Harmonic Analysis

• M. Sc. , 2002 , Banaras Hindu University
• Ph. D. , 2011 , University of Delhi

Assistant Professor at Hansraj College since November 2010 to November 2022.

Associate Professor at Hansraj College since November 2022 to date.

1. Calculus

2. Real Analysis

3. Complex Analysis

4. Number Theory

5. Group Theory

6. Linear Algebra

7. Ring and Field Theory

8. Cryptography and Network Security

9. Discrete Mathematics

10. Differential Geometry (PG)

11. Measure Theory and Integration (PG)

12. Lie Groups and Lie Algebras (Pre-PhD)

PhD Guidance:

1. Ms. Shivani Dubey (Awarded)

2. Mr. Devendra Tiwari (Awarded)

3. Mr. Ashutosh Pandey

4. Ms. Rachna Aggarwal

5. Ms. Surbhi Beniwal

6. Ms. Apeksha Verma

MPhil Guidance:

Ms. Shweta Gupta (Awarded)

1. Teacher-in-Charge, Department of Mathematics

2. Admission Convener (Sciences)

Potential Theory on Stratified Lie Groups

1. Polyharmonic Dirichlet problem on the Heisenberg group

(Ajay Kumar and Mukund Madhav Mishra)

Complex Variables and Elliptic Equations(Taylor & Francis Group, UK)

Vol. 53, No. 12(2008) p. 1103–1110,.

2. Green’s Functions on the Heisenberg Group

(Ajay Kumar and Mukund Madhav Mishra)

Analysis: International mathematical journal of analysis and its applications, (Oldenbourg Wissenschaftsverlag)

Volume 30, p. 147-155.

3. Green Functions and related boundary value problems on the Heisenberg Group

(Ajay Kumar and Mukund Madhav Mishra)

Complex Variables and Elliptic Equations (Taylor & Francis Group, UK)

Vol 58, No. 4 (2012), p 547-556.

4. Powers of Sub-Laplacian on Step Two Nilpotent Lie Groups

(Ajay Kumar and Mukund Madhav Mishra)

Journal of Geometric Analysis (Springer)

Vol. 23, Issue 3 (2013), p. 1559-1570

( DOI 10.1007/s12220-012-9298-0).

5. Green's function for certain domains in the Heisenberg group (Shivani Dubey, Ajay Kumar and Mukund Madhav Mishra)

Boundary Value Problems (Springer)

2014:182, p 1-16.

6. Green’s Function for a Slice of the Korányi Ball in the Heisenberg Group (Shivani Dubey, Ajay Kumar and Mukund Madhav Mishra)

International Journal of Mathematics and Mathematical Sciences (Hindawi)

2015, p 1-7.

7. Neumann Boundary Value Problem on the Heisenberg Group

(Shivani Dubey, Ajay Kumar and Mukund Madhav Mishra)

Potential Analysis (Springer)

Vol 45, Issue 1 (2016), p. 119-133

DOI 10.1007/s11118-016-9538-1

8. Polyharmonic Neumann and mixed boundary value problems in the Heisenberg group (Shivani Dubey, Ajay Kumar and Mukund Madhav Mishra)

Complex Variables and Elliptic Equations (Taylor and Francis)

2017, p. 1-14

http://dx.doi.org/10.1080/17476933.2016.1278439

1. Workshop on Euclidean Harmonic Analysis (From 11-12-2006 to 24-12-2006 at IIT Kanpur).

2. National Symposium on Functional Analysis, Optimization And Their Applications, Jan 19-20, 2007 at Deen Dayal Upadhayay College, University of Delhi.

3. National Workshop on Analysis, Sep 27-28, 2007 at Department of Mathematics, University of Delhi.

4. International Conference on Operator Theory and Related Areas,2007

Department of Mathematics, University of Delhi.

5. 10th Discussion Meeting in Harmonic Analysis, IISc Banglore(2008).

6. Pre ICM ICMS, 2008, Department of Mathematics, University of Delhi.

7. National Meet on History of Mathematics, 2009, Department of Mathematics, University of Delhi.

8. ICM 2010 at Hyderabad.

9. National Initiative in Mathematics Education: Northern Region Conference(2011).

10. 12th Discussion Meeting in Harmonic Analysis, ISI Calcutta(2011).

11. 13Th Discussion Meeting in Harmonic Analysis, IMSc (2013)

12. International Workshop on “Geometric and Analytic Aspects of Hyperbolic Spaces” during December 10-15, 2014, Department of Mathematics, DU.

13. International Workshop on Operator Spaces during December 7-9, 2015, Department of Mathematics, DU.

14. 14th Discussion Meeting in Harmonic Analysis, December 10-12, 2015, Department of Mathematics, DU.

1. Delivered contributed talk in “International Conference on Operator Theory and Related Areas, 2008” on “Polyharmonic Dirichlet Problem on the Heisenberg Group” at University of Delhi.

2. Delivered contributed talk in “Pre ICM International Convention in Mathematics and Mathematical Sciences, 2008” on “Green’s Functions on the Heisenberg Group” at the department of Mathematics, University of Delhi.

3. Delivered a talk in “Advances in Mathematics: Focus on women in Mathematics, Oct 2009’’ on “Potential Theory on the Heisenberg Group”. 

4. Delivered a talk in the Symposium on Analysis in the Annual Conference of the Ramanujan Mathematical Society at NIT Jalandhar(2010) on “Dirichlet Problem on the Heisenberg Group”.

5. Delivered a talk entitled “Green Function for the Annular Domain in the Heisenberg Group” in the 13th Discussion Meeting in Harmonic Analysis (2013).

6. Delivered a talk entitled “Am I Prime?” at the Indraprastha College of Women, University of Delhi (2014).