Russell Avdek

I am a mathematician working in the areas of contact and symplectic topology. In 2013 I received my PhD under the supervision of Ko Honda. In 2021 I joined the Algebra and Geometry research group at Uppsala University.

I can be reached via my personal email at first_name.last_name@gmail.com or my university email at first_name.last_name@math.uu.se (corrected in the obvious fashion).

Research articles

How do you count index 1 holomorphic curves on the Lagrangian cylinder over a Legendrian link in R3 when the domain is non-simply connected? This is an obstruction bundle problem which does not always admit a combinatorial solution. However, such curves can be "perturbed away" using a Legendrian isotopy.

We develop tools for studying Reeb dynamics on contact 3-manifolds determined by surgery diagrams and for counting holomorphic planes in surgery cobordisms. These tools are used to provide the first examples of closed, tight contact manifolds with vanishing contact homology. For an overview focused on applications, see these slides.

We describe factorizations of fibered Dehn twists along the boundary of Milnor fibers of Fermat singularities in terms of Dehn twists along Lagrangian spheres. In low dimensions, these factorizations generalize the classical chain relation.

Liouville hypersurfaces and connect sum cobordisms (Journal of Symplectic Geometry, 2021)

A symplectic cobordism construction is described which generalizes Weinstein handle attachment. Applications include proofs of the existence of "fillability" and "non-vanishing contact homology" monoids in the symplectomorphism groups of Liouville domains as well as proofs of the symplectic non-triviality of squares of Dehn twists on cotangent bundles of 2- and 6-dimensional spheres (which are smoothly trivial).

Contact surgery and supporting open books (Algebraic & Geometric Topology, 2013)

Algorithms are described for switching between open book and contact surgery descriptions of a given contact 3-manifold. We use these algorithms to show that every contact 3-manifold can be described by contact surgery along a Legendrian link in 3-space.

Recent seminar talks