Overview

Robert Fraser is an assistant professor in the department of mathematics, statistics, and physics. He graduated with his Ph.D. from the University of British Columbia in 2018 under the supervision of Malabika Pramanik. He then worked as an NSF postdoc at the University of Edinburgh under the supervision of Jim Wright from 2018-2021 before coming to Wichita State University.


Robert Fraser’s research work is in harmonic analysis, particularly in connections between harmonic analysis, fractal geometry, combinatorics, and Diophantine approximation. He has a particular interest in harmonic analysis on non-Archimedean local fields.

 

Robert Fraser has supervised one Ph.D. student, Mark Meyer, and two Master's students, Elton Bowman and Thanh Nguyen.

Information

Academic Interests and Expertise
  •  Euclidean and non-Archimedean harmonic analysis
  •  Fractal Geometry
  •  Additive Combinatorics
  •  Diophantine Approximation
Areas of Research Interest

Robert Fraser works in the areas of geometric measure theory, harmonic analysis, and addtive combinatorics. Much of his work concerns the use of the Fourier transform to study patterns in fractal sets.

Areas of Teaching Interest

Dr. Fraser has taught classes in analysis, differential equations, and number theory. In Fall 2025, Dr. Fraser is teaching Math 743 (Real Analysis I) and Math 555 (Introduction to Differential equations)

Publications
  1. Robert Fraser and Thanh Nguyen. Sharp Fourier decay estimates for measures supported on the well-approximable numbers. Ann. Fenn. Math., 50(2):483–510, 2025. doi:10.54330/afm.163951.
  2. Robert Fraser, Kyle Hambrook, and Donggeun Ryou. Fourier restrictionand well-approximable numbers. Math. Ann., 391(3):4233–4269, 2025. doi: 10.1007/s00208-024-03000-w.
  3. Robert Fraser and Reuben Wheeler. Fourier dimension estimates for sets of exact approximation order: the case of small approximation exponents. Int. Math. Res. Not. IMRN, (21):13651–13694, 2024. doi:10.1093/imrn/ rnae210.
  4. Robert Fraser and Kyle Hambrook. Explicit Salem sets in R n . Adv. Math., 416:Paper No. 108901, 23, 2023. doi:10.1016/j.aim.2023.108901.
  5. Robert Fraser and Reuben Wheeler. Fourier Dimension Estimates for Sets of Exact Approximation Order: The Well-Approximable Case. International Mathematics Research Notices, 10 2022. arXiv:https: //academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/ rnac256/46341586/rnac256.pdf, doi:10.1093/imrn/rnac256.
  6. Robert Fraser. Three-term arithmetic progressions in subsets of F ∞ q of large Fourier dimension. Annales Fennici Mathematici, 46(2):1007–1030, Aug. 2021. URL: https://afm.journal.fi/article/view/110939.
  7. Robert Fraser, Shaoming Guo, and Malabika Pramanik. Polyno- mial Roth Theorems on Sets of Fractional Dimensions. Inter- national Mathematics Research Notices, 01 2021. arXiv:https: //academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/ rnaa377/35434071/rnaa377.pdf, doi:10.1093/imrn/rnaa377.
  8. Robert Fraser and James Wright. The local sum conjecture in two di- mensions. Int. J. Number Theory, 16(8):1667–1699, 2020. URL: https: //doi-org.ezproxy.is.ed.ac.uk/10.1142/S1793042120500888, doi:10. 1142/S1793042120500888.
  9. Robert Fraser. A framework for constructing sets without configurations. Online J. Anal. Comb., (15):27, 2020
  10. Robert Fraser and Kyle Hambrook. Explicit Salem sets, Fourier restriction, and metric Diophantine approximation in the p-adic numbers. Proc. Roy. Soc. Edinburgh Sect. A, 150(3):1265–1288, 2020. URL: https://doi-org. ezproxy.is.ed.ac.uk/10.1017/prm.2018.115, doi:10.1017/prm.2018. 115.
  11. Robert Fraser and Malabika Pramanik. Large sets avoiding patterns. Anal. PDE, 11(5):1083–1111, 2018. doi:10.2140/apde.2018.11.1083.
  12. Robert Fraser. Kakeya-type sets in local fields with finite residue field. Mathematika, 62(2):614–629, 2016. URL: http://dx.doi.org/10.1112/ S0025579315000388, doi:10.1112/S0025579315000388.
  13. Guo-Qiang Zhang, Xiangnan Zhou, Robert Fraser, and Licong Cui. Con- catenation and kleene star on deterministic finite automata. In Proceedingsof the Twenty-Sixth Annual IEEE Symposium on Logic in Computer Science (LICS 2011). IEEE Computer Society Press, June 2011. Short Presentation.
Working Papers
  1. Robert Fraser. Oscillatory integrals with phases arising from algebraic num- ber fields. arXiv e-prints, page arXiv:2408.02776, August 2024. Submitted.
  2. Robert Fraser, Kyle Hambrook, and Donggeun Ryou. Sharpness of the Mockenhaupt-Mitsis-Bak-Seeger Fourier restriction theorem in all dimensions. In preparation.
  3. Robert Fraser. Fourier decay of measures supported on sets of numbers with consecutive partial quotients belonging to a given set. Submitted.
  4. Alan Chang, Robert Fraser, Alex McDonald, Mark Meyer, and Krystal Taylor. Prescribed projection theorems for smooth families of nonlinear projections. In preparation.
  5. Elton Bowman and Robert Fraser. A simple condition guaranteeing existence of three-term arithmetic progressions in subsets of R. In preparation.
Grants
  • PI for NSF standard grant Algebraic Number Fields in Fourier Analysis and Fractal Geometry, DMS # 2453364 for $210,000, 2025-2028
  • PI for WSU Multidisciplinary Research Project Award (MURPA) grant A resource for English language learners in first-year mathematics courses joint with Mythili Menon for $7,500, Summer 2024
  • PI for NSF Mathematical Sciences Postdoctoral Research Fellowship (MSPRF) grant DMS #1803086 for $150,000, 2018-2021
Areas of Service
  • University Exceptions Committee, 2023-2025
Other Interests

I run the Wichita State University mathematics competition team. Come join us on Tuesdays at 4:30 PM in JB 372 for practice!

Together with Yueh-Ju Lin, I am running the Math for everyone lecture series for undergraduate students.

Together with English faculty member Mythili Menon and undergraduate student Alec Schon, I created the Math language wiki for English language learners.