Institute for Advanced Study
photo by: Dan Komoda / IAS
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 (DMS-1606451).
I study low-dimensional topology, knot theory and contact and symplectic geometry.
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 special session, 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.
▪ Colloquium, Fordham University, December 2, 2019.
▪ Geometry and Topology workshop, UCLA, January 2-4, 2020.
▪ Colloquium, University of Illinois at Chicago, January 22, 2020.
▪ Colloquium, University of Notre Dame, February 5, 2020.
▪ Colloquium, Duke University, February 26, 2020.
▪ Bi-College Mathematics Colloquium, Bryn Mawr and Haverford Colleges, March 16, 2020.
▪ Geometry/Topology seminar, Boston College, March 19, 2020.
▪ Lafayette-Lehigh Geometry & Topology seminar, Lafeyette College, March 21, 2020.
▪ Low-dimensional topology, AMS special session, Purdue University, April 4-5, 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.
▪ Braids, fibered knots, and concordance questions
with Diana Hubbard, Keiko Kawamuro, Feride Ceren Kose, Gage Martin,
Olga Plamenevskaya, Katherine Raoux, and Hannah Turner.
▪ On the Upsilon invariant of fibered knots and right-veering open books
with Dongtai He and Diana Hubbard.
▪ Annular link invariants from the Sarkar-Seed-Szabó spectral sequence.
with Melissa Zhang.
▪ A refinement of the Ozsváth-Szabó large integer surgery formula and knot concordance
▪ More concordance homomorphisms from knot Floer homology
with Irving Dai, Jennifer Hom, and Matthew Stoffregen.
[arXiv]. To appear in Geometry & Topology.
▪ An infinite rank summand of the homology cobordism group
with Irving Dai, Jennifer Hom, and Matthew Stoffregen.
▪ A slicing obstruction from the 10/8+4 theorem.
[pdf]. To appear in MATRIX Annals.
▪ Extremal Measures and Clockwise Overlays
with Hari Bercovici and Wingsuet Li.
Discrete Mathematics, Vol. 315-316, (2014), 53-64.
▪ A family of almost quasipositive links
with Elaina Aceves, Keiko Kawamuro, and Gage Martin.
Draft available upon request.
▪ 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
The Association for Women in Mathematics mentor network at Columbia University matches faculty and graduate student mentors with women undergraduates majoring in mathematics.
The Columbia Undergraduate Mathematics Society brings together undergraduates studying mathematics in this weekly seminar.
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.
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.
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.
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.
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.