Anca Mustata
Teaching
Spring 2017


AM2072 Mathematical
Experimentation and Chaos

Winter 2016

MA3052 Rings and
Fields


Previous years:
Archive
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.
4,1728–1755
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 blowups, (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
· GromovWitten 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 GromovWitten 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