Postdoctoral Research Associate
University of Texas at Dallas
USD 45k-45k / month
Posted on Oct 17, 2025
| Posting Number | S06676P |
|---|---|
| Position Title | Postdoctoral Research Associate |
| Functional Title | Postdoctoral Research Associate |
| Department | Materials Science and Engineering |
| Salary Range | $45,000 DOQ |
| Pay Basis | Monthly |
| Position Status | Regular full-time |
| Location | Richardson |
| Position End Date (if temporary) | |
| Posting Open Date | 10/16/2025 |
| Posting Close Date | |
| Open Until Filled | Yes |
| Desired Start Date | 11/10/2025 |
| Job Summary | Looking for a post-doctoral Research Associate to perform full-time mathematical research with the goal of developing a practical yet rigorous mathematical framework for quantum mechanics. The researcher is expected to make contributions in the fields of functional analysis, complex analysis, spectral theory, and partial-differential equations, but also applications in number theory are of interest. Typically, the theory of quantum mechanics relies on the Hilbert space of square-integrable functions (L2) but when the domain space is not compact (e.g. L2), or the potential is singular, the eigenfunctions are not contained in the Hilbert space (e.g. e^(ikx)). In spectral theory, the absence of eigenvectors in the Hilbert space is typically circumvented by using a projection-valued measure. In the field of topological vector spaces, the problem is addressed using the nuclear spectral theorem which is set in the rigged Hilbert space (Gelfand’s triple) but the requirements imposed on the Schrodinger operator are non-trivial. Finally, the theory of non self-adjoint operators is very poorly developed. Current practice in physics is typically to ignore mathematical rigor because an easily accessible mathematical theory is lacking. Our goal is to develop a mathematically rigorous framework applicable to the Schrodinger equation where eigenvectors are tempered distributions (topological dual of the Schwartz space). The developed framework should be mathematically rigorous yet accessible to the physics community and applicable to existing problems in physics. As applications, open problems in the field of number theory, such as the Dirichlet divisor problem, the Riemann hypothesis (e.g., through the Hilbert-Polya conjecture) are also of interest. The position would have weekly meetings with prof. William Vandenberghe to discuss research progress and novel research directions. If interested, the research associate can also: • participate in research in physics, materials science, or electrical engineering relating to electron transport at the nanoscale. • Supervise Ph.D. students in Materials Science, Physics, and Electrical Engineering • Participate in teaching mathematics to undergraduate engineering students |
| Minimum Education and Experience | Ph.D in a related field. |
| Preferred Education and Experience | Ph.D. in Mathematics |
| Other Qualifications | To the extent this position requires the holder to research, work on, or have access to critical infrastructure as defined in Section 117.001(2) of the Texas Business and Commerce Code, the ability to maintain the security or integrity of the critical infrastructure is a minimum qualification to be hired and to continue to be employed in the position. |
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| Physical Demands and Working Conditions | |
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| Working Conditions | |
| Additional Information | A remote work schedule is not available for this position. What We Can Offer UT Dallas is an Equal Opportunity Employer with an employee-friendly and supportive work environment. Our comprehensive compensation and benefits package that is effective as of your hire date includes:
All UT Dallas employees have access to various professional development opportunities, including a membership to Academic Impressions, LinkedIn Learning, and UT Dallas Bright Leaders Program. Visit https://hr.utdallas.edu/employees/benefits/ for more information. If you are looking for a rewarding career opportunity with great benefits? Look no further! Join our team! |
| Special Instructions Summary | |
| Important Message | 1) All employees serve as a representative of the University and are expected to display respect, civility, professional courtesy, consideration of others and discretion in all interactions with members of the UT Dallas community and the general public. 2) The University of Texas at Dallas is committed to providing an educational, living, and working environment that is welcoming, respectful, and inclusive of all members of the university community. UT Dallas does not discriminate on the basis of race, color, religion, sex (including pregnancy), sexual orientation, gender identity, gender expression, age, national origin, disability, genetic information, or veteran status in its services, programs, activities, employment, and education, including in admission and enrollment. The University is committed to providing access, equal opportunity, and reasonable accommodation for individuals with disabilities. To request reasonable accommodation in the employment application and interview process, contact the ADA Coordinator. For inquiries regarding nondiscrimination policies, contact the Title IX Coordinator. |