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Mathematics

D-Index
36
Citations
5786
World Ranking
2632
National Ranking
1084

Research.com Recognitions

  • 2017 - Fellow of the American Mathematical Society For contributions to algebraic geometry and service to the mathematical community.
  • 1996 - Fellow of Alfred P. Sloan Foundation

Overview

Dan Abramovich is affiliated with Brown University in the United States. Their research spans multiple domains, primarily focused on advanced mathematics and computational theory.

Abramovich's work is concentrated in the fields of Mathematics and Computer Science. Within these broad domains, their subfields of study include:

  • Geometry and Topology
  • Computational Theory and Mathematics
  • Mathematical Physics
  • Algebra and Number Theory
  • Computational Mechanics

Their main topics of research cover:

  • Algebraic Geometry and Number Theory
  • Polynomial and algebraic computation
  • Commutative Algebra and Its Applications
  • Homotopy and Cohomology in Algebraic Topology
  • Advanced Algebra and Geometry
  • Advanced Differential Equations and Dynamical Systems
  • Advanced Numerical Analysis Techniques

Significant recent publications by Abramovich include:

  • "Decomposition of degenerate Gromov-Witten invariants," 2020, Compositio Mathematica
  • "Punctured logarithmic maps," 2020, arXiv (Cornell University)
  • "Principalization of ideals on toroidal orbifolds," 2020, Journal of the European Mathematical Society
  • "Relative desingularization and principalization of ideals," 2020, arXiv (Cornell University)
  • "On the hyperbolicity of base spaces for maximally variational families of smooth projective varieties (with an appendix by Dan Abramovich)," 2021, Journal of the European Mathematical Society

Abramovich's collaborative network includes frequent co-authors:

  • Michael Temkin
  • Jarosław Włodarczyk
  • Qile Chen
  • Mark Gross
  • Bernd Siebert

The scholar has published primarily in these venues:

  • arXiv (Cornell University)
  • Journal of the European Mathematical Society
  • Oberwolfach Reports
  • Notices of the American Mathematical Society
  • Compositio Mathematica

In addition to articles, Abramovich has authored books published by specialized academic presses:

  • Punctured Logarithmic Maps, Memoirs of the European Mathematical Society, 2025
  • New Techniques in Resolution of Singularities, Oberwolfach Seminars, 2023

Abramovich has been recognized with awards such as:

  • Fellow of the American Mathematical Society (2017) for contributions to algebraic geometry and service to the mathematical community
  • Fellow of Alfred P. Sloan Foundation (1996)

Best Publications

  • Gromov-Witten theory of Deligne-Mumford stacks

    Dan Abramovich;Tom Graber;Angelo Vistoli

  • Compactifying the space of stable maps

    D. Abramovich

  • Twisted Bundles and Admissible Covers

    Dan Abramovich;Alessio Corti;Angelo Vistoli

  • Torification and factorization of birational maps

    Dan Abramovich;Kalle Karu;Kenji Matsuki;Jarosław Włodarczyk

  • Weak semistable reduction in characteristic 0

    Dan Abramovich;Kalle Karu

  • Tame stacks in positive characteristic

    Dan Abramovich;Martin Olsson;Angelo Vistoli

  • Stable logarithmic maps to Deligne-Faltings pairs II

    Dan Abramovich;Qile Chen

  • The tropicalization of the moduli space of curves

    Dan Abramovich;Lucia Caporaso;Sam Payne

  • Lectures on Arakelov Geometry

    C. Soulé;D. Abramovich;J. F. Burnol;J. K. Kramer

  • Algebraic orbifold quantum products

    Dan Abramovich;Tom Graber;Angelo Vistoli

  • Equivariant resolution of singularities in characteristic 0

    Dan Abramovich;Jianhua Wang

  • Twisted stable maps to tame Artin stacks

    Dan Abramovich;Martin Olsson;Angelo Vistoli

  • A linear lower bound on the gonality of modular curves

    Dan Abramovich

  • Moduli of twisted spin curves

    Dan Abramovich;Tyler J. Jarvis

  • Sheaves of t-structures and valuative criteria for stable complexes

    Dan Abramovich;Alexander Polishchuk

  • Smoothness, Semistability, and Toroidal Geometry

    Dan Abramovich;Johan de Jong

  • Birational invariance in logarithmic Gromov–Witten theory

    Dan Abramovich;Jonathan Wise

  • Boundedness of the space of stable logarithmic maps

    Dan Abramovich;Qile Chen;Steffen Marcus;Jonathan Wise

  • On the geometry of Deligne-Mumford stacks

    A Kresch;D Abramovich;A Bertram;L Katzarkov

  • Decomposition of degenerate Gromov–Witten invariants

    Dan Abramovich;Qile Chen;Mark Gross;Bernd Siebert

  • Logarithmic Geometry and Moduli

    Dan Abramovich;Qile Chen;Danny Gillam;Yuhao Huang

  • Skeletons and Fans of Logarithmic Structures

    Dan Abramovich;Qile Chen;Steffen Marcus;Martin Ulirsch

  • Compactifying the space of stable maps

    Dan Abramovich;Angelo Vistoli

Frequent Co-Authors

Jan Denef
Jan Denef KU Leuven
Brendan Hassett
Brendan Hassett Brown University
Joe Harris
Joe Harris Harvard University
Mark Gross
Mark Gross University of Cambridge

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