Universiteit Utrecht Department of Mathematics Photo

Fabian Ziltener

universitair docent (permanent assistant professor)

Hans Freudenthalgebouw
office 606
Universiteit Utrecht
Budapestlaan 6
3584 CD Utrecht
The Netherlands

e-mail: f.ziltener at-symbol uu.nl
phone: +31 30 253 1520

TOP grant (module 2) from NWO

In January 2016 I was awarded a TOP grant (module 2) from NWO, the Netherlands Organisation for Scientific Research. I used this grant to fund the Ph.D. position of my Ph.D. student Dušan Joksimović, who defended his Ph.D. thesis on October 6, 2020. He is now a postdoctoral fellow at Sorbonne Université.

Events

Due to the coronavirus pandemic, we have decided to cancel our Two-Day Workshop on Symplectic Geometry.

Previous workshops:

Research

My research area is symplectic geometry. I have proved that in various situations a given Hamiltonian diffeomorphism of a symplectic manifold has leafwise fixed points with respect to a coisotropic submanifold. This has applications to symplectic nonsqueezing and the existence of stably exotic symplectic structures.

In another part of my research I have investigated the symplectic vortex equations. These are a gauge theoretic version of the Cauchy-Riemann equation. They are related to the Gromov-Witten invariants of symplectic quotients.

Publications and preprints

Teaching

師傅領進門,修行在個人
Teachers open the door. You enter by yourself.

2020/ 2021

blok 1: Bewijzen in de Wiskunde, WISB102

semester 1, at University College Utrecht: Calculus and Linear Algebra, UCSCIMAT11

second semester (blokken 3,4): mastermath course on symplectic geometry

Past teaching

Supervision of theses

Ph.D. theses

Dušan Joksimović: Locally uniform existence of leafwise fixed points for C0-small Hamiltonian flows & generating systems of symplectic capacities, 2020.

master theses:

Sebastiaan Smeenk, joint supervision with Heinz Hanssmann and Bram Mesland (main supervisor).

Aaron Gootjes-Dreesbach: Generating functions in symplectic and contact geometry, 2020.

David van der Giessen, joint supervision with Rob van der Vorst (main supervisor): Braid Floer Homology on Surfaces, 2016.

Luuk Hendrikx: Floer Homology and Rabinowitz-Floer homology, 2016.

Maxim van Oldenbeek: Morse homology and Novikov homology, 2015.

bachelor theses:

Christiaan van den Brink, The Banach-Alaoglu theorem for topological vector spaces, 2019.

Jens de Vries, A Characterization of Flat Pseudo-Riemannian Manifolds, 2019.

Mike de Vries, Best approximations in normed vector spaces, 2018.

Paul Horikx, The Kakeya conjecture in two dimensions, 2017.

Roy Smitshoek, Symplectic forms on fiber bundles and the Chern classes, 2017.

Rogier Mierop, Existence of Symplectic Forms on Fibre Bundles, 2017.

Luka Zwaan, The Conley-Zehnder Theorem, 2016.

Kars Mulder, Het Tweedimensionale Kakeya Vermoeden, 2016.

Maarten Mol, On the existence of symplectic forms on open manifolds, 2016.

Harm Backx: On Gompfs construction of symplectic manifolds, 2015.

Koen Vernooij: Partial Differential Equations, Convexity and Weak Lower Semi-Continuity, 2015.

Other activities

I am a member of the Library Users Committee at our Mathematics Department.

I am a member of GQT: Geometry and Quantum Theory.

I am in charge of keeping a list of local GQT-master courses updated.

I am the organizer of the Utrecht Running Club. We are a group of people gathering for weekly runs. Feel free to join us!