anca_mustata_bw                                                          Anca Mustata

School of Mathematical Sciences
University College Cork

Cork, Ireland

Office: Western Gateway Building 146
Tel:  353 21 420 5852
e-mail: A.Mustata at 


Autumn 2019

MA3052 Rings and Fields

MS2005/MS6005 Discrete Mathematics

Spring   2020

MA1057/MA1055 / MS3001 Introduction to Abstract Algebra

MA3062/MA4062 Modern Algebra

Previous years:     Archive


  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 spaces.

Papers and preprints

·  Intermediate moduli spaces of stable maps (with Andrei Mustata), Invent. 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. 4,17281755


·  Universal relations on stable map spaces in genus zero, (with Andrei Mustata), Trans. Amer. Math. Soc. 362 (2010), no. 4, 1699–1720


·  A Hilbert space analogue of Heron's reflection principle, (with Finbarr Holland)  Irish 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. 1, 97–130


·  The universal etale lift of a proper local embedding (with Andrei Mustata) arXiv


· Gromov-Witten invariants for varieties with -action (with Andrei Mustata) arxiv


·  A note on higher degree curves in the Dwork pencil, preprint

·  Stable map spaces for projective bundles and Gromov-Witten theory, with Andrei Mustata, in preparation

  PhD students: 

·        Jacob Bennett-Woolf   2017-2019

·        Vahid 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 students: 

·         Paul Ryan, “Applications of Methods from Algebraic Geometry in Robotics”, Summer 2015

·         Conor Heffernan, “Algebraic Methods in Finite Dynamical Systems with Applications to Traffic System Modelling”, Summer 2016


 Outreach: UCC Mathematics Enrichment Programme  and Maths Circles Ireland


Department Seminars

Conferences in algebraic geometry compiled by Ravi Vakil

George Boole Mathematical Sciences Conference


Irish Algebraic Geometry Seminar