Experimentation and Chaos
My main research interests are in the
area of Algebraic Geometry, which started from the study of geometrical shapes
defined as solutions of polynomial equations. I am particularly interested in
the study of moduli spaces. Each point in a moduli space can represent a
complex geometric object, so that the study of a moduli space reveals
information on all geometric objects which share a set of common features.
Because these shared features remain constant when the objects are deformed
according with reasonable rules, they are called invariants. Invariants can be
numbers, or groups, or rings ... I study invariants in, on and of moduli
Papers and preprints
Intermediate moduli spaces of stable maps (with Andrei
Math. 167(2007), no. 1, 47–90.
The Chow ring of ),
(with Andrei Mustata), J.
Reine Angew. Math. 615 (2008), 93–119.
Tautological rings of stable map
spaces (with Andrei Mustata), Adv.
Math. 217 (2008), no.
Universal relations on stable map spaces in genus zero,
(with Andrei Mustata), Trans.
Amer. Math. Soc. 362 (2010), no. 4,
Hilbert space analogue of Heron's reflection principle, (with Finbarr Holland)
Math. Soc. Bull. No.
67 (2011), 57–65.
IMS Bulletin website
The structure of a local embedding and Chern classes of weighted blow-ups, (with Andrei Mustata), J.
Eur. Math. Soc. (JEMS) 14 (2012), no. 6, 1739–1794
Degree 1 curves in the Dwork
pencil and the mirror quintic, Math.
Ann. 355 (2013), no.
The universal etale
lift of a proper local embedding (with Andrei Mustata) arXiv
· Gromov-Witten invariants for
varieties with -action (with Andrei Mustata) arxiv
note on higher degree curves in the Dwork pencil,
Stable map spaces for projective bundles and Gromov-Witten theory, with Andrei Mustata, in preparation
Bennett-Woolf – started in Oct 2017
Yazdanpanah, “Inverse limit of GIT quotients of
Grassmannians by a maximal torus action” -joint
supervision with Andrei Mustata – PhD in August 2015
Xiuyun He, “Kinematic analysis of 3,4,5R
mechanisms”, visiting graduate student – PhD
in August 2015
Past Undergraduate SEFS Summer Research Bursary
“Applications of Methods from Algebraic Geometry in Robotics”,
Heffernan, “Algebraic Methods in Finite Dynamical Systems with
Applications to Traffic System Modelling”, Summer 2016
Outreach: UCC Mathematics Enrichment
Programme and Maths Circles Ireland