publications

2026

  1. First Proof
    Mohammed Abouzaid , Andrew J. Blumberg , Martin Hairer , and 8 more authors
    arXiv, 2026

2025

  1. EmbedOR: Provable Cluster-Preserving Visualizations with Curvature-Based Stochastic Neighbor Embeddings
    Tristan Luca Saidi , Abigail Hickok , Bastian Rieck , and 1 more author
    arXiv, 2025
  2. Discrete scalar curvature as a weighted sum of Ollivier-Ricci curvatures
    Abigail Hickok and Andrew J. Blumberg
    arXiv, 2025
  3. A multiplicative version of the tom Dieck splitting
    Andrew J. Blumberg and Michael A. Mandell
    arXiv, 2025
  4. Multi-parameter module approximation: an efficient and interpretable invariant for multi-parameter persistence modules with guarantees
    David Loiseaux , Mathieu Carrière , and Andrew J. Blumberg
    J. Appl. Comput. Topol., 2025
  5. Recovering manifold structure using Ollivier Ricci curvature
    Tristan L. Saidi , Abigail Hickok , and Andrew J. Blumberg
    In ICLR , 2025
  6. A statistical framework for analyzing shape in a time series of random geometric objects
    Anne Delft and Andrew J. Blumberg
    Ann. Statist., 2025

2024

  1. Resampling and averaging coordinates on data
    Andrew J. Blumberg , Mathieu Carrière , Jun Hou Fung , and 1 more author
    arXiv, 2024
  2. Statistical estimation of sparsity and efficiency for molecular codes
    Jun Hou Fung , Mathieu Carrière , and Andrew J. Blumberg
    bioRxiv, 2024
  3. Foundation of Floer homotopy theory I: Flow categories
    Mohammed Abouzaid and Andrew J. Blumberg
    arXiv, 2024
  4. Subsampling, aligning, and averaging to find circular coordinates in recurrent time series
    Andrew J. Blumberg , Mathieu Carrière , Jun Hou Fung , and 1 more author
    arXiv, 2024
  5. The homotopy theory of cyclotomic spectra, 10 years later
    Andrew J. Blumberg and Michael A. Mandell
    arXiv, 2024
  6. Automated Cell Type Annotation with Reference Cluster Mapping
    Valerio Galanti , Lingting Shi , Elham Azizi , and 2 more authors
    bioRxiv, 2024
  7. Stability of 2-parameter persistent homology
    Andrew J. Blumberg and Michael Lesnick
    Found. Comput. Math., 2024

2023

  1. Universality of the homotopy interleaving distance
    Andrew J. Blumberg and Michael Lesnick
    Trans. Amer. Math. Soc., 2023
  2. A version of Waldhausen’s chromatic convergence for TC
    Andrew J. Blumberg , Michael A. Mandell , and Allen Yuan
    Bull. Lond. Math. Soc., 2023
  3. The eigensplitting of the fiber of the cyclotomic trace for the sphere spectrum
    Andrew J. Blumberg and Michael A. Mandell
    Trans. Amer. Math. Soc., 2023
  4. A Framework for Fast and Stable Representations of Multiparameter Persistent Homology Decompositions
    David Loiseaux , Mathieu Carrière , and Andrew J. Blumberg
    In NeurIPS , 2023
  5. Relative cyclotomic structures and equivariant complex cobordism
    Andrew J. Blumberg , Michael A. Mandell , and Allen Yuan
    arXiv, 2023
  6. An intrinsic approach to scalar-curvature estimation for point clouds
    Abigail Hickok and Andrew J. Blumberg
    arXiv, 2023
  7. CellStitch: 3D cellular anisotropic image segmentation via optimal transport
    Yining Liu , Yinuo Jin , Elham Azizi , and 1 more author
    BMC Bioinformatics, 2023

2022

  1. Efficient Representation of Numerical Optimization Problems for SNARKs
    Sebastian Angel , Andrew J. Blumberg , Eleftherios Ioannidis , and 1 more author
    In 31st USENIX Security Symposium , 2022
  2. Bi-incomplete Tambara functors
    Andrew J. Blumberg and Michael A. Hill
    In Equivariant topology and derived algebra , 2022
  3. Norms for compact Lie groups in equivariant stable homotopy theory
    Andrew J. Blumberg , Michael A. Hill , and Michael A. Mandell
    arXiv, 2022

2021

  1. Arnold Conjecture and Morava K-theory
    Mohammed Abouzaid and Andrew J. Blumberg
    arXiv, 2021
  2. Equivariant stable categories for incomplete systems of transfers
    Andrew J. Blumberg and Michael A. Hill
    J. Lond. Math. Soc. (2), 2021
  3. Chromatic convergence for the algebraic K-theory of the sphere spectrum
    Andrew J. Blumberg , Michael A. Mandell , and Allen Yuan
    arXiv, 2021

2020

  1. K-theoretic Tate-Poitou duality and the fiber of the cyclotomic trace
    Andrew J. Blumberg and Michael A. Mandell
    Invent. Math., 2020
  2. Localization for THH(ku) and the Topological Hochschild and Cyclic Homology of Waldhausen Categories
    Andrew Blumberg and Michael Mandell
    Mem. Amer. Math. Soc., 2020
  3. G-symmetric monoidal categories of modules over equivariant commutative ring spectra
    Andrew J. Blumberg and Michael A. Hill
    Tunis. J. Math., 2020
  4. Topological Data Analysis for Genomics and Evolution: Topology in Biology
    Raul Rabadan and Andrew J. Blumberg
    2020
  5. A random matrix theory approach to denoise single-cell data
    Luis C. Aparicio , Mykola Bordyuh , Andrew J. Blumberg , and 1 more author
    Patterns, 2020
  6. Multiparameter Persistence Image for Topological Machine Learning
    Mathieu Carrière and Andrew J. Blumberg
    In NeurIPS , 2020
  7. MREC: a fast and versatile framework for aligning and matching point clouds with applications to single cell molecular data
    Andrew J. Blumberg , Mathieu Carrière , Michael A. Mandell , and 2 more authors
    arXiv, 2020

2019

  1. The right adjoint to the equivariant operadic forgetful functor on incomplete Tambara functors
    Andrew J. Blumberg and Michael A. Hill
    In Homotopy theory: tools and applications , 2019
  2. The Witt vectors for Green functors
    Andrew J. Blumberg , Teena Gerhardt , Michael A. Hill , and 1 more author
    J. Algebra, 2019
  3. The homotopy groups of the algebraic K-theory of the sphere spectrum
    Andrew J. Blumberg and Michael A. Mandell
    Geom. Topol., 2019
  4. E_2 structures and derived Koszul duality in string topology
    Andrew J. Blumberg and Michael A. Mandell
    Algebr. Geom. Topol., 2019
  5. Fast estimation of recombination rates using topological data analysis
    Devon P. Humphreys , Melissa R. McGuirl , Michael Miyagi , and 1 more author
    Genetics, 2019
  6. Genomic architecture and introgression shape a butterfly radiation
    Nathaniel B. Edelman , Paul B. Frandsen , Michael Miyagi , and 1 more author
    Science, 2019

2018

  1. Parametrized spectra, multiplicative Thom spectra and the twisted Umkehr map
    Matthew Ando , Andrew J. Blumberg , and David Gepner
    Geom. Topol., 2018
  2. Topological cyclic homology via the norm
    Vigleik Angeltveit , Andrew J. Blumberg , Teena Gerhardt , and 3 more authors
    Doc. Math., 2018
  3. Testing to distinguish measures on metric spaces
    Andrew J. Blumberg , Prithwish Bhaumik , and Stephen G. Walker
    arXiv, 2018

2017

  1. The nilpotence theorem for the algebraic K-theory of the sphere spectrum
    Andrew J. Blumberg and Michael A. Mandell
    Geom. Topol., 2017
  2. The strong Künneth theorem for topological periodic cyclic homology
    Andrew J. Blumberg and Michael A. Mandell
    arXiv, 2017
  3. Geometry and topology of genomic data
    Andrew J. Blumberg and Raul Rabadan
    In Handbook of Discrete and Computational Geometry , 2017
  4. Spatiotemporal genomic architecture informs precision oncology in glioblastoma
    Jin-Ku Lee , Jiguang Wang , and  others
    Nature Genetics, 2017
  5. Full Accounting for Verifiable Outsourcing
    Riad S. Wahby , Ye Ji , Andrew J. Blumberg , and 4 more authors
    In ACM CCS , 2017

2016

  1. Interpreting the Bökstedt smash product as the norm
    Vigleik Angeltveit , Andrew J. Blumberg , Teena Gerhardt , and 2 more authors
    Proc. Amer. Math. Soc., 2016
  2. Defending against Malicious Peripherals with Cinch
    Sebastian Angel , Riad S. Wahby , Max Howald , and 5 more authors
    In 25th USENIX Security Symposium , 2016
  3. K-theory of endomorphisms via noncommutative motives
    Andrew J. Blumberg , David Gepner , and Gonçalo Tabuada
    Trans. Amer. Math. Soc., 2016
  4. A polynomial-time relaxation of the Gromov-Hausdorff distance
    Soledad Villar , Afonso S. Bandeira , Andrew J. Blumberg , and 1 more author
    arXiv, 2016
  5. Genomic data analysis in tree spaces
    Sakellarios Zairis , Hossein Khiabanian , Andrew J. Blumberg , and 1 more author
    arXiv, 2016
  6. Clonal evolution of glioblastoma under therapy
    Jiguang Wang , Emanuela Cazzato , Erik Ladewig , and 1 more author
    Nature Genetics, 2016

2015

  1. The homotopy theory of cyclotomic spectra
    Andrew J. Blumberg and Michael A. Mandell
    Geom. Topol., 2015
  2. Operadic multiplications in equivariant spectra, norms, and transfers
    Andrew J. Blumberg and Michael A. Hill
    Adv. Math., 2015
  3. Efficient RAM and control flow in verifiable outsourced computation
    Riad S. Wahby , Srinath Setty , Zuocheng Ren , and 2 more authors
    In NDSS , 2015
  4. Verifying computations without reexecuting them
    Michael Walfish and Andrew J. Blumberg
    Commun. ACM, 2015

2014

  1. Robust Statistics, Hypothesis Testing, and Confidence Intervals for Persistent Homology on Metric Measure Spaces
    Andrew J. Blumberg , Itamar Gal , Michael A. Mandell , and 1 more author
    Found. Comput. Math., 2014
  2. An ∞-categorical approach to R-line bundles, R-module Thom spectra, and twisted R-homology
    Matthew Ando , Andrew J. Blumberg , David Gepner , and 2 more authors
    J. Topol., 2014
  3. Units of ring spectra, orientations, and Thom spectra via rigid infinite loop space theory
    Matthew Ando , Andrew J. Blumberg , David J. Gepner , and 2 more authors
    J. Topol., 2014
  4. Uniqueness of the multiplicative cyclotomic trace
    Andrew J. Blumberg , David Gepner , and Gonçalo Tabuada
    Adv. Math., 2014
  5. Moduli Spaces of Phylogenetic Trees Describing Tumor Evolutionary Patterns
    Sakellarios Zairis , Hossein Khiabanian , Andrew J. Blumberg , and 1 more author
    In Brain Informatics and Health , 2014
  6. Homotopical resolutions associated to deformable adjunctions
    Andrew J. Blumberg and Emily Riehl
    Algebr. Geom. Topol., 2014

2013

  1. A universal characterization of higher algebraic K-theory
    Andrew J. Blumberg , David Gepner , and Gonçalo Tabuada
    Geom. Topol., 2013
  2. Quantitative Homotopy Theory in Topological Data Analysis
    Andrew J. Blumberg and Michael A. Mandell
    Found. Comput. Math., 2013
  3. Verifying computations with state
    Benjamin Braun , Ariel J. Feldman , Zuocheng Ren , and 3 more authors
    In SOSP , 2013
  4. A hybrid architecture for interactive verifiable computation
    Victor Vu , Srinath Setty , Andrew J. Blumberg , and 1 more author
    In IEEE Symposium on Security and Privacy , 2013
  5. Resolving the conflict between generality and plausibility in verified computation
    Srinath T. V. Setty , Benjamin Braun , Victor Vu , and 3 more authors
    In EuroSys , 2013

2012

  1. Localization theorems in topological Hochschild homology and topological cyclic homology
    Andrew J. Blumberg and Michael A. Mandell
    Geom. Topol., 2012
  2. Taking proof-based verified computation a few steps closer to practical
    Srinath Setty , Victor Vu , Nikhil Panpalia , and 3 more authors
    In USENIX Security , 2012
  3. Making argument systems for outsourced computation practical (sometimes)
    Srinath Setty , Richard McPherson , Andrew J. Blumberg , and 1 more author
    In NDSS , 2012

2011

  1. Algebraic K-theory and abstract homotopy theory
    Andrew J. Blumberg and Michael A. Mandell
    Adv. Math., 2011
  2. Derived Koszul duality and involutions in the algebraic K-theory of spaces
    Andrew J. Blumberg and Michael A. Mandell
    J. Topol., 2011
  3. Privacy and accountability for location-based aggregate statistics
    Raluca A. Popa , Andrew J. Blumberg , Hari Balakrishnan , and 1 more author
    In ACM CCS , 2011
  4. Toward Practical and Unconditional Verification of Remote Computations
    Andrew J. Blumberg
    In HotOS XIII , 2011

2010

  1. Topological Hochschild homology of Thom spectra and the free loop space
    Andrew J. Blumberg , Ralph L. Cohen , and Christian Schlichtkrull
    Geom. Topol., 2010
  2. Topological Hochschild homology of Thom spectra which are E_∞ ring spectra
    Andrew J. Blumberg
    J. Topol., 2010
  3. Twists of K-theory and TMF
    Matthew Ando , Andrew J. Blumberg , and David Gepner
    In Superstrings, Geometry, Topology, and C^*-Algebras , 2010

2009

  1. VPriv: Protecting Privacy in Location-Based Vehicular Services
    Raluca A. Popa , Hari Balakrishnan , and Andrew J. Blumberg
    In 18th USENIX Security Symposium , 2009
  2. Open-closed field theories, string topology, and Hochschild homology
    Andrew J. Blumberg , Ralph L. Cohen , and Constantin Teleman
    In Alpine perspectives on algebraic topology , 2009

2008

  1. The localization sequence for the algebraic K-theory of topological K-theory
    Andrew J. Blumberg and Michael A. Mandell
    Acta Math., 2008

2007

  1. A discrete model of S^1-homotopy theory
    Andrew J. Blumberg
    J. Pure Appl. Algebra, 2007

2006

  1. Continuous functors as a model for the equivariant stable homotopy category
    Andrew J. Blumberg
    Algebr. Geom. Topol., 2006
  2. Congestion Pricing That Preserves Driver Privacy
    Andrew Justin Blumberg and Robin Chase
    In IEEE Intelligent Transportation Systems Conference (ITSC) , 2006

2004

  1. Searching for Stable Mechanisms: Automated Design for Imperfect Players
    Andrew J. Blumberg and Abhi Shelat
    In AAAI , 2004

1999

  1. Parallel computation on a DNA substrate
    Andrew J. Blumberg
    In DNA based computers III (Philadelphia, PA, 1997) , 1999

1997

  1. A Randomized Algorithm for Deciding the Functional Equivalence of Neural Networks
    Andrew J. Blumberg
    In ICONIP , 1997