Qiuyu Ren

I am a fifth year PhD student in pure mathematics at UC Berkeley working with Ian Agol. My research interests include low-dimensional topology (mostly 4-manifolds and knot theory) and some symplectic geometry. During the 2026-2027 academic year, I will be at Stanford.

Here is my cv (10/07/2025).

Ongoing/Upcoming Events

• Participating in the Topological and Geometric Structures in Low Dimensions program at SLMath, Berkeley, Spring 2026.
• Will give a talk in the online International Young Seminar on Bounded Cohomology and Simplicial Volume, May 19, 2026.
• Will visit the University of Hamburg, Germany, May-June 2026.
• Will participate in the PCMI 2026 Research Program, Park City, June-July 2026.

Publications/Preprints/Expositories

• Families of cosmetic surgeries
• Ribbon concordance of fibered knots and compressions of surface homeomorphisms, with Ian Agol
• Khovanov skein lasagna modules with $1$-dimensional inputs, with Ian Sullivan, Paul Wedrich, Michael Willis, and Melissa Zhang
• Intrinsic Khovanov homology in $\mathbb{RP}^3$, with Hongjian Yang
• Adjunction inequality for spatially refined $s$-invariants
• Cosmetic surgery on satellite knots, Bull. Lond. Math. Soc. 57 (2025) 3934-3940
• Khovanov homology and exotic $4$-manifolds, with Michael Willis
• Toroidal Hitomezashi Patterns, with Shengtong Zhang, Discrete Math. 348 (2025) 114231
• Slice genus bound in $DTS^2$ from $s$-invariant, Algebr. Geom. Topol. 24 (2024) 4115-4125
• Lee filtration structure of torus links, Geom. Topol. 28 (2024) 3935-3960
• A succinct proof of Defant and Kravitz's Theorem on the length of Hitomezashi loops, with Shengtong Zhang, Ann. Comb. 29 (2025) 117-122
• Spectral asymptotics for kinetic Brownian motion on Riemannian manifolds, with Zhongkai Tao, Math. Ann. 393 (2025) 1175–1194
• Spectral asymptotics for kinetic Brownian motion on locally symmetric spaces, with Zhongkai Tao

Below are some expository papers. Read with caution.

• Toric varieties in algebraic and symplectic geometry (final paper for MATH 256A, UCB Fall 2021)
• Spectral Properties of the Laplacian on Compact Lie Groups (one of the projects for 18.821, MIT Fall 2020; see the end to see my part of writing)
• Quantization commutes with reduction (UChicago REU 2020)
• Equivariant de Rham theory (notes for an independent reading course, MIT Spring 2020)
• Nonnegatively curved sl_2(R)-connections on surfaces, with Zhuofan Xie (undergraduate research supervised by Professor Paul Seidel, MIT Spring 2020)
• Complex Analytic Proofs of Bernstein's Theorem (final paper for 18.994, MIT Spring 2020; I wrote Section 4 and 6)
• Conjugacy of Cartan Subalgebras (final paper for 18.745, MIT Fall 2019)
• On the union of essentially distinct δ-tubes (MIT SPUR Summer 2019, mentored by Yuqiu Fu, problem proposed by Professor Larry Guth; my paper won the Hartley Rogers Jr. Prize)
• Linear fractional transformations on the Berkovich projective line (final paper for an independent study course in p-adic analysis, MIT Spring 2019)
• Points of Continuity of Real Functions on the Real Line (random thing asked by a friend)

Past Events

• Participated in the Simons Collaboration on New Structures in Low-Dimensional Topology Annual Meeting, New York, March 2026.
• Gave talks in the Online Geometry and Physics Seminar at the IASM, Zhejiang University, March 2026.
• Visited the University of Seville, Spain, January 2026.
• Co-mentored the 2nd Scottish Talbot on Algebra and Topology workshop on skein lasagna modules, Crianlarich, Scotland, January 2026.
• Gave a talk in the Southern University of Science and Technology (SUSTech) geometry and topology seminar, December 2025.
• Gave a talk in the 2025 Virginia Topology Conference - New developments in 4-manifold topology, December 2025.
• Gave a talk in the Ohio State University topology seminar, December 2025.
• Gave a talk in the online quantum topology seminar organized by L. Kauffman, December 2025.
• Gave a talk in the Knots and representation theory seminar (online), December 2025.
• Coorganized the student low-dimensional topology seminar at UC Berkeley with Audrey Rosevear, Fall 2024 - Fall 2025.
• Participated in the workshop Low-dimensional topology and Floer theory at CRM, Montréal, Canada, August 2025.
• Gave a talk in the conference Knots, groups, and manifolds at CRM, Montréal, Canada, August 2025.
• Visited Tsinghua University, Beijing, China, August 2025.
• Gave a talk in the workshop New perspectives on skein modules at CIRM, Luminy, France, July 2025.
• Participated in the workshop and conference Categorification in Low Dimensional Topology, Ruhr University Bochum, Germany, July 2025.
• Gave a talk in the Max Planck Institute for Mathematics (MPIM) low-dimensional topology seminar, Bonn, Germany, July 2025.
• Participated in the workshop Multisectors at CIRM, Luminy, France, July 2025.
• Gave a talk in the Research Seminar on Quantum Topology and Categorification (QTCat) at the University of Hamburg, Germany, June 2025.
• Gave a talk in the geometric topology seminar at Humboldt University of Berlin, Germany, June 2025.
• Led exercise sessions and gave a talk in the Summer School and Conference on Modern Developments in Low-Dimensional Topology at ICTP, Triste, Italy, June 2025.
• Participated in the 2025 Georgia international topology conference, University of Georgia, May 2025.
• Gave a talk in the AMS 2025 Spring Western Sectional Meeting, California Polytechnic, May 2025.
• Participated in the Simons Collaboration on New Structures in Low-Dimensional Topology Annual Meeting, New York, March 2025.
• Gave a talk in the University of Oregon topology seminar, February 2025.
• Gave a talk (online) in the workshop Knots, Quivers & Beyond, February 2025.
• Gave a talk in the online Geometric Topology Grad and Postdoc Seminar (GT GAPS), February 2025.
• Gave a talk in the First International Online Knot Theory Congress, February 2025.
• Gave a talk at Sungkyunkwan University, South Korea, December 2024.
• Gave a talk in the UCSB topology seminar, December 2024.
• Gave a talk in the University of Georgia research topology seminar, October 2024.
• Gave a talk in the Knots and representation theory seminar (online), September 2024.
• Gave a talk in the Columbia University geometric topology seminar, September 2024.
• Gave a talk in the AMS 2024 Fall Central Sectional Meeting, University of Texas, San Antonio, September 2024.
• Gave lectures on lasagna s-invariants at a conference in quantum topology at Belalp, Switzerland, September 2024.
• Visited the University of Zürich, Switzerland, August 2024.
• Gave a talk in the Conference - New structures in low-dimensional topology at the Erdös Center, Rényi Institute, Budapest, Hungary, July 2024.
• Participated in the Summer school in Mathematics: Low dimensional topology at the Institut Fourier, Grenoble, France, June 2024.
• Gave a talk in the Knot Online Seminar (K-OS), June 2024.
• Gave a talk in the Research Seminar on Quantum Topology and Categorification (QTCat) at the University of Hamburg, Germany, June 2024.
• Participated in the conference Combinatorial and Gauge theoretical methods in low dimensional topology and geometry at the Centro di Ricerca Matematica Ennio De Giorgi, Pisa, Italy, June 2024.
• Participated in the 2024 Georgia topology summer school and conference, May 2024.
• Coorganized the student 3-manifold seminar at UC Berkeley with Ethan Dlugie, Fall 2023 to Spring 2024.
• Gave a talk in the University of South Florida geometry and topology seminar, April 2024.
• Gave a talk in the Simons Collaboration satellite conference: Floer homology, low-dimensional topology, and algebra, Princeton University, March 2024.
• Gave a talk in the UC Davis geometry and topology seminar, March 2024.
• Participated in the 2024 Geometry and Topology Workshop at UCLA, January 2024.
• Participated in the Workshop on exotic 4-manifolds at Stanford University, December 2023.
• Gave a talk in the Texas A&M University topology seminar, October 2023.
• Gave a talk in the Caltech geometry and topology seminar, September 2023.
• Gave a talk in the Stanford University topology seminar, September 2023.
• Gave a talk in the MIT geometry and topology seminar, September 2023.
• Participated in the conference Gauge Theory and Topology: in Celebration of Peter Kronheimer's 60th Birthday at the Clay Mathematics institute in Oxford, July 2022.
• Visited Instituto de Ciencias Matemáticas (ICMAT) in Madrid for the conference Geometric group theory and low-dimensional geometry and topology, June-July 2022.
• Participated in the Analytic and Geometric Aspects of Gauge Theory and Floer Homotopy Theory programs at MSRI/SLMath, Berkeley, Fall 2022.
• Coorganized a reading group on the Kobayashi-Hitchin correspondence with Yueqing Feng, Fall 2022.
• Organized a reading group on Donaldson & Kronheimer's The Geometry of Four-Manifolds, Summer 2021. I am also maintaining an errata list for the book.

Others

• I am a marathon runner. I won first place in the Baystate Half Marathon (under 20 age group), 2018. I won third place in the Baystate Marathon (20-29 age group), 2019. I won third place in the Berkeley Half Marathon (20-29 age group), 2022. Here is a photo of me.
  My PRs are 1:19:02 (02/27/2022 Berkeley Half Marathon); 2:38:07 (12/04/2022 California International Marathon (CIM)).
• I'm a contributor to the FrontierMath benchmark, Humanity's Last Exam, and the GAUSS benchmark.
• If you're looking to pass the time and can read Chinese, here are some fun logic puzzles.