Linh Truong

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 grant DMS-2104309.

I organize the University of 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.

Papers

▪ Homology concordance homomorphisms
with Irving Dai, Jennifer Hom, and Matthew Stoffregen.
[pdf].

▪ A combinatorial description of the LOSS Legendrian knot invariant
with Dongtai He.
[arXiv]. Submitted.

▪ 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.
[arXiv]. To appear in the Proceedings Volume of the 2019 Research Collaboration
Conference for Women in Symplectic and Contact Geometry and Topology.

▪ On the Upsilon invariant of fibered knots and right-veering open books
with Dongtai He and Diana Hubbard.
[arXiv]. To appear in Math. Res. Lett.

▪ Annular link invariants from the Sarkar-Seed-Szabó spectral sequence.
with Melissa Zhang.
[arXiv]. To appear in Michigan Math. J.

▪ 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.
[arXiv]. Submitted.

▪ 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

University of Michigan

Math 215: Multivariable and Vector Calculus (Section 060, Fall 2021)

Past Courses

University of Michigan

Math 697: Topics in Topology (Winter 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.

I am on the Math Department Climate and Inclusion Committee at Princeton University during 2020-2022.

Outreach and Mentorship

▪ I volunteered to tutor math with Ypsi Super Saturdays. 2020 - 2021.

Ypsi Super Saturdays is a virtual program for middle school and high school students, inspired by Math Corps Super Saturdays. The program is run by Stephen DeBacker and Sarah Koch in the Department of Mathematics at University of Michigan.

▪ I am a mentor for the AWM Mentor Network. Spring 2021.

The Association for Women in Mathematics (AWM) Mentor Network provides mentoring opportunities to girls and women including: recent PhD's, graduate students, undergraduates, high school and grade school students, and teachers.

▪ I co-hosted the Princeton Math Department Open House for the Prospective Ph.D. Preview (P3). Fall 2020.

The Prospective Ph.D. Preview (P3) aims to recruit first-generation or low-income students and those from historically underrepresented groups. The P3 program is organized by the Access, Diversity & Inclusion Team in the Graduate School at Princeton University.

▪ 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.