anca_mustata_bw                                                          Anca Mustata

Lecturer
School of Mathematical Sciences
University College Cork

Cork, Ireland

Office: Western Gateway Building 1-46
Tel:  353 21 420 5852
e-mail: A.Mustata at ucc.ie 

  Teaching

Spring 2017

MA1057/MA1055/MS3001 Introduction to Abstract Algebra

AM2072 Mathematical Experimentation and Chaos

Winter 2016

MA3052 Rings and Fields

MS2005/MS6005 Discrete Mathematics

Previous years:     Archive

PhD Studentship 2017

Applications are invited for a PhD position in the Mathematics Department at UCC, commencing no later than 1 September 2017. The post will provide an annual stipend of €16,500 + fees, funded for 3 or 4 years (depending on qualifications). Applications should be sent by email no later than 26 January 2017 and should contain a statement of purpose, a CV, university transcripts and addresses of three academic referees. 

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. 4,17281755

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

  Past PhD students: 

·        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 Bursaries students: 

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

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

        

     Outreach: UCC Mathematics Enrichment Programme  and  Maths Circles Ireland

      Events:

George Boole Mathematical Sciences Conference

Irish Algebraic Geometry Seminar 

Conferences in algebraic geometry compiled by Ravi Vakil
Department calendar