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:

 

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.

Bibliography:

1)     A note on the involutive invariants of splices

K. Hendricks, M. Stoffregen and I. Zemke

2)     Gompf's cork and Heegaard Floer homology

I. Dai, A. Mallick and I. Zemke

3)     A general Heegaard Floer surgery formula

I. Zemke

4)     Connected sums and directed systems in knot Floer homologies

S. Ghosh and I. Zemke

5)     Lattice homology, formality, and plumbed L-space links

M. Borodzik, B. Liu, and I. Zemke

To appear, Journal of the European Math. Society

6)     An involutive dual knot formula

K. Hendricks, J. Hom, M. Stoffregen and I. Zemke

7)     Naturality and functoriality in involutive Heegaard Floer homology

K. Hendricks, J. Hom, M. Stoffregen and I. Zemke

To appear, Quantum Topology

8)     The equivalence of lattice and Heegaard Floer homology

I. Zemke

To appear, Duke Math. Journal

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

I. Zemke

10) A note on PL-slice disks and rationally slice knots

K. Hendricks, J. Hom, M. Stoffregen and I. Zemke

To appear, Proceedings of the Conference and Summer School on Frontiers in Geometry and Topology.

11) Heegaard Floer homology and plane curves with non-cuspidal singularities

M. Borodzik, B. Liu, and I. Zemke

To appear Alg. Geom. Top.

12) On the quotient of the homology cobordism group by Seifert spaces

K. Hendricks, J. Hom, M. Stoffregen and I. Zemke

Trans. Amer. Math. Soc. Ser. B 9 (2022), 757-781.

13) Surgery exact triangles and involutive Heegaard Floer homology

K. Hendricks, J. Hom, M. Stoffregen and I. Zemke

14) New Heegaard Floer slice genus and clasp number bounds

A. Juhasz, and I. Zemke

15) Transverse invariants and exotic surfaces in the 4-ball

A. Juhasz, M. Miller and I. Zemke

Geom. Topol. 25 (2021), no. 6, 2963-3012.

16) Knot cobordisms, bridge index, and torsion in Floer homology

A. Juhasz, M. Miller, and I. Zemke

J. Topol. 13 (2020), no. 4, 1701-1724.

17) Knot Floer homology and strongly-homotopy ribbon concordances

M. Miller and I. Zemke

Math. Res. Lett. 28 (2021), no. 3, 849-861.

18) Khovanov homology and ribbon concordances

A.S. Levine and I. Zemke

Bull. Lond. Math. Soc. 51 (2019), 6, 1099-1103.

19) Knot Floer homology obstructs ribbon concordance

I. Zemke

Annals of Mathematics (2) 190 (2019), no. 3, 931-947.

20) Stabilization distance bounds from link Floer homology

A. Juhasz, and I. Zemke

To appear, Journal of Topology.

21) Distinguishing slice disks using knot Floer homology

A. Juhasz and I. Zemke

Selecta Math. (N.S.) 26, 5 (2020)

22) Concordance surgery and the Ozsvath-Szabo 4-manifold invariant

A. Juhasz and I. Zemke

To appear, Journal of the European Math. Society

23) Contact handles, duality, and sutured Floer homology

A. Juhasz and I. Zemke

Geometry & Topology, 24 (2020) 179-307

24) Duality and mapping tori in Heegaard Floer homology.

I. Zemke

Journal of Topology, 14 (3), 1027-1112. (2021)

25) Connected sums and involutive knot Floer homology.

I. Zemke

Proc. London Math. Soc. (2019) 119: 214-265.

26) Link cobordisms and absolute gradings on link Floer homology.

I. Zemke

Quantum Topology. 10 (2019), 207-323.

27) Link cobordisms and functoriality in link Floer homology.

I. Zemke

Journal of Topology. (2019) 12: 94-220.

28) Naturality and mapping class groups in Heegaard Floer homology

A. Juhasz, D. Thurston and I. Zemke.

Mem. Amer. Math. Soc. 273 (2021), no. 1338, v+174 pp.

29) A connected sum formula for involutive Heegaard Floer homology

K. Hendricks, C. Manolescu and I. Zemke.

Selecta Math. (N.S.), (2018) 24; 1183-1245

30) Quasistabilization and basepoint moving maps in link Floer homology.

I. Zemke

Algebraic & Geometric Topology, Volume 17, Number 6 (2017) 3461-3518

31) Graph cobordisms and Heegaard Floer homology

I. Zemke

32) A graph TQFT for hat Heegaard Floer homology.

I. Zemke

To appear, Quantum Topology.

Notes:

Here are some exercises I wrote for a 2024 minicourse at IBS.

Here are some informal notes I wrote for the Princeton RTG 2023 Summer School.

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