Currently, I am studying various first-order inequalities, such as Poincare, Sobolev, and Morrey type inequalities, associated to the Monge-Ampere gradient in the Monge-Ampere quasi-metric structure shaped by convex functions.  These inequalities find applications in the elliptic Partial Differential Equations, and in other branches of mathematics.

Publications:

• First order inequalities via Riesz potentials in the Monge-Ampere quasi-metric structure, J. Math. Anal. Appl 2024. pdf 

• Solvability of Inclusions Involving Perturbations of Positively Homogeneous Maximal Monotone Operators, Electronic Journal of Differential Equations - 2022 pdf  (Co-authors: Dhruba R. Adhikari, Ashok Aryal, Ghanshyam Bhatt, Ishwari J. Kunwar, Rajan Puri).

• Poincare and Sobolev inequalities in the Monge-Ampere quasi-metric structure, J. Math. Anal. Appl. 2020 pdf (Co-author: Diego Maldonado).

• Poincare and Sobolev inequalities in the Monge-Ampere quasi-metric structure, Ph.D Dissertation, Kansas State University, 2020. 

Talks and Presentations:

• Department of Mathematics, Prithivi Narayan Campus, Pokhara "Teaching Mathematics at US Universities and Experience Sharing" (June 1, 2023).

• Third International Conference on Applications of Mathematics to Nonlinear Sciences, ''First-order inequalities associated to convex functions" (May 27, 2023).

• International Conference on Analysis and Its Applications (ICAA) - 2021, ''First-order inequalities in the Monge-Ampere quasi-metric structure" (April 10, 2021).

• Joint Mathematics Meetings (JMM) in Denver, Colorado "Recent updates on Poincare and Sobolev inequalities in the Monge-Ampere quasi-metric structure" (January 17, 2020).

• Prairie Analysis Seminar at Kansas State University "Poincare and Sobolev inequalities associated to certain convex functions" (November 9, 2019).

• DE and Applied Analysis Seminar at University of Nebraska, Lincoln “Poincare and Sobolev inequalities in the Monge-Ampere quasi-metric structure” (October 15, 2019).

• Analysis seminar at Kansas State University “Poincare and Sobolev inequalities in the Monge-Ampere quasi-metric structure” (October 1, 2019).

• Analysis seminar at Kansas State University “Poincare inequalities in the Monge-Ampere quasi-metric structure” (April 30, 2019).

• MSRI-University of California at Berkeley “Bergman theory” (June 22, 2018).

• Presentation for the major part of preliminary exam "Geometric properties of the cross sections of convex functions" (May 04, 2018).

• Analysis seminar at Kansas State University “An introduction to the Monge-Ampere measure and generalized solutions to the Monge-Ampere equation” (November 28, 2017).

• Graduate student seminar at Kansas State University “Qualifying exam on Applied Mathematics” (September 21, 2017).