Research

My main area of research is symplectic/contact topology and symplectic/contact dynamics, but my mathematical interests are broad. A large part of my PhD was dedicated to studying quantitative aspects of the theory of Lagrangian cobordisms and what implications this has for Lagrangian topology. Lately I have been thinking a lot about questions closer to dynamics (such as Aubry-Mather theory and Arnold' diffusion) from the point of view of symplectic topology. I have been trying to apply pseudo holomorphic curve techniques in combination with Viterbo's homogenization procedure to obtain new insights into (generalized) Aubry-Mather theory.

One problem which fascinates me is to compute numerical symplectic invariants. Generally, it seems fair to say that, whatever interesting quantity you take in symplectic topology it will be very hard to compute in any reasonable level of generality. I follow a paradigm which says that one should connect symplectic topology to other relevant fields and use insights from those fields to perform computations. Examples of such fields could be convex geometry or Aubry-Mather theory.

Papers

The published version might differ slightly from the arXiv preprint.

• Mather theory and symplectic rigidity. Journal of Modern Dynamics 15 (2019), 165-207. Preprint

• Topology of (small) Lagrangian cobordisms. Algebraic & Geometric Topology 19-2 (2019), 701-742. Preprint

• A distance expanding flow on exact Lagrangian cobordism classes. Preprint

• Invariants of Lagrangian cobordisms via spectral numbers. Journal of Topology and Analysis Vol 11, No. 01, 2019. Preprint

• The intersection product on Morse-Bott homology. MSc thesis at the ETH Zürich. Abstract. Advised by Will Merry.

Talks

• March 2019: Algebra/Topology seminar, University of Copenhagen

• March 2019: CAST 2019, Humboldt Universität zu Berlin

• October 2018: Geometry seminar, Heidelberg University

• June 2018: Symplectix seminar, Institut Henri Poincarè, Sorbonne University

• May 2018: Geometry seminar, Université Claude Bernard Lyon 1

• April 2018: Symplectic geometry seminar, ETH Zurich

• March 2018: Dynamics seminar, University of Maryland

• November 2017: Geometry and Dynamics seminar, Tel Aviv University

• October 2017: Geometry seminar, IRMA, Université de Strasbourg

• October 2016: Symplectic geometry seminar, ETH Zurich

Awards and Distinctions

• 2019: ETH Medal for outstanding doctoral dissertation. Awarded to at most top 8% of all PhDs at the ETH Zurich.

Teaching

• Autumn semester 2018: I will be teaching exercise classes for Differential Geometry I (bachelor/master's level)

• July-August 2018: Teaching assistant at the MSRI graduate summer school From Symplectic Geometry to Chaos.

• Spring semester 2018: Übungsorganisator for Analysis I D-INFK (bachelor level)

• Autumn semester 2017: Übungsorganisator for Analysis II D-INFK (bachelor level)

• Spring semester 2017: Teaching assistant for Dynamical Systems II (bachelor/master's level)

• Autumn semester 2016: Teaching assistant for Dynamical Systems I (bachelor/master's level)

Videos

Here are some videos of some talks I gave at the MSRI summer school From Symplectic Geometry to Chaos:

• Introduction to Aubry Mather theory

• Symplectic Mather theory

Service

I have done referee work for Algebraic & Geometric Topology

Contact

My email address is madsbisgaard88 at hotmail dot com.