About

I am a Ph.D. candidate in the Department of Mathematics at the University of Alabama at Birmingham, advised by Prof. Yanni Zeng. My research is in nonlinear partial differential equations, in particular global existence of solutions for chemotaxis models arising in mathematical biology. I also work on problems in computational mathematics, data science, and scientific machine learning.

I have taught mathematics for over ten years, at UAB, Florida Atlantic University, and Himalaya College of Engineering (Tribhuvan University) in Nepal, including Intermediate Algebra, Precalculus, Calculus, and Probability and Statistics. I expect to complete my Ph.D. in Spring 2027 and am currently seeking tenure-track faculty positions.

Education

Teaching

I want students to understand why mathematics works, not only how to carry out procedures. Whenever I can, I let students discover an idea before I formalize it: before we cover trigonometric equations, for example, students first work through an inquiry-based activity in small groups, so that the method they later learn is one they have already begun to build themselves. Inquiry turns a lesson from mastering a skill into understanding an idea.

I pair this with clear structure, frequent low-stakes practice, and real data and applications, so that students leave my courses with both skill and confidence. Having taught for more than ten years on two continents, I adapt my teaching to students of very different backgrounds and preparation.

  • 2022 – present
    Instructor of Record, University of Alabama at Birmingham
    Introduction to Statistics (MA 180) · Calculus I (MA 125) · Precalculus: Algebra and Trigonometry (MA 107) · Precalculus: Trigonometry (MA 106) · Precalculus: Algebra (MA 105) · Intermediate Algebra (MA 102)
  • 2020 – 2022
    Instructor of Record, Recitation Leader and Teaching Assistant, Florida Atlantic University
    Methods of Calculus (Instructor of Record) · Recitation Leader for Calculus II and Calculus III · Calculus I and II (MAC 2311, 2312) · Engineering Mathematics I (MAP 3305) · Tutor, Engineering Mathematics and Mathematics for Liberal Arts
  • 2015 – 2019
    Lecturer, Himalaya College of Engineering (affiliated to Tribhuvan University), Nepal
    Probability and Statistics for Engineers (B.E. and B.Sc. CSIT) · Differential Calculus · Integral Calculus · Vector Analysis/Calculus · Linear Algebra . Statistics I, II ·

Teaching Statistics

Statistics is a central part of my teaching. I have taught Probability and Statistics to engineering and computer science students for several years in Nepal and Introduction to Statistics at UAB, and I hold an M.S. in Applied Mathematics and Statistics (Biostatistics track). In my statistics courses, students work with real data sets, interpret results in context, and use software such as R, Python and Minitab, so that statistical reasoning becomes a practical tool rather than a set of formulas.

I am prepared to teach introductory and applied statistics, probability, statistics for engineers and scientists, regression and data analysis, and Bayesian methods.

Course pages, notes, slides and syllabi →

Teaching Development

  • CTL LIFT Teaching Certificate, UAB Center for Teaching and Learning
  • Inquiry-Based Learning Workshop, Department of Mathematical Sciences, FAU
  • CRLA Certification, Levels 1 and 2, FAU Mathematics Learning Center
  • Flex/Online Teaching Orientation and Teaching Assistant Basics for Online Courses, FAU

Research

Interests: partial differential equations, mathematical biology and chemotaxis, hyperbolic–parabolic systems, computational mathematics, data science, and machine learning.

Dissertation

Global Existence of Solutions on the Quarter Plane for a Chemotaxis Model with Logistic Growth and Logarithmic Sensitivity.

I study a Keller–Segel type system with logarithmic sensitivity and logistic growth on the half-line \(x>0\), of the form

$$ \begin{cases} u_t = D\,u_{xx} - \chi\,\big(u\,(\ln v)_x\big)_x + a\,u\left(1-\dfrac{u}{K}\right),\\[6pt] v_t = \varepsilon\, v_{xx} - \mu\, u\, v, \end{cases} \qquad x>0,\ t>0, $$

subject to initial and boundary data. The goal is to prove that solutions exist globally in time. The main tool is a Nakamura–Nishibata boundary-cancellation energy method, which I extend to the fully nonlinear setting.

Selected Presentations

  • Aug 2025
    Learning the Solution Operator of the Heat Equation
    Summer School on Scientific Machine Learning, Brin Mathematics Research Center, University of Maryland
  • Feb 2025
    On One-Dimensional Advection–Diffusion Equation with Variable Diffusivity
    MAA–FTYCMA Joint Conference, Embry-Riddle Aeronautical University

Publications

Journal Articles

  1. D. Dulal, M. Gallagher, C. Navasca, P. Acharya, and N. Skowronski. Leveraging advanced machine learning to predict turbulence dynamics from temperature observations at an experimental prescribed fire. IEEE Access 14 (2026), 112481–112498. DOI
  2. K. Acharya and P. Acharya. Adaptive filtering via canonical systems with time-varying Hamiltonians. Int. J. Adv. Eng. Sci. Appl. Math. 18 (2026), 20–30. DOI
  3. E. P. Poudel, P. Acharya, J. Kafle, and S. Khadka. On one-dimensional advection–diffusion equation with variable diffusivity. Appl. Math. J. Chinese Univ. 41 (2026), 181–193. DOI

Submitted and in Preparation

  1. E. P. Poudel, P. Acharya, J. Kafle, and S. Khadka. Modeling and analysis of two-dimensional contaminant dispersion in turbulent atmospheric flows. Submitted to Electron. J. Differential Equations.
  2. D. Bastola, P. Acharya, and D. Dulal. Predicting anemia among under-five children in Nepal using machine learning and deep learning. Submitted to Public Health Nutrition. Preprint
  3. K. Acharya, P. Acharya, and D. Bastola. Random Schrödinger operators on data graphs: a data science perspective on robust spectral embedding. In preparation.

See also Google Scholar.

Awards and Service

  • 2025
    James Robert Ward, Jr. Memorial Endowed Award
    For excellence in graduate studies in differential equations / mathematical biology, UAB
  • 2023 – 2025
    Travel Awards
    Ohio River Analysis Meeting (2025); Texas Summer School in Mathematical Physics (2023)
  • 2024 – present
    Secretary, SIAM Student Chapter, UAB
  • 2017, 2019
    Deputy Leader, International Mathematical Olympiad
    Team Nepal, Rio de Janeiro (2017) and Bath (2019)
  • 2017 – 2019
    Vice President, Mathematical Association of Nepal

Contact

Department of Mathematics
University of Alabama at Birmingham
Birmingham, AL, USA
pacharya@uab.edu

Curriculum Vitae (PDF)
Google Scholar
ORCID
LinkedIn
GitHub