Özgür Yılmaz

Professor of Mathematics, University of British Columbia
Director, Pacific Institute for the Mathematical Sciences (PIMS)

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About

My research is on the mathematical foundations of artificial intelligence and the broader mathematics of information and data. I work at the intersection of computational harmonic analysis, mathematical signal processing, and information theory. Current work focuses on compressed sensing with deep generative models, optimized sampling with denoising guarantees, and applications of deep learning to retinal fundus imaging for medical diagnosis, in collaboration with colleagues in ophthalmology.

Recent results include denoising guarantees for optimized sampling schemes in compressed sensing (SIMODS, 2026), a coherence framework characterizing generative compressed sensing with Fourier measurements (IEEE JSAIT, 2022), and, with colleagues in ophthalmology, explainable AI for novel retinal biomarker discovery (PNAS Nexus, 2023). Earlier landmarks include the PLUGIn algorithm for inverting generative networks, fundamental results on the quantization of redundant expansions, and the DUET algorithm for the "cocktail party problem."

At UBC since 2004; Professor since 2014; PIMS Director since July 2022. Ph.D. Princeton 2001, with Ingrid Daubechies.

Research Interests

News

Selected Publications

Denoising guarantees for optimized sampling schemes in compressed sensing
Y. Plan, M. Scott, X. Sheng, O. Yilmaz
SIAM Journal on Mathematics of Data Science, accepted 2026
AI-assisted identification of sex-specific patterns in diabetic retinopathy using retinal fundus images
P. Delavari, G. Ozturan, E. Navajas, O. Yilmaz, I. Oruc
PLoS One 20(8): e0327305 · 2025
A coherence parameter characterizing generative compressed sensing with Fourier measurements
A. Berk, S. Brugiapaglia, B. Joshi, Y. Plan, M. Scott, O. Yilmaz
IEEE Journal on Selected Areas in Information Theory 3(3): 502–512 · 2022
Sub-Gaussian matrices on sets: optimal tail dependence and applications
H. Jeong, X. Li, Y. Plan, O. Yilmaz
Communications on Pure and Applied Mathematics 75(8): 1713–1754 · 2022
PLUGIn: A simple algorithm for inverting generative models with recovery guaranteesSpotlight
B. Joshi, X. Li, Y. Plan, O. Yilmaz
NeurIPS · 2021
Artificial intelligence, explainability, and the scientific method
P. Delavari, G. Ozturan, O. Yilmaz, I. Oruc
PNAS Nexus 2(9): 1–14 · 2023

→ Full publication list

Recent Talks

Group

Current

Postdoctoral alumni

Doctoral alumni

Master's alumni

Teaching

I have taught broadly at UBC since 2004 — undergraduate and graduate courses across analysis, applied mathematics, and the mathematics of data and signal processing.

Designed: Math 555 (Compressed Sensing). Co-designed: Math 264 (vector calculus), taught jointly with EECE 261.

Courses taught include Math 100, 105, 120, 152, 200, 263, 264, 265, 267, 300, 301, 307, 320, 321, 340, 420/507, 555, 605D, and 605F.

Full teaching history in the CV.

Service & Leadership

Director, Pacific Institute for the Mathematical Sciences (PIMS), 2022–present. PIMS is a Canadian mathematical sciences institute with nine member universities across Western Canada and the University of Washington. It also serves as a CNRS International Research Laboratory (IRL #3069), one of two in mathematics in Canada. Recent highlights: led the 2024 PIMS–CNRS renewal; secured two Simons Foundation Targeted Grants for PIMS (2022, 2026); co-founded MATHAM (2026); PI on the Syzygy national computing platform (2026–29).

Editorial: Assoc. Editor, Applied and Computational Harmonic Analysis (2017–) · Editorial Board, Sampling Theory, Signal Processing, and Data Analysis (2020–) · Editorial Board, Mathematics, Computation and Geometry of Data (2019–) · formerly Assoc. Editor, IEEE TSP (2014–19).

Boards: Canadian Mathematical Society (2023–) · Banff International Research Station (2023–) · External Review Committee, Mathematisches Forschungsinstitut Oberwolfach (2023).

Software & Patents

Contact

Department of Mathematics, University of British Columbia
1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada

Email: oyilmaz@math.ubc.ca