I am an Assistant Professor at the University of Michigan. My research is in low-dimensional topology, with a focus on topological applications of Heegaard Floer homology and Khovanov homology.

My research is partially supported by NSF CAREER grant DMS-2237131.

Michigan Topology Intercity Symposium will be held on November 9, 2024.

Michigan Topology Seminar

email: tlinh@umich.edu
office: 4842 East Hall

I'm interested in low-dimensional topology. My work focuses on topological applications of Heegaard Floer homology and Khovanov homology.

▪ Khovanov homology and the Involutive Heegaard Floer homology of branched double covers
  with Akram Alishahi and Melissa Zhang.
  [arXiv].

▪ A note on knot Floer thickness and the dealternating number
  Topology Appl. 337 (2023), Paper No. 108638, 5.
  [arXiv]. [published].

▪ Homology concordance and knot Floer homology
  with Irving Dai, Jennifer Hom, and Matthew Stoffregen.
  To appear Math. Ann.
  [arXiv].

▪ A combinatorial description of the LOSS Legendrian knot invariant
  with Dongtai He.
  J. Knot Theory Ramifications 31 (2022), no. 13, 2250093.
  [arXiv]. [published].

▪ Comparing Bennequin-type inequalities
  with Elaina Aceves and Keiko Kawamuro.
  New York J. Math. 27 (2021), 124-140.
  [arXiv]. [published].

▪ Braids, fibered knots, and concordance questions
  with Diana Hubbard, Keiko Kawamuro, Feride Ceren Kose, Gage Martin,
  Olga Plamenevskaya, Katherine Raoux, and Hannah Turner.
  Research directions in symplectic and contact geometry and topology, 293-324, Assoc. Women Math. Ser., 27, Springer, Cham, 2021.
  [arXiv]. [published].

▪ On the Upsilon invariant of fibered knots and right-veering open books
  with Dongtai He and Diana Hubbard.
  Math. Res. Lett. 29 (2022), no. 2, 421-444.
  [arXiv]. [published].

▪ Annular link invariants from the Sarkar-Seed-Szabó spectral sequence
  with Melissa Zhang.
  Michigan Math. J. 71 (2022), no. 4, 725-763.
  [arXiv]. [published].

▪ A slicing obstruction from the 10/8+4 theorem.
  2019-20 MATRIX Annals, MATRIX Book Ser., Springer, (2021), 167-172.
  [published].

▪ More concordance homomorphisms from knot Floer homology
  with Irving Dai, Jennifer Hom, and Matthew Stoffregen.
  Geom. Topol. 25 (2021) 275-338.
  [arXiv]. [published].

▪ An infinite rank summand of the homology cobordism group
  with Irving Dai, Jennifer Hom, and Matthew Stoffregen.
  Duke Math. J. 172 (2023), no. 12, 2365-2432.
  [arXiv].

▪ A refinement of the Ozsváth-Szabó large integer surgery formula and knot concordance
  Proc. Amer. Math. Soc. 149 (2021), no. 4, 1757-1771.
  [arXiv]. [published].

▪ Truncated Heegaard Floer homology and knot concordance invariants
  Algebr. Geom. Topol. 19 (2019), no. 4, 1881-1901.
  [arXiv]. [published].

▪ Extremal Measures and Clockwise Overlays
  with Hari Bercovici and Wingsuet Li.
  Discrete Math. 315 (2014), 53-64.
  [published].

Current Courses

  I am not teaching during 2024-25.

Past Courses

University of Michigan

  Math 697: Topics in Topology (Winter 2021, Fall 2023)

  Math 490: Introduction to Topology (Fall 2023)

  Math 590: Introduction to Topology (Winter 2022)

  Math 215: Multivariable and Vector Calculus (Fall 2021)

  Math 115: Calculus I (Fall 2020)

Columbia University

  Math 2000: Intro to Higher Mathematics (Fall 2018)

  Math 1201: Calculus III (Spring 2019)

  Math 1101: Calculus I (Fall 2018, Fall 2017)

Princeton University

  MAT 201: Multivariable Calculus (Fall 2014)

Other Teaching Experiences

▪ At the Perspectives on Dehn surgery workshop at ICERM at Brown University in July 2019, I served as the teaching assistant for Yi Ni's course on Heegaard Floer homology and Dehn surgery.

▪ At the PCMI Graduate Summer School in July 2019, I served as a teaching assistant for Jen Hom's course on Heegaard Floer homology.

▪ In spring 2019, I supervised an undergraduate independent reading course on the topics of knot Floer homology, Khovanov homology and applications to knot concordance and contact geometry.

▪ In summer 2018, Akram Alishahi and I mentored a group of six undergraduates in the Columbia Summer Undergraduate Research Program.