Qiuyu Ren

Qiuyu Ren is a low-dimensional topologist whose work connects Khovanov homology, AI benchmarks, and machine-checked proofs. In 2024, he and Michael Willis use Khovanov homology to distinguish an exotic pair of four-manifolds, and he coauthors FrontierMath, where state-of-the-art models solve under 2% of expert-vetted problems. In October 2026, he contributes a paper on a universal group whose proof, writeup, and Lean 4 formalization GPT-6 Astra generates. He is a Clay Research Fellow spending the 2026–2027 academic year at Stanford.

Now at: Stanford University and Clay Mathematics Institute
Works: 23
Citations: 71
h-index: 3

Publication numbers from OpenAlex, as of 22 October 2026.

Timeline

2019

A Hartley Rogers Jr. Prize

In 2019, he shares the Hartley Rogers Jr. Prize with Yuqiu Fu for an MIT SPUR paper.
2024

Exotic 4-manifolds from Khovanov homology

In 2024, he and Michael Willis show that the skein lasagna module, an invariant derived from Khovanov homology, distinguishes an exotic pair of knot traces. Their result gives the first analysis-free proof that exotic compact orientable four-manifolds exist.
November 2024

Co-authoring FrontierMath

In November 2024, he coauthors FrontierMath, a benchmark of hundreds of original mathematics problems crafted and vetted by expert mathematicians. State-of-the-art AI models solve under 2% of its problems.
January 2026

A Clay Research Fellowship

In January 2026, the Clay Mathematics Institute appoints him a Clay Research Fellow for five years beginning in July 2026. He completes his UC Berkeley PhD in 2026 under Ian Agol.
June 2026

Chern-Vorlesung in Hamburg

In June 2026, he gives the first Chern-Vorlesung at the University of Hamburg's Mathematisches Seminar, with the talk titled “Khovanov skein lasagna modules and exotic 4-manifolds.” He presents his joint work with Michael Willis on detecting exotic smooth structures on four-manifolds.
September 2026

Undecidable groups checked in Lean

In September 2026, he coauthors “Small undecidable groups and unrecognizable 4-manifolds” with Marc Kegel and Shana Yunsheng Li. It constructs a 3-generator, 9-relator group with an unsolvable word problem. ChatGPT 5.6 Sol develops the paper's main results, and the authors provide a machine-checked Lean 4 formalization of the algebraic results.
October 2026

A universal group with 13 relators

In October 2026, he contributes “A universal group with thirteen relators” to Hexagon. The group contains a copy of every finitely presented group and improves Valiev's bound of 21 relators; GPT-6 Astra generates the proof, writeup, and Lean 4 formalization.
As of October 2026

Clay Fellow at Stanford

He is a Clay Research Fellow, appointed for five years beginning in July 2026, and spends the 2026–2027 academic year at Stanford. His research includes Khovanov homology, smooth four-manifolds, three-manifolds, surfaces, and knots.