Research Profile

Anca Mustata

Biography

Research Interests

My research is in the area of algebraic geometry, with connections to topology and string theory. More precisely, I have studied algebraic and topological properties of parameter spaces of curves embedded in projective spaces.   Parameter spaces are sets whose elements share a number of common features. They have come to play a central role in Algebraic Geometry in recent years. For example, the geometry of parameter spaces of rational curves on a complex projective space is strongly related to such important properties of the space like rationality, unirationality or rational connectedness. In a distinct direction, counting rational curves, either via Gromov-Witten and Donaldson-Thomas invariant theories, was found by physicists working in string theory to describe observables in certain conformal quantum field theories.   In previous and current work, we explore the relation between the geometry of the parameter spaces of curves and that of the space where these curves live. For example, in joint work with Andrei Mustata, we have calculated the Chow and cohomology rings of a recently preeminent type of parameter spaces ¿ the moduli spaces of stable maps. These rings are algebraic structures encoding algebraic and topological invariants of the moduli spaces. We have shown a close, though intricate connection between the invariants of the moduli space of curves in a projective space and the invariants of the space itself. These cohomological data are generalising Gromov-Witten invariant calculations, a very active area of research in algebraic geometry. 

Research Grants

 ProjectFunding
Body
Start DateEnd DateAward
Vertical and Horizontal Integration of Mathematics EducationNAIRTL04-JAN-1216-DEC-12€10,000.00
SFI "Parameter Spaces for Rational Curves in Complex Projective Varieties"Science Foundation of Ireland12-JUN-0811-DEC-11€124,749.00
Maths Outreach Research.Miscellaneous01-SEP-1330-NOV-15€20,001.00
SFI OIP 2011 StaffScience Foundation of Ireland01-JAN-1121-DEC-11€547.00
The Maths Circles Initiative.Science Foundation of Ireland06-JAN-1420-DEC-14€22,000.00

Publications

Peer Reviewed Journals

 YearPublication
(2013)'Degree 1 curves in the Dwork pencil and the mirror quintic'
Mustata, A (2013) 'Degree 1 curves in the Dwork pencil and the mirror quintic'. Mathematische Annalen, 355 :97-130 [DOI] [Details]
(2012)'The structure of a local embedding and Chern classes of weighted blow-ups'
Anca Mustata and Andrei Mustata (2012) 'The structure of a local embedding and Chern classes of weighted blow-ups'. Journal of the European Mathematical Society, [Details]
(2011)'A Hilbert space analogue of Heron's reflection principle'
Finbarr Holland, Anca Mustata (2011) 'A Hilbert space analogue of Heron's reflection principle'. Bulletin of the Irish Mathematical Society, 67 (2011):57-65 [Details]
(2010)'Universal Relations on Stable Map Spaces in Genus Zero'
Anca Mustata, Andrei Mustata (2010) 'Universal Relations on Stable Map Spaces in Genus Zero'. Transactions of The American Mathematical Society, 362 :1699-1720 [DOI] [Details]
(2008)'The Chow ring of M_{0,m}(P^n,d)'
Anca Mustata and Andrei Mustata ; (2008) 'The Chow ring of M_{0,m}(P^n,d)'. Journal Fur Die Reine Und Angewandte Mathematik, 615 :93-119 [Details]
(2008)'Tautological rings of stable map spaces'
Anca Mustata, Andrei Mustata (2008) 'Tautological rings of stable map spaces'. Advances In Mathematics, 217 :1728-1755 [DOI] [Details]
(2007)'Intermediate moduli spaces of stable maps'
Anca Mustata and Andrei Mustata; (2007) 'Intermediate moduli spaces of stable maps'. Inventiones Mathematicae, 167 :47-90 [Details]

Professional Activities

Conference Contributions

 YearPublication
(2014)Workshop on Kähler Geometry and Geometric Analysis,
Anca Mustata (2014) Stable map spaces for varieties with C×-actions. [Invited Lectures (Workshops)], Workshop on Kähler Geometry and Geometric Analysis, UCC , 12-MAY-14 - 14-JUN-14. [Details]
(2013)Workshop on Hodge Theory in String Theory,
Anca Mustata (2013) The Dwork Pencil of Quintic Threefolds. [Invited Lectures (Workshops)], Workshop on Hodge Theory in String Theory, The Fields Mathematical Institute, Toronto , 18-NOV-14 - 23-NOV-13. [Details]
(2013)The Irish Mathematical Society Meeting,
Anca Mustata, Andrei Mustata (2013) Gromov-Witten invariants for varieties with C∗-actions. [Invited Lectures (Conference)], The Irish Mathematical Society Meeting, NUI Maynooth , 26-AUG-13 - 27-AUG-13. [Details]
(2011)Irish Algebraic Geometry Conference,
Anca Mustata (2011) organizing committee. [Conference Organising Committee Member], Irish Algebraic Geometry Conference, UCC, Cork, Ireland , 11-MAR-11 - 12-MAR-11. [Details]
(2011)Irish Geometry Conference,
Anca Mustata (2011) Local embeddings of algebraic stacks. [Invited Lectures (Conference)], Irish Geometry Conference, NUI Galway , 13-MAY-11 - 14-MAY-11. [Details]
(2010)Algebraic Geometry Conference,
Mustata, Anca; (2010) The Universal Lift of a Local Embedding. [Invited Lectures (Conference)], Algebraic Geometry Conference, St. Patrick's College, Dublin , 26-NOV-10 - 27-NOV-10. [Details]
(2010)Cambridge-Oxford-Warwick (COW :) Seminar,
Mustata, Anca; (2010) The Universal Lift of a Local Embedding. [Invited Seminars/Guest Lectures], Cambridge-Oxford-Warwick (COW :) Seminar, University of Bath, UK , 18-NOV-10 - 19-NOV-10. [Details]
(2009)Graduate Lectures on Moduli Spaces,
Mustata, Anca; (2009) Moduli spaces of weighted stable maps. [Invited Seminars/Guest Lectures], Graduate Lectures on Moduli Spaces, Sogang University, Seoul, Korea , 05-DEC-09 - 06-JAN-09. [Details]
(2009)Workshop on Moduli Spaces,
Mustata, Anca; (2009) Chern classes of weighted blow-ups along regular local embeddings. [Invited Lectures (Workshops)], Workshop on Moduli Spaces, Seoul, Korea , 07-JAN-09 - 08-JAN-09. [Details]
(2008)Pure Mathematics Research Centre Colloquium:,
Anca Mustata ; (2008) Stability conditions and moduli spaces for curves in projective manifolds. [Oral Presentation], Pure Mathematics Research Centre Colloquium:, Queen's University Belfast , 11-APR-08 - 11-APR-08. [Details]
(2008)International Conference in Algebraic Geometry,
Anca Mustata ; (2008) Weighted stable map spaces and their cohomology. [Oral Presentation], International Conference in Algebraic Geometry, Bucharest , 01-JUL-08 - 31-JUL-08. [Details]
(2008)Algebraic Geometry Seminar:,
Anca Mustata ; (2008) Tautological rings of stable map spaces. [Oral Presentation], Algebraic Geometry Seminar:, University of Warwick , 25-FEB-08 - 25-FEB-08. [Details]
(2008)First de Brun Workshop in Computational Algebra,
Anca Mustata ; (2008) Intersection theory on the space of stable maps from curves to P^n. [Oral Presentation], First de Brun Workshop in Computational Algebra, Galway , 01-AUG-08 - 31-AUG-08. [Details]
(2007)Irish Mathematical Society Meeting,,
Anca Mustata ; (2007) On spaces of rational curves and their cohomology. [Oral Presentation], Irish Mathematical Society Meeting,, UCD, Dublin , 03-SEP-07 - 04-SEP-07. [Details]
(2007)Dublin Area Mathematics Colloquium:,
Anca Mustata ; (2007) Stability conditions and moduli spaces for curves in projective manifolds. [Oral Presentation], Dublin Area Mathematics Colloquium:, TCD, Dublin , 09-NOV-07 - 09-NOV-07. [Details]

Employment

 EmployerPositionFrom / To
Department of Mathematics, UCC Lecturer01-AUG-07 /
University of Illinois at Urbana-Champaign Visiting Assistant Professor01-JAN-05 / 31-JUL-07
Mathematical Sciences Research Institute, Berkeley, CA. Postdoctoral Fellow01-JAN-06 / 31-MAY-06
University of British Columbia Postdoctoral Fellow01-JAN-03 / 31-DEC-05

Education

 YearInstituionQualificationSubject
2003University of Utah PHDMathematics
1998University of Bucharest MScMathematics
1997University of Bucharest BSCMathematics

Outreach Activities

 Description

Organizer, UCC Mathematics Enrichment Programme for secondary school students. 2009-current

Co-founding member, the Maths Circles initiative

Journal Activities

 JournalRoleTo / From
Bulletinetin Of The London Mathematical Society Referee-
International Mathematics Research Notices Referee-
Transactions Of The American Mathematical Society Referee-

Teaching Activities

Teaching Interests

Recently I have taught modules in Algebra, Geometry, Differential Equations, Discrete Mathematics. 

Modules taught in 2011-2012:

MA3052 Rings and Fields  (P1)
MA1057 Introduction to Abstract Algebra  (P1)
MS3001 Introduction to Abstract Algebra  (P1)
MA2059/MA3060 Introduction/Topics in Discrete Mathematics (P2)
MS2013 Euclidean Geometry (P2)

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