Daren Chen

Address: 200 Linde Hall, 1200 East California Blvd,

              Pasadena, CA 91125

Email: darenc@caltech.edu


I am a postdoctoral scholar in mathematics at Caltech. My postdoc mentors are Yi Ni and Sergei Gukov. I am interested in low-dimensional topology, in particular Khovanov homology and knot Floer homology of links in \(S^3\), sometimes in other 3-manifolds. Before that, I obtained my PhD at Stanford University. My PhD advisor is Ciprian Manolescu.

Curriculum Vitae




Research

  1. A note on rational band moves

    (with J. Hom, M. H. Kim, J, Park and Z. Wu), La Matematica, Vol.3 (2024), 777-782 | arXiv:2311.11507

  2. Bar-Natan Homology for null homologous links in \(\mathbb{RP}^3\)

    preprint | arXiv:2307.11461

  3. Adiabatic compactness for holomorphic curves with boundary on nearby Lagrangians

    (with D. Cant) accepted to Kyoto J. Math | arXiv:2302.13391

  4. Floer lasagna modules from link Floer homology

    preprint | arXiv:2203.07650

  5. Twistings and the Alexander polynomial

    preprint | arXiv:2202.12489

  6. Generalised homomorphisms, measuring coalgebras and extended symmetries

    (with M. Batchelor, W. Boulton, J.Rawlinson, M.Warsi) preprint | arXiv:2105.02527

  7. Khovanov-type homologies of null homologous links in \(\mathbb{RP}^3\)

    Quantum Topology, under revision | arXiv:2104.04779




Talks

Dec. 2024      UC Irvine Geometry and Topology Seminar
L-space satellite operators and knot Floer homology
Nov. 2024      LA Joint Topology Seminar
L-space satellite operators and knot Floer homology
Oct. 2024      AMS Sectional Meeting, UC Riverside
Formality of Link Floer homology of 2-component L-space links
May 2024      Institute of Mathematics, Chinese Academy of Sciences
Some variations of Khovanov homology for null homologous links in \(\mathbb{RP}^3\)
Mar. 2024      Caltech-Tsinghua Joint Colloquium
Khovanov homology for null homologous links in \(\mathbb{RP}^3\)
Feb. 2024      Univeresity of South Florida Geometry/Topology Seminar
Bar-Natan homology for null-homologous links in \(\mathbb{RP}^3\) and genus bound
Nov. 2023      Ohio State University Topology Seminar
Bar-Natan homology for null-homologous links in \(\mathbb{RP}^3\) and genus bound
Jun. 2023      Virginia Topology Conference
Some variations of Khovanov homology for null homologous links in \(\mathbb{RP}^3\) and genus bound
Apr. 2023      Stanford University Topology Seminar
Bar-Natan homology for null-homologous links in \(\mathbb{RP}^3\) and genus bound
Jan. 2023      Caltech Geometry & Topology Seminar
Khovanov-type homologies of null homologous links in \(\mathbb{RP}^3\)
Oct. 2022      AMS sectional meeting, University of Utah
Introduction to Floer lasagna modules
Sep. 2022      Australian Geometric Topology Webinar
Khovanov-type homologies of null homologous links in \(\mathbb{RP}^3\)
Aug. 2022      University of Hamburg
Introduction to Floer lasagna modules
Apr. 2022      Knots in Washington 49.75
Twistings and the Alexander polynomial | slides
Mar. 2022      GT GAPS
Lasagna algebra and Floer lasagna module
Mar. 2022      GSTGC 2022 GaTech
Khovanov-type homologies of null homologous links in \(\mathbb{RP}^3\) | slides
Sep. 2021      Stanford University Topology Seminar
Khovanov-type homologies of null homologous links in \(\mathbb{RP}^3\)



Teaching

As a lecturer at Caltech:
Ma 151a          Algebraic and differential topology
Autumn 2023, Autumn 2024
Ma 151c          Algebraic and differential topology
Spring 2024
Ma 157a          Topics in Geometry and Topology
Autumn 2024

As a teaching assistant at Stanford University:
Math 20       Calculus
Autumn 2018
Math 51       Linear Algebra, Multivariable Calculus, and Modern Applications
Winter 2020, Winter 2021, Summer 2021, Winter 2022
Math 53       Differential Equations with Linear Algebra, Fourier Methods, and Modern Applications
Spring 2023
Math 116       Complex Analysis
Autumn 2022
Math 120       Groups and Rings
Autumn 2019
Math 143       Differential Geometry
Spring 2019
Math 148       Algebraic Topology
Winter 2023
Math 215A       Algebraic Topology
Autumn 2020, Autumn 2021