•  Professor   2018 -- 

• Associate Professor  2008-2018

•   Reader   2005-2008

•   Senior Lecturer 2000-2005

•   Lecturer 1996-2000

Under - Graduate Teaching

• 1991-1994: Senior Research Fellow, taught undergraduate classes in the department of mathematics ,Benaras Hindu University, Varanasi (Real Analysis)

• 1996-1997: Temporary Lecturer, taught undergraduate classes in the department of mathematics, Deen Dayal Upadhyaya College(DU) (Real analysis, Mechanics, algebra)

• 1997-2005: Lecturer, taught undergraduate classes in the department of Mathematics, Deen Dayal Upadhyaya College (DU) (Real analysis, algebra, Differential Equations) 

• 2005- 2008. : Reader, taught undergraduate classes in the department of Mathematics, Deen Dayal Upadhyaya College (DU) (Real analysis, Algebra, Differential Equations, Linear algebra)

• 2008- 2018: Associate Professor, taught undergraduate classes in the department of Mathematics, Deen Dayal Upadhyaya College (DU) (Real analysis, Algebra, Differential Equations, Linear algebra, Advanced calculus, complex analysis)

• 2016-2017: (on sabbatical leave), taught undergraduate classes in the department of mathematics, SSJ Campus, Kumaun University (Group Theory and Analysis)

• 2018-contd: Professor, taught undergraduate classes in the department of Mathematics, Deen Dayal Upadhyaya College (DU) (Real analysis, Algebra, Differential Equations( Generic Elective), Linear algebra ( Generic Elective), Calculus(Honors/GE), Skill Enhancement Courses)

Post-Graduate Teaching

• 1986-1988: Part-time Lecturer, department of mathematics, UTD, APS University, Rewa (MP), (Riemannian Geometry)

• 2001-2014 : Under Cooperative - teaching ,postgraduate (M.Sc.) classes in the department of Mathematics,South Campus (Delhi University) (Differential Geometry, Calculus in Euclidean Spaces, Complex Analysis, Differentiable Manifolds, Algebraic Topology)

• 2004-2005: Under Cooperative - teaching ,postgraduate (M.Sc.) classes in the department of Mathematics, North campus (Delhi University)   (Complex Analysis)

• 2016-2017:(on sabbatical leave), M.Sc.classes in the department of mathematics, SSJ Campus, Kumaun University ( Analysis and Measure Theory)

M.Phil./PhD Course -Work Teaching

• Introduced  a course since 2019 on Several  Complex Variables in the Department of Mathematics DU for MPhil/PhD students

MATH19 -R10  &  MATH20-R11 Introduction to Several Complex Variables

• This academic year (2021-22) I am offering a new MPhil/PhD course work

              MATH21 - R11 Introduction to Minimal Surfaces 

• This academic year (2022-23) 

              MATH22 - R11 Introduction to Minimal Surfaces 

P1. Non-compactness of derivations on B (l^2), (with Nand Lal), J.Indian Math.Soc.(N.S.),

Vol.61, No. 3-4, 255-259, 1995. (MR1457942) (SCOPUS) (ISSN: 0019-5839 ) 

P2. Polynomial compactness of derivations, (with Nand Lal), J.Indian Math.Soc.(N.S.), Vol.

72, No. 1-4, 211-220, 2005.(MR2291490) (SCOPUS) (ISSN: 0019-5839 )

P3. A class of polynomially compact composition operators on disc algebra, (with Harish Chandra), Progr.  Math. (Varanasi), vol. 39, No. 1&2, 9-17, 2005. ( MR2438059) (Peer reviewed) 

P4. Compactness of generalized derivations, Proceedings of the national conference

on mathematical techniques(MATIET 2006) , Allied Publishers, 30-33, 2006. (Conference)

P5. Polynomial derivations, (with Harish Chandra), Progr. Math.(Varanasi),vol. 40,No.1-2,109-118,2006.( MR2560139) (Peer reviewed) 

P6.  Common fixed points of weekly compatible maps in symmetric spaces, (with Arvind Bhatt and Harish Chandra), Appl.Math.Sci. (Ruse) Vol.6 , No.53-56, pp. 2703-2710, 2012. (MR2915526) (SCOPUS) (ISSN: 1312-885X) 

P7. On dynamics of composite entire functions and singularities, (with D. Kumar), Bull. Cal. Math. Soc. Vol. 106, No. 1, pp. 65-72, 2014. (MR3380950) (UGC CARE) (ISSN: 0008-0659)

P8.Dynamics of composite entire functions,(with D. Kumar and G. Datt),  J. Indian Math. Soc. (N.S.), Vol. 82, No. 3-4, 107-114, 2015.(MR3467620) (SCOPUS)(ISSN: 0019-5839) 

P9. The dynamics of semigroups of transcendental entire functions I, (with D. Kumar), Indian J. Pure Appl. Math. Vol.46, Issue1, pp. 11-24, 2015. (MR3332953)(SCIE)

(ISSN/eISSN: 0019-5588/0975-7465) (https://doi.org/10.1007/s13226-015-0104-0) 

P10. Normality and Sharing functions,(with G. Datt),  Indian J. Pure Appl. Math. Vol. 46 , Issue 6, pp. 853-864, 2015.(MR3438040) (SCIE) (ISSN/eISSN: 0019-5588/0975-7465)  (https://doi.org/10.1007/s13226-015-0155-2) 

P11. The dynamics of semigroups of transcendental entire functions II, (with D. Kumar), Indian J. Pure Appl. Math. Vol. 47, Issue 3, pp. 409 - 423, 2016.(MR3552957) (SCIE) 

  (ISSN/eISSN: 0019-5588/0975-7465). (https://doi.org/10.1007/s13226-016-0173-8)

P12. A Normality Criterion for a Family of Meromorphic Functions , (with G. Datt), Monatsh. Math. Vol. 180, Issue 2, pp. 193-204, 2016.(MR3502624) (SCIE)  (ISSN/eISSN: 0026-9255 / 1436-5081) (https://doi.org/10.1007/s00605-016-0896-y)

P13. On a Theorem of Schwick , (with G. Datt),  Bull. Cal. Math. Soc. Vol.108, No.3, pp.225-234, 2016.(MR3560656) (UGC CARE) 

  (ISSN: 0008-0659)

P14. Normality and Montel’s Theorem , (with G. Datt),  Arch. Math.(Basel) Vol.107, Issue 5, 511-521, 2016 .(MR3562379) (SCIE)  (ISSN/eISSN: 0003-889X / 1420-8938) (https://doi.org/10.1007/s00013-016-0954-7 ) 

P15. Some normality criteria , (with G. Datt),  Turkish J. Math. , Vol.40, No.6, 1258-1273, 2016.(MR3583245) (SCIE) (ISSN: 1300-0098 / 1303-6149). ( https://doi.org/10.3906/mat-1508-7 )

P16. Escaping Set and Julia Set of Transcendental Semigroups , (with D. Kumar and K K Poon) , Advances in Theoretical and Applied Mathematics, Vol. 11, Number 4, 423 - 436, 2016.(ISSN/eISSN:  0973-4554)

P17. Escaping sets of e^z -1,  (with Dinesh Kumar) Thai J. Math., Vol.15, No.2, 517-522, 2017.(MR3770086) (SCOPUS)  (ISSN/eISSN: 1686-0209 ) 

P18. Semigroups of transcendental entire functions and their dynamics,(with D. Kumar) Proc.Indian Acad.Sci.Math.Sci., Vol. 127, no.2 , 349-360, 2017.(MR3647157) (SCIE) (ISSN/eISSN:0253-4142 / 0973-7685) (https://doi.org/10.1007/s12044-016-0298-z) 

P19. A criterion for Quasinormality in C^n, (with Gopal Datt) Proc.Indian Acad.Sci.Math.Sci., Vol. 129, no. 1, Art. 11. 13pp , 2019.(MR3892779) (SCIE) (ISSN/eISSN:0253-4142 / 0973-7685) ( https://doi.org/10.1007/s12044-018-0449-5) 

P20. On Solutions of Second Order Complex Differential Equations, (with Dinesh Kumar and  Manisha Saini) Bull. Cal.  Math. Soc. , 111 (4), 331-340, 2019. (UGC CARE) (ISSN: 0008-0659)

P21. On Zeros and Growth of Solutions of Second Order Linear Differential Equations, (with Manisha Saini) , Commun. Korean Math. Soc. 35 No 1, 229-241, 2020. (SCOPUS)(ISSN/eISSN: 1225-1763/2234-3024)( https://doi.org/10.4134/CKMS.c180494)

P22. Normality criteria for families of meromorphic functions (with Poonam Rani) Indian J. Pure Appl. Math.51,Issue 2,  579-588,  2020  (SCIE) (ISSN/eISSN: 0019-5588/0975-7465)(https://doi.org/10.1007/s13226-020-0418-4) 

P23. Order and Hyper-order of Solutions of Second Order Linear Differential Equations (with Manisha Saini) B Malays Math Sci So, 2020 (SCIE)(ISSN/eISSN: 0126-6705/2180-4206) (https://doi.org/10.1007/s40840-020-00993-w)

P24.  d-balanced Squeezing Function (with Naveen Gupta) accepted for publication in Complex Variables and Elliptic Equations. 2021(https://doi.org/10.1080/17476933.2021.2007380) (SCIE)

P25. Squeezing function corresponding to polydisk (with Naveen Gupta), Complex Analysis and its Synergies 8, 12 (2022). https://doi.org/10.1007/s40627-022-00100-8

P26. Entire Solutions of Certain Non-Linear Differential -Difference Equations (with Garima Pant), Journal of the Indian Math. Soc. 90, Nos. 3-4, 275-288 (2023)

P27. Study of Solutions of Certain Kind of Non-Linear Differential Equations (with Garima Pant), Indian J Pure Appl Math (2023),https://doi.org/10.1007/s13226-023-00398-y (SCIE)

P28. A Note on Schwarzian Derivatives and Normal Families (with Dinesh Kumar), Ganita, Vol. 73(1), 59-63 (2023)

preprint/communicated

• (with P. Rani) Normality Criteria for Families of Meromorphic Functions about Shared Functions 

[ arXiv:1906.02966 ]. 

• (with K. Lalwani), Attractors and chain recurrence in non-compact spaces for generalized semigroup, [Communicated] 

• (with Naveen Gupta) A note on squeezing function and its generalisations [ communicated]

Books

• Study Guide: MMT-005 Complex Analysis, ISBN-978-81-266-3210-7, Indira Gandhi National Open University, (2007, Reprint March 2012) (with Poornima Mital)

• MMT-005  Complex Analysis, ISBN: 978-93-89969-18-4, Indira Gandhi National Open University, (December 2019 )(Co-authors- Sumit Nagpal, Poornima Mital)

Thesis

• https://drive.google.com/file/d/1iWg_bDdlo1Y-a6bay6miKiXDFW_spV9_/view?usp=sharing

M.Phil

1.Dinesh Kumar (2011),Thesis titled “Fatou's No Wandering Domain Conjecture: Sullivan's  Proof ” [arXiv:1101.5456]

2.Kushal Lalwani (2014) “Triangulation and  Classification of 2-Manifolds”  [arXiv:1407.8478]

3.Naveen Gupta  (2014) “ Injectivity in Higher Order Complex Domains” [arXiv:1810.10707v1]

4. Manisha Saini (2015)  “Nevanlinna Theory and Normal families”  [ arXiv:1810.07015 ]

5. Mohd Vaseem (2021)  "Dynamics of Rational Functions in the Extended Complex Plane"

6. Akhil Kumar (2021)  "Squeezing Functions on Planar Domains" 

7. Simran  (2022-23) Joined PhD

8. Hariom Dhakar (2022-23) Joined PhD

Ph.D

1.Dinesh Kumar (2016) Semigroups of Transcendental Entire functions and their Dynamical Properties

(Assistant Professor, BIT, Mesra )

2.Gopal Datt (2017) Normal Families in One and Several Complex Variables: Looking through Zalcman’s Lemma

(Assistant Professor, BBAU, Lucknow)

3. Poonam Rani (2021)  Normality for Families of Meromorphic Functions

4. Kushal Lalwani (2021)  Topological Dynamics for Generalized Semigroups: Attractors,Recurrence and Escaping Set (Assistant Professor, Manav Rachana University,  Faridabad)

5. Manisha Saini (2022) The Growth of Solutions of Complex Differential Equations with Entire Coefficients 

(Assistant Professor, Hansraj College, Delhi University)

6. Ramanpreet Kaur (2023) On Certain Aspects of Fatou Components and Escaping Set of a Transcendental Entire Functions (Post Doctoral Fellow, Department of Mathematics, IISER, Mohali)

7. Sakshi Jain (2017-2019) (she got research fellowship for PhD in University of Rome, Italy)**

8. Naveen Gupta (2023) Squeezing Function and its Generalizations (Assistant Professor , Department of Mathematics, NSUT, Delhi)

9. Garima Pant (2025) On Solutions of Certain Complex Differential, Differenc and Delay-Differential Equations 

10. Nidhi Gahlian (2021 - ) ( Lecturer (PGT) -HPSC)

11. Mohd Vaseem (2022 -)

12. Akhil Kumar (2022-)

13. Simran (2023-)

14. Hariom Dhakar (2023-)

15. Ashish Kumar Trivedi (2024-)(Under co-supervision of Dr Gopal Datt, BBAU, Lucknow)

16, Rahul Gogoi (2024-)(Under co-supervision of Dr Gopal Datt, BBAU, Lucknow)

Workshops and Conferences (Participated/Attended as speaker/organised)

Conference on Functional Analysis and Linear Algebra, ISI, Delhi Centre, Stat. & Math.Unit ,January 3-7, 2000

Instructional School on Linear Algebra, Punjab University, Chandigarh (December, 2000)

Workshop on Banach Algebras and International conference on Analysis, Sardar Patel University,Vallabh Vidyanagar, Gujarat (2002)

Joint India-AMS Meeting, IISc-ISI, Bangalore ,December 2003

Conference on Functional Analysis and its Applications, Sardar Patel University, Vallabh Vidyanagar Nagar, Gujarat (March 2005)

Quasiconformal Mappings and Their Applications (IWQCMA 05), IIT Madras, Chennai ,December

27, 2005- January 1, 2006

International Workshop on Teichmuller Theory & Moduli Problems, Harish Chandra Research Institute (HRI), Allahabad 

January 5, 2006-15, 2006 (Invited Participant)

Annual Foundation School II (ATM) NBHM, BIM and Pune University, Pune, June 1-28, 2006

(as associate teacher)

Advanced Instructional School on Differential Geometry and Lie groups (ATM) NBHM, BIM and Pune University, Pune

December 4-28, 2006 (as associate teacher)

Workshop on the geometry and topology of low-dimensional manifolds: Poincare conjecture and Teichmuller theory

Department of mathematics and Bhaskaracharya Pratishthan, Pune, 2nd – 16th January, 2008.

Compact course on dynamics in Higher Dimensions by  Nessim Sibony, Department of Mathematics, IISc, Bangalore 

21st Dec, 2008-6th January,2009.

 ATM School for Lecturers in Complex Analysis, 16th March 2009 - 4th April 2009, Department of Mathematics, University of Delhi. (organiser)

ATM School for Lecturers in Real Analysis, 22nd March 2009 -3rd April 2010, Department of Mathematics, University of Delhi. (organiser)

ATM Workshop on Several Complex Variables and Complex Dynamics,1st March,2010-13th March,2010, Department of Mathematics, IISc, Bangalore. (Invited Resource Person)

ATM School for Lecturers in Geometric Complex Analysis,21st March 2011 -2nd April 2011, Department of Mathematics, University of Delhi. (organiser)

Kyoto Symposium on Complex Analysis in Several Variables XIV, 19-22 July,2011, Kyoto University, Kyoto,Japan (participated)

Instructional school for Lecturers on Differential Geometry, 21 May-9 June, 2012, CEMS, Kumaun University, Almora(organizer)

Almora Mathematical Surveys, NCM School, 3rd October-6th October, 2012, CEMS, Kumaun University, Almora(organizer)

ICTS Discussion Meeting and Conference ( Groups, Geometry and Dynamics), 3rd December-16th December, 2012, CEMS, Kumaun University (organiser)

Geometric Aspects in Modern Dynamics, 11th January 2016 - 15th January 2016, University of Porto (Portugal) (participated)

International Workshop and Conference ( Complex Analysis: Geometric and Dynamical Aspects), 14th November -19th  November, 2016, CEMS, Kumaun University (organiser)

HAYAMA Symposium on Complex Analysis in Several Variables XX and Pacific Rim Complex-Symplectic Geometry Conference , 13 July - 17 July, 2018, Shonan Village Centre, Hayama, Japan (Invited Participant)

Discussion Meeting on Several Complex Variables , 17th December  - 21st  December, 2018 , TIFR-CAM , Bengaluru (invited participant)

Cauchy - Riemann Equations in Higher Dimensions (ICTS, Bengaluru Programme, 15th July -2nd August, 2019, International Centre for Theoretical Sciences, Bengaluru (Invited Participant) 

Workshop on Several Complex Variables , 9th December  - 13th   December, 2019 , Kerala School of Mathematics (KSOM) , Kozhikode (invited speaker)

Refresher Course in Mathematics , 16-30 March 2021, Ramanujan College (University of Delhi), ( recorded talks on Singularities in Complex Analysis)

Open Problems: Why we should care about them (A Talk), 25 April 2022, Department of Mathematics, I P College , Delhi Unioversity

Teaching in odd-even  semesters (2021-2022)

Semester-I

• Generic Elective - 1 ( Calculus) (https://classroom.google.com/c/NDQxNDIzMTA0MTIy?cjc=nu3sc4n)

Semester -II

• Real Analysis  ( https://classroom.google.com/c/NDgzNzA1MDE0ODU0?cjc=d7ltv5h )

Semester-III

• Generic Elective-3 ( DE) ( https://classroom.google.com/c/Mzg2NTI3Mzk0ODU3?cjc=3phjecu)

Semester-VI

• Ring Theory and Linear Algebra -II  (https://classroom.google.com/c/NDUwMzU1Mzc4MjM2?cjc=wzx3wpa )

Teaching in odd-even  semesters (2022-2023)

Semester - V

• Group Theory - II ( https://classroom.google.com/c/NTM2MTA0ODg5NjU0?cjc=itvptcb )

     Semester - I & II

• Elementary Real Analysis  & Calculus (https://classroom.google.com/c/NTA0NzE0MDM5Njg1?cjc=zhdhl5h )

    Semester - II

• Generic Elective - Linear Algebra  

Teaching Odd Semester (2023-2024)

Semester-I

• Generic Elective - Fundamentals of Calculus

Teaching Even Semester (2023-2024)

Semester - VI

• Ring Theory and Linear Algebra -II

• Complex Analysis with Practicals

Teaching Odd Semester (2024-2025)

Semester - III

• Riemann Integration

Semester - V

• Metric Spaces

Teaching Even Semester(2024-25)

Semester - IV

• Multi Variables Calculus

Semester - VI

• Complex Analysis