Research Interest of Piotr Sulkowski

      Publication 1: Instantons on ALE spaces and orbifold partitions (URL)
      Publication 2: Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions (URL)
      Publication 3: Crystal Model for the Closed Topological Vertex Geometry (URL)

    URL of Research: 

Statement of Interest:


  My main scientific interests concern topological string and field theories. My PhD thesis “Calabi-Yau crystals in topological string theory”, supervised by Prof. Robbert Dijkgraaf and Prof. Jacek Pawelczyk, was concerned mainly with topological string theories and their relations to the so-called Calabi-Yau crystals (whose origin, in fact, dates back to the first Simons Workshop). Among the others, in my thesis new crystal models are introduced and their relations with the topological vertex theory and knot invariants are studied.

Recently I was working on topological aspects and various realizations of gauge theories with extended supersymmetry; the results are presented in publications 1 and 2 mentioned in my application. In particular, those papers present the relation between supersymmetric gauge theories and a system of free fermions on a Riemann surface. For N=4 theories this surface is a torus; then the fermionic viewpoint leads to new perspectives on McKay correspondence and level-rank duality, and a combinatorial description of gauge theory on ALE spaces - in terms newly-introduced orbifold-partitions - can be given. For N=2 theories the corresponding Riemann surface is curved and non-commutative, and by a chain of string dualities it can be related to topological string theory.  

Currently I continue my work on fermionic and string theory realizations of supersymmetric theories, study their relation to matrix models, as well as try to understand certain aspects of integrability in gauge theories. These topics immediately relate to the “Strings” and “Geometry” themes of this year’s Simons Workshop. I believe that at some point these topics will become relevant also in the context of discoveries of LHC, which is the third theme of this year’s Simons Workshop, and therefore my participation in the workshop would be important from the point of view of connecting more formal and phenomenological aspects of high energy physics.