Filip Zivanovic

Hello! I am a Research Assistant Professor at the Simons Center for Geometry and Physics.

Previously, I was a Postdoctoral Research Associate at the University of Edinburgh with Nick Sheridan,

after a PhD at the University of Oxford under the supervision of Alexander Ritter and Kevin McGerty.

Research Interests

Symplectic Topology: Symplectic cohomology, Exact Lagrangians, Mirror Symmetry.

Algebraic Geometry: Higgs moduli spaces, Perverse Filtrations, Mirror Symmetry.

Geometric Representation Theory: Symplectic resolutions, Springer fibers.

My CV can be found here.

I am on the job market this Fall.

Email: fzivanovic [at] scgp [dot] stonybrook [dot] edu

Papers and Preprints

(2022) Exact Lagrangians from contracting ℂ*-actions, arXiv:2206.06361, 46pp, Under revision.
(2023) Filtrations on quantum cohomology from the Floer theory of ℂ*-actions (with A. Ritter), arXiv:2304.13026, 72pp, to appear in Mathematische Annalen.
(2023) Filtrations on quantum cohomology via Morse-Bott-Floer Spectral Sequences (with A. Ritter), arXiv:2304.14384, 90pp, Under revision.
(2024) Floer-theoretic filtration on Painlevé Hitchin systems (with S. Szabó), arXiv:2405.14850, 22pp, Under revision.
(2024) Filtrations on equivariant quantum cohomology and Hilbert-Poincaré series (with A. Ritter), arXiv:2410.17237, 75pp, Submitted.
(2025) Quantum cohomology and Floer invariants of semiprojective toric varieties (with A. Ritter), arXiv:2501.09011, 38pp
(2026) Equivariant multiplicities and mirror symmetry for Hilbert schemes (with A. Minets), arXiv:2602.14897, 44pp, Submitted.
(2026) Perverse filtration on Hilbert schemes via upward flow, arXiv:2606.06449, 21pp, Submitted.

(2026) Equivariant Floer rotation maps and filtration invariants (with A. Ritter), to appear soon.
(2026) Floer-theoretic filtration for Hilbert schemes of points (with A. Minets), to appear soon.

Teaching

In Spring 2027, I will lecture MAT 211 (Introduction to Linear Algebra) at Stony Brook.
In Fall 2026, I lecture MAT 310 (Linear Algebra) at Stony Brook.
In Spring 2026, I lectured MAT 566 (Differential Topology) at Stony Brook.
In Fall 2025, I lectured MAT 315/ MAT 526 (Advanced Linear Algebra) at Stony Brook.
In Spring 2025, I lectured MAT 127 (Calculus C) at Stony Brook.
In Fall 2024, I was the course coordinator and lecturer for MAT 131 (Calculus I) at Stony Brook.
In Spring 2022, I was a lecturer on a PhD course in Homological Algebra at the GlaMS PhD Centre.
In the 2019/20 academic year, I was a Retained Lecturer in Mathematics at Jesus College, Oxford. I was tutoring courses in Linear Algebra, Group Theory, and Topology.
In Michaelmas Term 2018, I was a class tutor on the 3rd-year course Geometry of Surfaces at the University of Oxford
In Hilary Term 2018, I was a TA for the 3rd-year course Algebraic Curves at the University of Oxford.
In Hilary Term 2017, I was a TA for the 3rd-year course Algebraic Curves at the University of Oxford.
In Michaelmas Term 2016, I was a TA on the Master's course Algebraic Topology at the University of Oxford.
In the 2015/16 academic year, I was a class tutor for the 1st-year Analysis 1 and 2nd-year Analysis 3 courses at the University of Belgrade.

Selected Talks

Closed-string mirror symmetry for semiprojective toric manifolds, The Joint Los Angeles Topology Seminar, UCLA 2026
Upward flows and mirror symmetry for Hilbert schemes, Math-Physics Joint Seminar, UPenn 2025
Curious filtration from the Floer theory and C*-actions, Lefschetz Centennial Conference, IMSA 2025
Symplectic Cohomology Construction Via C*-actions, Symplectic Seminar, IAS Princeton 2025
Filtration from Floer theory of holomorphic C*-actions, Theory of Atoms workshop, Sofia 2024
Equivariant Floer theory for symplectic C*-manifolds, Symplectic seminar, Stanford 2024
Exact Lagrangians in hyperkähler manifolds, Workshop of Symplectic Topology, Belgrade 2024.
Floer-theoretic filtration on Painlevé spaces, Web-seminar on Painlevé Equations, France-Japan 2024
Floer-theoretic filtrations on cohomology via C*-actions, Hausel Seminar, ISTA 2024
Filtrations of cohomology rings from Floer theory of contracting C*-actions, Geometria em Lisboa Seminar, Técnico Lisboa 2023
Symplectic C*-manifolds, SGGT Seminar, Columbia University 2023
Symplectic Cohomology of symplectic manifolds admitting contracting C*-actions, Workshop of Symplectic Topology, Belgrade 2022.
Symplectic Geometry of Conical Symplectic Resolutions, Geometry & Physics seminar, Northwestern University 2021.
Canonical bases from Floer theory, Reading group on mirror symmetry of character varieties, Edinburgh 2020.
McKay correspondence, resolutions of Kleinian singularities and Slodowy slices, Reading group on braid group actions on derived categories, Edinburgh 2020.
Symplectic Geometry of Conical Symplectic Resolutions, Hodge Seminar, Edinburgh 2020.
Quiver varieties and Kac-Moody algebras, Junior Geometry and Topology seminar, Oxford 2020.
C*-Symplectic Cohomology of hyperkähler manifolds, Workshop of Symplectic Topology, Belgrade 2019.
Introduction to Symplectic Cohomology, BIG workshop, Jersey 2018.

Organizational

2023–present: Co-Organizer, Symplectic Geometry, Gauge Theory, and Low-Dimensional Topology Seminar, Stony Brook University.
2023–2024: Co-organizer, Mathematics Colloquium, Stony Brook University.
2017–2019: Organizer, Junior Geometry and Topology Seminar, Mathematical Institute, University of Oxford.

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