Anca Mustata

Lecturer School of Mathematical Sciences University College Cork Cork, Ireland

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

Teaching

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

Research

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.

arXiv:math/0409569

· The Chow ring of ), (with Andrei Mustata), J. Reine Angew. Math. 615 (2008), 93–119. 

arXiv:math/0507464

· Tautological rings of stable map spaces (with Andrei Mustata), Adv. Math. 217 (2008), no. 4,1728–1755

arXiv:math/0607432

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

arXiv:math/0607431

· 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

arXiv:0812.3101

· Degree 1 curves in the Dwork pencil and the mirror quintic,  Math. Ann. 355 (2013), no. 1, 97–130

arXiv:math/0311252

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

arXiv:1011.1596

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

arXiv:1505.01471

· 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

Events:

Department Seminars

Conferences in algebraic geometry compiled by Ravi Vakil

George Boole Mathematical Sciences Conference

Irish Algebraic Geometry Seminar