About

Andrew Blumberg is the Herbert and Florence Irving Professor of Cancer Data Research at Columbia University, holding positions in the Herbert and Florence Irving Institute of Cancer Dynamics and the Herbert Irving Comprehensive Cancer Center. He is also a Professor of Mathematics and Computer Science. His research interests encompass mathematics and computer science, with particular focus on algebraic topology, topological data analysis, and computer security and privacy. He is especially interested in applying geometry and topology to the analysis of genomic data. Prior to his tenure at Columbia University, Andrew was a Professor of Mathematics at the University of Texas. His academic journey includes a PhD from the University of Chicago obtained in 2005, a postdoctoral fellowship at Stanford University from 2005 to 2009, and a stint as a member at the Institute for Advanced Study during 2007-2008. He serves as an editor for the Journal of Topology, an associate editor for Advances in Mathematics, and an editor for the Journal of Applied and Computational Topology. Andrew is a member of the Center for Topology of Cancer Evolution and Heterogeneity at Columbia University and participates in the Pepper project at NYU on verifiable outsourced computing.

Research topics

• Computer Science
• Mathematics
• Algorithm
• Genetics
• Artificial Intelligence
• Machine Learning
• Pure mathematics
• Biology
• Combinatorics
• Psychology
• History
• Genealogy
• Mathematical economics
• Theoretical computer science
• Data science

Selected publications

• Chromatic convergence for the algebraic K‐theory of the sphere spectrum

  Journal of the London Mathematical Society · 2026-04-01 · 1 citations

  preprintOpen access1st authorCorresponding

  Abstract We show that the map from to its chromatic completion is a connective cover and identify the fiber in ‐theoretic terms. We combine this with recent work of Land–Mathew–Meier‐Tamme to prove a form of “Waldhausen's Chromatic Convergence Conjecture”: we show that the map is the inclusion of a wedge summand.

  PublisherOA PDFDOI

• First Proof

  Open MIND · 2026-01-01

  article

  To assess the ability of current AI systems to correctly answer research-level mathematics questions, we share a set of ten math questions which have arisen naturally in the research process of the authors. The questions had not been shared publicly until now; the answers are known to the authors of the questions but will remain encrypted for a short time.

• First Proof

  arXiv (Cornell University) · 2026-02-05

  preprintOpen access

  To assess the ability of current AI systems to correctly answer research-level mathematics questions, we share a set of ten math questions which have arisen naturally in the research process of the authors. The questions had not been shared publicly until now; the answers are known to the authors of the questions but will remain encrypted for a short time.

  PublisherDOI

• First Proof

  ArXiv.org · 2026-02-05

  articleOpen access

  To assess the ability of current AI systems to correctly answer research-level mathematics questions, we share a set of ten math questions which have arisen naturally in the research process of the authors. The questions had not been shared publicly until now; the answers are known to the authors of the questions but will remain encrypted for a short time.

  PublisherOA PDF

• Optimizing Delaware's Corporate Law Amendment Process: Ideas for the Next 20 Years

  SSRN Electronic Journal · 2025-01-01

  preprintOpen access
  PublisherDOI

• Discrete scalar curvature as a weighted sum of Ollivier-Ricci curvatures

  ArXiv.org · 2025-10-06

  preprintOpen accessSenior author

  We study the relationship between discrete analogues of Ricci and scalar curvature that are defined for point clouds and graphs. In the discrete setting, Ricci curvature is replaced by Ollivier-Ricci curvature. Scalar curvature can be computed as the trace of Ricci curvature for a Riemannian manifold; this motivates a new definition of a scalar version of Ollivier-Ricci curvature. We show that our definition converges to scalar curvature for nearest neighbor graphs obtained by sampling from a manifold. We also prove some new results about the convergence of Ollivier-Ricci curvature to Ricci curvature.

  PublisherOA PDFDOI

• A multiplicative version of the tom Dieck splitting

  ArXiv.org · 2025-05-05

  preprintOpen access1st authorCorresponding

  While the classical tom Dieck splitting in equivariant stable homotopy theory is typically regarded as a formula for suspension spectra in the genuine equivariant stable category, it can be interpreted as a calculation of the fixed points of $G$-spectra that are derived pushforwards from the naive equivariant stable category. We then establish a corresponding multiplicative splitting formula for derived pushforwards of $N_{\infty}$ ring spectra. Just as the usual tom Dieck splitting characterizes the equivariant stable category associated to an $N_{\infty}$ operad $\mathcal{N}$, the multiplicative tom Dieck splitting characterizes the $G$-symmetric monoidal structure on the genuine equivariant stable category associated to $\mathcal{N}$.

  PublisherOA PDFDOI

• Homotopical Combinatorics

  Notices of the American Mathematical Society · 2024-01-10 · 1 citations

  articleOpen access1st authorCorresponding

  Communities summer conference Homotopical Combinatorics, one of four topical research conferences offered this year that are focused on collaborative research and professional development for early-career mathematicians.Additional information can be found at https://www.

  PublisherDOI

• The Strong Künneth Theorem for Topological Periodic Cyclic Homology

  Memoirs of the American Mathematical Society · 2024 · 10 citations

  1st authorCorresponding
  • Mathematics
  • Pure mathematics
  • Combinatorics

  Topological periodic cyclic homology (i.e., <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper T"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">T</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathbb {T}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -Tate fixed points of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper T upper H upper H"> <mml:semantics> <mml:mrow> <mml:mi>T</mml:mi> <mml:mi>H</mml:mi> <mml:mi>H</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">THH</mml:annotation> </mml:semantics> </mml:math> </inline-formula> ) has the structure of a strong symmetric monoidal functor of smooth and proper dg categories over a perfect field of finite characteristic.

  PublisherDOI

• Subsampling, aligning, and averaging to find circular coordinates in recurrent time series

  arXiv (Cornell University) · 2024-12-24

  preprintOpen access1st authorCorresponding

  We introduce a new algorithm for finding robust circular coordinates on data that is expected to exhibit recurrence, such as that which appears in neuronal recordings of C. elegans. Techniques exist to create circular coordinates on a simplicial complex from a dimension 1 cohomology class, and these can be applied to the Rips complex of a dataset when it has a prominent class in its dimension 1 cohomology. However, it is known this approach is extremely sensitive to uneven sampling density. Our algorithm comes with a new method to correct for uneven sampling density, adapting our prior work on averaging coordinates in manifold learning. We use rejection sampling to correct for inhomogeneous sampling and then apply Procrustes matching to align and average the subsamples. In addition to providing a more robust coordinate than other approaches, this subsampling and averaging approach has better efficiency. We validate our technique on both synthetic data sets and neuronal activity recordings. Our results reveal a topological model of neuronal trajectories for C. elegans that is constructed from loops in which different regions of the brain state space can be mapped to specific and interpretable macroscopic behaviors in the worm.

  PublisherOA PDFDOI

Recent grants

• FRG: Collaborative Research : Floer homotopy theory

  NSF · $199k · 2016–2019

• CAREER: Algebraic K-theory, trace methods, and non-commutative geometry

  NSF · $426k · 2012–2017

• Algebraic invariants of structured ring spectra, arithmetic, and geometry

  NSF · $147k · 2009–2013

• Collaborative Research: Algebraic K-Theory, Topological Periodic Cyclic Homology, and Noncommutative Algebraic Geometry

  NSF · $275k · 2018–2022

Frequent coauthors

• Michael A. Hill

  60 shared

• Michael A. Mandell

  57 shared

• Tyler Lawson

  44 shared

• Teena Gerhardt

  Michigan State University

  44 shared

• Vigleik Angeltveit

  41 shared

• David Gepner

  21 shared

• Michael Walfish

  20 shared

• Michael A. Mandell

  Indiana University Bloomington

  17 shared