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 Universiteit Utrecht on March 17, 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 fifth 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

2016/ 2017

spring semester: mastermath course M2: Symplectic Geometry

blok 4: Analyse in meer variabelen (WISB212)

blok 2: Functionaalanalyse (WISB315).

blok 1 (October 17, 24, and 31, 2016): Orientation on Mathematical Research (WISM102).

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:

Roy Smitshoek

Rogier Mierop

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!