Ian Zemke

Ian Zemke


Assistant Professor
Princeton Mathematics Department
Fine Hall, 304 Washington Rd,
Princeton, NJ, 08544

Office:

Fine Hall 1207

E-Mail:

izemke at math dot princeton dot edu

Teaching: Summer 2023: Princeton RTG Summer School. Here are some informal and preliminary notes.

 

About me: I finished my PhD at UCLA in 2017. My advisor was Ciprian Manolescu.

I study low dimensional topology using symplectic geometry.

My research is partially supported by NSF grants DMS-1703685 and DMS-2204375 and a Sloan Research Fellowship. In Fall of 2024, I will be moving to University of Oregon.

Papers and Preprints:

1)     Gompf's cork and Heegaard Floer homology (with I. Dai and A. Mallick)

2)     A general Heegaard Floer surgery formula

3)     Connected sums and directed systems in knot Floer homologies (with S. Ghosh)

4)     Lattice homology, formality, and plumbed L-space links (with M. Borodzik and B. Liu) accepted Journal of the European Math. Society

5)     An involutive dual knot formula (with K. Hendricks, J. Hom, and M. Stoffregen)

6)     Naturality and functoriality in involutive Heegaard Floer homology (with K. Hendricks, J. Hom, and M. Stoffregen) accepted Quantum Topology

7)     The equivalence of lattice and Heegaard Floer homology

8)     Bordered manifolds with torus boundary and the link surgery formula

9)     A note on PL-slice disks and rationally slice knots (with K. Hendricks, J. Hom, and M. Stoffregen) Accepted for the Proceedings of the Conference and Summer School on Frontiers in Geometry and Topology.

10) Heegaard Floer homology and plane curves with non-cuspidal singularities (with M. Borodzik and B. Liu) Accepted Alg. Geom. Top.

11) On the quotient of the homology cobordism group by Seifert spaces (with K. Hendricks, J. Hom, and M. Stoffregen) Trans. Amer. Math. Soc. Ser. B 9 (2022), 757-781.

12) Surgery exact triangles and involutive Heegaard Floer homology (with K. Hendricks, J. Hom, and M. Stoffregen)

13) New Heegaard Floer slice genus and clasp number bounds (with A. Juhasz)

14) Transverse invariants and exotic surfaces in the 4-ball (with A. Juhasz and M. Miller) Geom. Topol. 25 (2021), no. 6, 2963-3012.

15) Knot cobordisms, bridge index, and torsion in Floer homology (with A. Juhasz and M. Miller) J. Topol. 13 (2020), no. 4, 1701-1724.

16) Knot Floer homology and strongly-homotopy ribbon concordances (with M. Miller) Math. Res. Lett. 28 (2021), no. 3, 849-861.

17) Khovanov homology and ribbon concordances (with A.S. Levine) Bull. Lond. Math. Soc. 51 (2019), 6, 1099-1103.

18) Knot Floer homology obstructs ribbon concordance Annals of Mathematics (2) 190 (2019), no. 3, 931-947.

19) Stabilization distance bounds from link Floer homology (with A. Juhasz) accepted Journal of Topology.

20) Distinguishing slice disks using knot Floer homology (with A. Juhasz) Selecta Math. (N.S.) 26, 5 (2020)

21) Concordance surgery and the Ozsvath-Szabo 4-manifold invariant (with A. Juhasz) Accepted, Journal of the European Math. Society

22) Contact handles, duality, and sutured Floer homology (with A. Juhasz) Geometry & Topology, 24 (2020) 179-307

23) Duality and mapping tori in Heegaard Floer homology. Journal of Topology, 14 (3), 1027-1112. (2021)

24) Connected sums and involutive knot Floer homology. Proc. London Math. Soc. (2019) 119: 214-265.

25) Link cobordisms and absolute gradings on link Floer homology. Quantum Topology. 10 (2019), 207-323.

26) Link cobordisms and functoriality in link Floer homology. Journal of Topology. (2019) 12: 94-220.

27) Naturality and mapping class groups in Heegaard Floer homology (with A. Juhasz and D. Thurston). Mem. Amer. Math. Soc. 273 (2021), no. 1338, v+174 pp.

28) A connected sum formula for involutive Heegaard Floer homology (with K. Hendricks and C. Manolescu). Selecta Math. (N.S.), (2018) 24; 1183-1245

29) Quasistabilization and basepoint moving maps in link Floer homology. Algebraic & Geometric Topology, Volume 17, Number 6 (2017) 3461-3518

30) Graph cobordisms and Heegaard Floer homology

31) A graph TQFT for hat Heegaard Floer homology. Accepted, Quantum Topology.

Slides:

1.     The link surgery formula as a bordered theory

2.     The involutive mapping cone formula

3.     Ribbon concordances and knot Floer homology

Code:

1)     Some code for computing genus and clasp number bounds: CFK-infty.ipynb

2)     Some code to accompany Stabilization distance bounds from link Floer homology:

a.      A Sage notebook to compute tau, Vk and upsilon of certain pairs of deform spun slice disks: slice.ipynb

3)     Some Sage code to accompany Connected sums and involutive knot Floer homology, which computes involutive invariants for knots involutive.ipynb