David Gepner

Department of Mathematics, Johns Hopkins University

arXivScholarKrieger 410

I study algebraic topology. More specifically, homotopy theory and its interactions with algebraic geometry, algebraic K-theory, and higher category theory.

Δ⁰ Δ¹ Δ² Δ³

Oriented simplices Δ⁰ through Δ³, faces oriented

Preprints & publications31 records

#YearTypeTitleAuthors / venueRef
0312026preprintColimits in Oriented Category Theorywith Hadrian HeinearXiv:2608.02592
0302026preprintFibrations in Oriented Category Theorywith Hadrian HeinearXiv:2607.18418
0292026preprintAn Oriented Street–Roberts Conjecturewith Hadrian HeinearXiv:2606.29373
0282026preprintHomotopy Posets, Postnikov Towers, and Hypercompletions of ∞-Categorieswith Hadrian HeinearXiv:2603.09903
0272025preprintOriented Category Theorywith Hadrian HeinearXiv:2510.10504
0262024acceptedGlobal 2-rings and genuine refinementswith Sil Linskens and Luca Pol · accepted, Compositio MathematicaarXiv:2407.05124
0252023articleThe tom Dieck splitting theorem in equivariant motivic homotopy theorywith Jeremiah Heller · Journal of the Institute of Mathematics of Jussieu 22, no. 3, 1181–1250DOI arXiv:1910.11485
0242023articleOn equivariant topological modular formswith Lennart Meier · Compositio Mathematica 159, no. 12, 2638–2693DOI arXiv:2004.10254
0232022article∞-Operads as analytic monadswith Rune Haugseng and Joachim Kock · International Mathematics Research Notices 2022, 12516–12624DOI arXiv:1712.06469
0222021articleBrauer groups and Galois cohomology of commutative ring spectrawith Tyler Lawson · Compositio Mathematica 157, 1211–1264DOI arXiv:1607.01118
0212021bookDifferential function spectra, the differential Becker–Gottlieb transfer, and applications to differential algebraic K-theorywith Ulrich Bunke · Memoirs of the American Mathematical SocietyDOI arXiv:1306.0247
0202020preprintIntegral representation theorems for DQ-moduleswith François PetitarXiv:2004.10176
0192019articleK-theoretic obstructions to bounded t-structureswith Benjamin Antieau and Jeremiah Heller · Inventiones mathematicaeDOI arXiv:1610.07207
0182019bookAn Introduction to Higher Categorical AlgebraChapter in Handbook of Homotopy Theory, CRC PressDOI arXiv:1907.02904
0172018articleOn localization sequences in the algebraic K-theory of ring spectrawith Benjamin Antieau and Tobias Barthel · Journal of the European Mathematical Society 20, no. 2, 459–487DOI arXiv:1412.4041
0162018articleParametrized spectra, multiplicative Thom spectra, and the twisted Umkehr mapwith Matthew Ando and Andrew Blumberg · Geometry & Topology 22, no. 7, 3761–3825DOI arXiv:1112.2203
0152017articleLax colimits and free fibrations in ∞-categorieswith Rune Haugseng and Thomas Nikolaus · Documenta Mathematica 22, 1225–1266DOI arXiv:1501.02161
0142017articleUnivalence in locally cartesian closed ∞-categorieswith Joachim Kock · Forum Mathematicum 29, 617–652DOI arXiv:1208.1749
0132016articleK-theory of endomorphisms via noncommutative motiveswith Andrew Blumberg and Gonçalo Tabuada · Transactions of the AMS 368, 1435–1465DOI arXiv:1302.1214
0122015articleEnriched ∞-categories via non-symmetric ∞-operadswith Rune Haugseng · Advances in Mathematics 279, 575–716DOI arXiv:1312.3178
0112015articleUniversality of multiplicative infinite loop space machineswith Moritz Groth and Thomas Nikolaus · Algebraic & Geometric Topology 15, 3107–3153DOI arXiv:1305.4550
0102014articleBrauer groups and étale cohomology in derived algebraic geometrywith Benjamin Antieau · Geometry & Topology 18, 1149–1244DOI arXiv:1210.0290
0092014articleUniqueness of the multiplicative cyclotomic tracewith Andrew Blumberg and Gonçalo Tabuada · Advances in Mathematics 260, 191–232DOI arXiv:1103.3923
0082014articleUnits of ring spectra, orientations, and Thom spectra via rigid infinite loop space theorywith Matthew Ando, Andrew Blumberg, Michael Hopkins and Charles Rezk · Journal of Topology 7, no. 4, 1077–1117DOI arXiv:1403.4320
0072014articleAn ∞-categorical approach to R-line bundles, R-module Thom spectra, and twisted R-homologywith Matthew Ando, Andrew Blumberg, Michael Hopkins and Charles Rezk · Journal of Topology 7, 869–893DOI arXiv:1403.4325
0062014articleActions of Eilenberg–MacLane spaces on K-theory spectra and uniqueness of twisted K-theorywith Benjamin Antieau and José Manuel Gómez · Transactions of the AMS 366, 3631–3648DOI arXiv:1106.5099
0052013articleA universal characterization of higher algebraic K-theorywith Andrew Blumberg and Gonçalo Tabuada · Geometry & Topology 17, 733–838DOI arXiv:1001.2282
0042010articleTwists of K-theory and TMFwith Matthew Ando and Andrew Blumberg · in Superstrings, Geometry, Topology, and C*-algebras, Proc. Sympos. Pure Math. 81, AMSDOI arXiv:1002.3004
0032009articleOn the motivic spectra representing algebraic cobordism and algebraic K-theorywith Victor Snaith · Documenta Mathematica 14, 359–396DOI arXiv:0712.2817
0022007preprintHomotopy theory of orbispaceswith André HenriquesarXiv:math/0701916
0012006thesisHomotopy topoi and equivariant elliptic cohomologyPhD thesis, University of Illinois at Urbana-Champaign

Teaching11 records · Johns Hopkins

#TermTypeCourseTitleEnrolment
—Fall 2026courseAS.110.615Algebraic Topology I
—Spring 2026courseAS.110.201Linear Algebra
—Spring 2025courseAS.110.601Algebra I
—Fall 2024courseAS.110.601Algebra I~12
—Spring 2024courseAS.110.727Topics in Algebraic Topology~15
—Fall 2023courseAS.110.407Honors Complex Analysis~12
—Spring 2023courseAS.110.616Algebraic Topology II~12
—Spring 2023courseAS.110.602Algebra II~12
—Spring 2022courseAS.110.616Algebraic Topology II~15
—Fall 2021courseAS.110.615Algebraic Topology I~15
—Fall 2021courseAS.110.411Honors Algebra I~20

Prospective PhD students must apply through the department's graduate admissions process.

Students & postdocs10 records

#YearTypeNamePosition
—currentPhDNooria Ahmed
—2026PhDAnish Chedalavada
—2026PhDFan Huang
—currentPhDJiacheng Liang
—2025PhDMilton LinFellow, National Institute for Theory and Mathematics in Biology, Chicago
—2024PhDNaruki MasudaBoas Assistant Professor, Northwestern University
—currentPhDSwaminathan Rajagopalan
—2026PhDAkira Tominaga
—currentPhDHongxiang Zhao
—2023–2026postdocRok GregoricPostdoctoral Fellow, Max Planck Institute for Mathematics, Bonn

Contact

Emailgepner@jhu.edu
OfficeKrieger Hall, Room 410
PostDepartment of Mathematics, Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD 21218