I am a member at the IAS. Previously, I was a Ritt Assistant Professor in the Department of Mathematics at Columbia University, and an NSF Postdoctoral Fellow at Columbia University and at MIT. In 2016 I completed my Ph.D. from Princeton University, advised by Peter Ozsváth and Zoltán Szabó.

My research is partially supported by an NSF Postdoctoral Research Fellowship (grant DMS-1606451).

I study low-dimensional topology, knot theory and contact and symplectic geometry.

email: ltruong@math.ias.edu
office: Fuld Hall 422, 1 Einstein Drive, Princeton, NJ 08540

recent and upcoming talks
  ▪ PCMI Research Program, July 1, 2019. slides
  ▪ Women in Symplectic and Contact Geometry and Topology, July 25, 2019. video
  ▪ Geometry and Topology seminar, CIRGET, September 13, 2019.
  ▪ Floer Homology in Dimensions 3 and 4, AMS Sectional, September 14-15, 2019.
  ▪ Geometry seminar, University of Virginia, October 1, 2019.
  ▪ RTG seminar on Geometry, Topology, and Dynamics, University of Michigan, October 9, 2019.
  ▪ Colloquium, University of Michigan, October 10, 2019.
  ▪ Topology seminar, Princeton University, October 17, 2019.
  ▪ Noetherian Ring, Princeton University, November 8, 2019.
  ▪ Topology seminar, Rice University, November 25, 2019.
  ▪ Geometry and Topology workshop, UCLA, January 2-4, 2020.
  ▪ Bi-College Mathematics Colloquium, Bryn Mawr and Haverford Colleges, Spring 2020.

I'm interested in low-dimensional topology, knot theory and contact and symplectic geometry.
My work focuses on topological applications of Heegaard Floer homology and Khovanov homology.

papers

▪ Annular link invariants from the Sarkar-Seed-Szabó spectral sequence.
 with Melissa Zhang.
  [arXiv]. Preprint.

▪ A slicing obstruction from the 10/8+4 theorem.
  [pdf]. Submitted.

▪ A refinement of the Ozsváth-Szabó large integer surgery formula and knot concordance
  [arXiv]. Submitted.

▪ More concordance homomorphisms from knot Floer homology
  with Irving Dai, Jennifer Hom, and Matthew Stoffregen.
  [arXiv]. Submitted.

▪ An infinite rank summand of the homology cobordism group
  with Irving Dai, Jennifer Hom, and Matthew Stoffregen.
  [arXiv]. Submitted.

▪ Truncated Heegaard Floer homology and knot concordance invariants
  Algebraic & Geometric Topology, 19-4 (2019), 1881-1901.
  [arXiv] [published]

▪ Extremal Measures and Clockwise Overlays
  with Hari Bercovici and Wingsuet Li.
  Discrete Mathematics, Vol. 315-316, (2014), 53-64.
  [published]

articles in preparation

▪ Upsilon invariant, fibered knots, and right-veering open books
 with Dongtai He and Diana Hubbard.
 In preparation.

▪ A family of almost quasipositive links
 with Elaina Aceves, Keiko Kawamuro, and Gage Martin.
 In preparation.

past courses

Columbia University

  Calculus III (Spring 2019)

  Calculus I (Fall 2018, Fall 2017)

  Intro to Higher Mathematics (Fall 2018)

Princeton University

  Multi-variable Calculus (Fall 2014)

other teaching/mentorship

▪ 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.

outreach and mentorship

▪ I served as a faculty mentor for the AWM Chapter at Columbia University. 2018 - 2019.

The Association for Women in Mathematics mentor network at Columbia University matches faculty and graduate student mentors with women undergraduates majoring in mathematics.

▪ I gave a topology talk aimed at undergraduate math majors at Undergraduate Math Society. Spring 2018.

The Columbia Undergraduate Mathematics Society brings together undergraduates studying mathematics in this weekly seminar.

▪ I presented a "Knots and Mathematics" talk to high school students in NYC at the S.T.E.M. Outreach Colloquium. Spring 2018.

STEM outreach entails bringing science to K-12 students and the broader public and is vital to spark interest in STEM careers for K-12 students and improve the public's science literacy. With this in mind, the Office of Postdoctoral Affairs organized a STEM outreach colloquium in partnership with the NYC Department of Education. The event took place in the evening of March 27th, 2018, and featured 4 selected talks by postdocs, followed by a networking session. The audience comprised of high school students and teachers that belong to the NYC Department of Education's High School Science Research Pathways Program as well as postdocs and PhD students from Columbia.

▪ I reviewed abstracts for the 2nd Annual WISC Graduate Research Symposium. Spring 2018.

The Women in Science at Columbia (WISC) Graduate Research Symposium is a multi-disciplinary research conference that aims to highlight and celebrate emerging research conducted by women graduate students in the science, technology, engineering, and math fields. The format of the symposium is designed to encourage discussion across an array of STEM disciplines by sharing the details of current research and placing them in a broader context, making connections and engaging in research networking.

▪ I judged the STEM poster fair at the Scientista Symposium. Spring 2018.

The Scientista Symposium is an intercollegiate conference for women in STEM that brings together women undergraduates and graduate students from across the country for a weekend of inspirational talks, workshops, networking, and research. The conference includes a science research poster fair, where students present their work to the conference's international audience of STEM students and professionals. Judges provide valuable feedback to female students on their original scholarly research projects.

▪ I proctored for PUMaC, a math contest for high school students. Fall 2014.

The Princeton University Mathematics Competition (PUMaC) is an annual competition run by the Princeton University Math Club. Participants from all over the US and various international teams come to the Princeton University campus and spend the day taking various mathematics assessment tests and having fun. PUMaC aims to foster a love for mathematics among high school students.

▪ I was a panelist for an info session on graduate school at the IAS Women and Mathematics Program. Spring 2012.

The Program for Women and Mathematics brings together research mathematicians with women undergraduates, graduate students, and postdoctoral scholars for an intensive workshop held on the campus of the Institute for Advanced Study.