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 will use this grant to fund a Ph.D. position in symplectic geometry.

Events

I'm co-organizing a Mini-Workshop on Symplectic Geometry, which will take place at the Vrije Universiteit Amsterdam on October 9, 2017. The workshop is aimed at researchers, Ph.D. students, and advanced master's students working in symplectic geometry and related areas.

This will be the sixth instance of this mini-workshop. 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

2017/ 2018

blok 2: Functionaalanalyse (WISB315).

blok 1: Maat en integratie (WISB312).

2016/ 2017

August 14-25, 2017: Utrecht Summer School on Geometry. On August 16, 2017 I will give a minicourse on ``Some highlights of symplectic geometry''. Here are some lecture notes for this minicourse, the assignment and solutions therefor.

Past teaching

Supervision of theses

Ph.D. theses

Dušan Joksimović, starting in November 2016.

master theses:

David van der Giessen (joint supervision with Rob van der Vorst, who was the 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:

Mike de Vries, 2017.

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 an organizer of Geometry and Algebra, Geometry and Analysis, a weekly research seminar.

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