Alexander Iosevich

Professor of Mathematics, University of Rochester

Department of Mathematics, University of Rochester, Rochester, New York 14627
Email: iosevich@math.rochester.edu

Complete CV and professional archive Google Scholar Research overview

Academic profile

Harmonic analyst working at the intersections of geometric measure theory, geometric and additive combinatorics, analytic number theory, spectral synthesis, signal recovery, and the mathematical foundations of data science. The research program uses Fourier-analytic and geometric methods to study rigidity, configuration problems, complexity, uncertainty, and recovery.

Current appointments and distinctions

• 2010–present: Professor of Mathematics, University of Rochester.
• 2019–present: Affiliated Faculty, Goergen Institute for Data Science and Artificial Intelligence.
• 2026: Simons Fellow in Mathematics.
• 2014: Fellow of the American Mathematical Society.
• 2024: London Mathematical Society Distinguished Visiting Fellow at the International Centre for Mathematics in Ukraine.
• 2024: International Congress of Chinese Mathematicians Best Paper Award.
• 2025: Frontiers of Science Best Paper Award.
• 2015: Professor of the Year Award in the Natural Sciences, University of Rochester.

Editorial leadership

• Research in the Mathematical Sciences — Editor-in-Chief for Analysis.
• Journal of Functional Analysis — Associate Editor.
• Journal of Fourier Analysis and Applications — Editorial Board.
• Boletín de la Sociedad Matemática Mexicana — Editorial Board.
• Journal of Pseudo-Differential Operators and Applications — Editorial Board.
• Integers — Editorial Board.
• Complete current and past editorial service.

Research areas

• Harmonic analysis, Fourier restriction, oscillatory integrals, and averaging operators.
• Geometric measure theory and Falconer-type distance and configuration problems.
• Geometric combinatorics in Euclidean spaces, finite fields, and finite rings.
• Uncertainty principles, spectral synthesis, sampling, and signal recovery.
• The Fourier ratio, learning theory, and mathematical foundations of data science.
• Additive and analytic number theory, exponential bases, and tiling.

Selected publications

The 33 works below are organized by research program rather than by chronology. See the complete CV for the full publication record.

Harmonic analysis, averaging, and Fourier decay

1. Maximal operators associated to families of flat curves in the plane, Duke Mathematical Journal 76 (1994), no. 2, 633–644.
2. Oscillatory integrals and maximal averages over homogeneous surfaces, with E. Sawyer, Duke Mathematical Journal 82 (1996), no. 1, 103–141.
3. Maximal averages over surfaces, with E. Sawyer, Advances in Mathematics 132 (1997), no. 1, 46–119.
4. On averaging operators associated with convex hypersurfaces of finite type, with E. Sawyer and A. Seeger, Journal d'Analyse Mathématique 79 (1999), 159–187.
5. Sharp rate of average decay of the Fourier transform of a bounded set, with L. Brandolini and S. Hofmann, Geometric and Functional Analysis 13 (2003), 671–680.

Exponential bases and frames

1. Fourier bases and a distance problem of Erdős, with N. Katz and S. Pedersen, Mathematical Research Letters 6 (1999), 251–255.
2. Convex bodies with a point of curvature do not have Fourier bases, with N. Katz and T. Tao, American Journal of Mathematics 123 (2001), 115–120.
3. Fuglede conjecture holds for convex planar domains, with N. Katz and T. Tao, Mathematical Research Letters 10 (2003), 559–569.
4. The Fuglede conjecture holds in Z_p × Z_p, with A. Mayeli and J. Pakianathan, Analysis & PDE 10 (2017), no. 4, 757–764.
5. Gabor orthogonal bases on convexity, with A. Mayeli, Discrete Analysis 2018, Paper No. 19, 11 pp.
6. Fourier frames for surface-carried measures, with C.-K. Lai, B. Liu, and E. Wyman, International Mathematics Research Notices 2022, no. 3, 1644–1665.

Falconer distance problems and configurations in thin sets

1. Fourier integral operators, fractal sets, and the regular value theorem, with S. Eswarathasan and K. Taylor, Advances in Mathematics 228 (2011), no. 4, 2385–2402.
2. A group-theoretic viewpoint on Erdős–Falconer problems and the Mattila integral, with A. Greenleaf, B. Liu, and E. Palsson, Revista Matemática Iberoamericana 31 (2015), no. 3, 799–810.
3. Finite chains inside thin subsets of R^d, with M. Bennett and K. Taylor, Analysis & PDE 9 (2016), no. 3, 597–614.
4. Pinned distance problem, slicing measures, and local smoothing estimates, with B. Liu, Transactions of the American Mathematical Society 371 (2019), no. 6, 4459–4474.
5. On Falconer's distance set problem in the plane, with L. Guth, Y. Ou, and H. Wang, Inventiones Mathematicae 219 (2020), no. 3, 779–830.
6. An improved result for Falconer's distance set problem in even dimensions, with X. Du, Y. Ou, H. Wang, and R. Zhang, Mathematische Annalen 380 (2021), nos. 3–4, 1215–1231.
7. Microlocal decoupling inequalities and the distance problem on Riemannian manifolds, with B. Liu and Y. Xi, American Journal of Mathematics 144 (2022), no. 6, 1601–1639.
8. Simplices in thin subsets of Euclidean spaces, with Á. Magyar, Analysis & PDE 16 (2023), no. 7, 1485–1496.

Restriction theory

1. Fourier transform, L² restriction theorem, and scaling, Bollettino dell'Unione Matematica Italiana, Serie 8, 2-B (1999), no. 2, 383–387.
2. L^p integrability of functions with Fourier support on a smooth space curve, with S. Guo, R. Zhang, and P. Zorin-Kranich, Indiana University Mathematics Journal 74 (2025), no. 6, 1849–1853.
3. A distinction between the paraboloid and the sphere in weighted restriction, with R. Zhang, Selecta Mathematica 32 (2026), no. 3, Paper No. 49.

Signal recovery, uncertainty, and Fourier complexity

1. Uncertainty principles, restriction, Bourgain's Lambda(q) theorem, and signal recovery, with A. Mayeli, Applied and Computational Harmonic Analysis 76 (2025), Article 101734.
2. The Fourier Ratio: A Unifying Measure of Complexity for Recovery, Localization, and Learning, with W. Burstein and H. S. Nathan, Applied and Computational Harmonic Analysis (2026), published online.

Geometric combinatorics

1. A combinatorial approach to orthogonal exponentials, with M. Rudnev, International Mathematics Research Notices 2003, no. 50, 2671–2685.
2. Erdős distance problem in vector spaces over finite fields, with M. Rudnev, Transactions of the American Mathematical Society 359 (2007), no. 12, 6127–6142.
3. Sum-product estimates in finite fields via Kloosterman sums, with D. Hart and J. Solymosi, International Mathematics Research Notices 2007, no. 5, Article rnm007, 14 pp.
4. Geometric incidence theorems via Fourier analysis, with H. Jorati and I. Łaba, Transactions of the American Mathematical Society 361 (2009), no. 12, 6595–6611.
5. Averages over hyperplanes, sum-product theory in vector spaces over finite fields and the Erdős–Falconer distance conjecture, with D. Hart, D. Koh, and M. Rudnev, Transactions of the American Mathematical Society 363 (2011), no. 6, 3255–3275.
6. Group actions and geometric combinatorics in F_q^d, with M. Bennett, D. Hart, J. Pakianathan, and M. Rudnev, Forum Mathematicum 29 (2017), no. 1, 91–110.
7. The VC-dimension and point configurations in F_q², with D. Fitzpatrick, B. McDonald, and E. Wyman, Discrete & Computational Geometry 71 (2024), no. 4, 1167–1177.

Selected expository articles

1. Curvature, combinatorics, and the Fourier transform, Notices of the American Mathematical Society 48 (2001), no. 6, 577–583.
2. What is Falconer's conjecture?, Notices of the American Mathematical Society 66 (2019), no. 4, 552–555.

Books

• Decay of the Fourier Transform: Analytic and Geometric Aspects, with E. Liflyand, Birkhäuser Basel, 2014.
• A View from the Top: Analysis, Combinatorics and Number Theory, American Mathematical Society, Student Mathematical Library 39, 2007.
• The Erdős Distance Problem, with J. Garibaldi and S. Senger, American Mathematical Society, Student Mathematical Library 56, 2011.

Current research directions

• Fourier ratio and effective complexity in discrete, continuous, geometric, and learning-theoretic settings.
• Spectral synthesis on Euclidean spaces, manifolds, graphs, and arithmetic structures.
• Restriction theory, uncertainty principles, sparse recovery, and sampling.
• Falconer–Erdős problems, positive-measure unions, and geometric configurations in thin sets.

See the research overview and the complete publication record.

External research support

More than $3 million in external research support as principal investigator or co-investigator. Selected recent awards include:

• 2025: NSF DMS-2506858, The uncertainty principle, restriction theory, signal recovery and sampling on manifolds, $301,542.
• 2024: European Union-supported program, Analytical methods in geodesy, cryptography and machine learning, $335,000.
• 2022: NSF DMS-2154232, On problems and connections between analysis, geometry and combinatorics, $322,800.
• 2019: NSF HDR TRIPODS collaborative grant, Foundations of Greater Data Science, $814,165.

Complete funding history.

Selected distinguished lectures and invited talks

Over the course of my career, I have given more than 500 invited lectures. The entries below are selected for the distinction of the lectureship or venue.

Distinguished lecture series and mini-courses

• September 2024: London Mathematical Society Distinguished Visiting Fellowship Lecture Series, International Centre for Mathematics in Ukraine, Lviv and Kyiv.
• September 2024: Four-lecture series on signal recovery, restriction theory, and applications, Hausdorff Research Institute for Mathematics, Bonn.
• August 2023: Four-lecture series, Kent State University Informal Analysis Seminar: Geometric measure theory and applications to data science.
• November 2006: Four-lecture series, University of Bristol: Harmonic analysis in vector spaces over finite fields.
• June 2002: Minicorsi di Analisi Matematica, University of Padova, three lectures: Geometric combinatorics and applications to analysis.

Selected plenary and invited lectures

• June 2026: Plenary lecture, Workshop on Harmonic Analysis and Applications to Ramsey Theory, Rényi Institute, Budapest: Spectral synthesis in Euclidean space and Riemannian manifolds.
• January 2024: Invited plenary lecture, Rényi Institute Conference on Fourier Analysis and Additive Problems, Budapest: Uniform distribution and pseudo-randomness.
• February 2019: Plenary lecture, Weizmann Institute conference in honor of Alexander Olevskii: Geometric measure theory and applications to frame theory.
• October 2017: Invited lecture, Oberwolfach Meeting on Geometric Measure Theory: L^p-dimension and application to the Furstenberg intersection conjecture.
• September 2017: Invited lecture, conference in honor of Elias Stein, University of Wrocław: Finite point configurations: analysis, combinatorics and number theory.
• August 2017: Plenary lecture, CIMPA 2017, Buenos Aires: Finite point configurations: analysis, combinatorics and number theory.
• May 2017: Invited lecture, MSRI Workshop on Harmonic Analysis, Berkeley: Rigidity, simplexes and multi-linear operators.
• July 2014: Invited lecture, Oberwolfach Harmonic Analysis Meeting: Fractal analogs of classical Fourier inequalities.
• July and September 2008: Invited lectures at the Oberwolfach meetings on Harmonic Analysis and Discrete Geometry: Geometric configurations in Euclidean, integer and finite-field geometries.
• March and October 2007: Plenary addresses to the American Mathematical Society at Davidson College and DePaul University: Incidence theory: discrete, continuous and arithmetic aspects.
• July 2005: Invited lecture, Oberwolfach: Some observations on the interaction of harmonic analysis and geometric combinatorics.
• May 2003: Princeton University Analysis Seminar: Combinatorics of distance sets and applications.

Selected recorded talks · Complete talks and research-visits record

Mentoring and research-program leadership

I have graduated 30 Ph.D. students and advised 15 postdoctoral researchers.

• Advisor or co-advisor of 39 past and current Ph.D. students.
• Mentor of 15 past and current postdoctoral researchers.
• More than 200 research collaborators, including more than 60 undergraduate coauthors.
• Year-round undergraduate research programs at the University of Rochester since 2011.
• Founder and organizer of StemForAll, an interdisciplinary summer research program operating since 2018.
• Research and mentoring programs connecting faculty, postdocs, graduate students, undergraduates, and high-school students.

Students, postdocs, collaborators, and advising · Research programs and outreach

Positions held

• 2010–present: Professor of Mathematics, University of Rochester.
• 2005–2010: Professor of Mathematics, University of Missouri.
• 2002–2005: Associate Professor of Mathematics, University of Missouri.
• 2000–2002: Assistant Professor of Mathematics, University of Missouri.
• 1998–2001: Assistant and tenured Associate Professor, Georgetown University.
• 1995–1998: Assistant Professor, Wright State University.
• 1993–1995: Postdoctoral Fellow, McMaster University.

Education

• 1993: Ph.D. in Pure Mathematics, University of California, Los Angeles. Advisor: Christopher Sogge.
• 1989: B.S. in Pure Mathematics, University of Chicago.

Complete record

The full archival CV remains available at alexiosevich.com/cvweb.html. It contains the complete chronological record and is not replaced by this page.