About

Ionut Ciocan-Fontanine is a professor at the School of Mathematics at the University of Minnesota. He earned his PhD from the University of Utah in 1996. His research interests include algebraic geometry, moduli spaces, and Gromov-Witten theory. Further details about his specific contributions or publications are not provided on the page.

Research topics

• Physics
• Pure mathematics
• Geometry
• Mathematics
• Algorithm

Selected publications

• A mirror theorem for partial flag bundles

  arXiv (Cornell University) · 2026-02-10

  articleOpen access1st authorCorresponding

  We construct a family of points on the Lagrangian cone of a partial flag bundle associated to a (possibly non-split) vector bundle from any Weyl-invariant $I$-function of a prequotient. This result can be seen as the nonabelian analogue of the mirror theorem for projective bundles in arXiv:2307.03696, and generalizes Oh's mirror theorem for split partial flag bundles in arXiv:1607.08326.

  PublisherOA PDF

• A mirror theorem for partial flag bundles

  Open MIND · 2026-02-10

  preprint1st authorCorresponding

  We construct a family of points on the Lagrangian cone of a partial flag bundle associated to a (possibly non-split) vector bundle from any Weyl-invariant $I$-function of a prequotient. This result can be seen as the nonabelian analogue of the mirror theorem for projective bundles in arXiv:2307.03696, and generalizes Oh's mirror theorem for split partial flag bundles in arXiv:1607.08326.

  DOI

• Fundamental Factorization of a GLSM Part I: Construction

  Memoirs of the American Mathematical Society · 2023 · 24 citations

  1st authorCorresponding
  • Mathematics
  • Pure mathematics
  • Algorithm

  We define enumerative invariants associated to a hybrid Gauged Linear Sigma Model. We prove that in the relevant special cases these invariants recover both the Gromov–Witten type invariants defined by Chang–Li and Fan–Jarvis–Ruan using cosection localization as well as the FJRW type invariants constructed by Polishchuk–Vaintrob. The invariants are defined by constructing a “fundamental factorization” supported on the moduli space of Landau–Ginzburg maps to a convex hybrid model. This gives the kernel of a Fourier–Mukai transform; the associated map on Hochschild homology defines our theory.

  PublisherOA PDFDOI

• Big $I$-functions

  Advanced studies in pure mathematics · 2019-03-07 · 18 citations

  article1st authorCorresponding

  <!-- *** Custom HTML *** --> We introduce a new big $I$-function for certain GIT quotients $W/\!\!/\mathbf{G}$ using the quasimap graph space from infinitesimally pointed $\mathbb{P}^1$ to the stack quotient $[W/\mathbf{G}]$. This big $I$-function is expressible by the small $I$-function introduced in [6, 10]. The $I$-function conjecturally generates the Lagrangian cone of Gromov-Witten theory for $W/\!\!/\mathbf{G}$ defined by Givental. We prove the conjecture when $W/\!\!/\mathbf{G}$ has a torus action with good properties.

  PublisherDOI

• Fundamental Factorization of a GLSM, Part I: Construction

  arXiv (Cornell University) · 2018-02-14 · 1 citations

  preprintOpen access1st authorCorresponding

  We define enumerative invariants associated to a hybrid Gauged Linear Sigma Model. We prove that in the relevant special cases, these invariants recover both the Gromov-Witten type invariants defined by Chang-Li and Fan-Jarvis-Ruan using cosection localization as well as the FJRW type invariants constructed by Polishchuk-Vaintrob. The invariants are defined by constructing a "fundamental factorization" supported on the moduli space of Landau-Ginzburg maps to a convex hybrid model. This gives the kernel of a Fourier-Mukai transform; the associated map on Hochschild homology defines our theory.

  PublisherDOI

• Higher genus quasimap wall-crossing for semipositive targets

  Journal of the European Mathematical Society · 2017-05-22 · 32 citations

  article1st authorCorresponding

  In previous work we have conjectured wall-crossing formulas for genus zero quasimap invariants of GIT quotients and proved them via localization in many cases. We extend these formulas to higher genus when the target is semipositive, and prove them for semipositive toric varieties, in particular for toric local Calabi–Yau targets. The proof also applies to local Calabi–Yau's associated to some nonabelian quotients.

  PublisherDOI

• Orbifold quasimap theory

  Mathematische Annalen · 2015-02-28 · 58 citations

  article
  PublisherDOI

• Wall-crossing in genus zero quasimap theory and mirror maps

  Algebraic geometry · 2014-10-01 · 96 citations

  articleOpen access1st authorCorresponding

  For each positive rational number , the theory of -stable quasimaps to certain GIT quotients W/ /G developed in [CKM14] gives rise to a Cohomological Field Theory. Furthermore, there is an asymptotic theory corresponding to 0. For > 1 one obtains the usual Gromov-Witten theory of W/ /G, while the other theories are new. However, they are all expected to contain the same information and, in particular, the numerical invariants should be related by wall-crossing formulas. In this paper we analyze the genus zero picture and find that the wall-crossing in this case significantly generalizes toric mirror symmetry (the toric cases correspond to abelian groups G). In particular, we give a geometric interpretation of the mirror map as a generating series of quasimap invariants. We prove our wall-crossing formulas for all targets W/ /G which admit a torus action with isolated fixed points, as well as for zero loci of sections of homogeneous vector bundles on such W/ /G.

  PublisherDOI

• Big I-functions

  arXiv (Cornell University) · 2014-01-29 · 12 citations

  preprintOpen access1st authorCorresponding

  We introduce a new big I-function for certain GIT quotients W//G using the quasimap graph space from infinitesimally pointed $\mathbb{P}^1$ to the stack quotient [W/G]. This big I-function is expressible by the small I-function introduced in arXiv:0908.4446 [math.AG] and arXiv:1106.3724 [math.AG]. The I-function conjecturally generates the Lagrangian cone of Gromov-Witten theory for W//G defined by Givental. We prove the conjecture when W//G has a torus action with good properties.

  Publisher

• Big I-functions

  arXiv (Cornell University) · 2014-01-29

  preprintOpen access1st authorCorresponding

  We introduce a new big I-function for certain GIT quotients W//G using the quasimap graph space from infinitesimally pointed $\mathbb{P}^1$ to the stack quotient [W/G]. This big I-function is expressible by the small I-function introduced in arXiv:0908.4446 [math.AG] and arXiv:1106.3724 [math.AG]. The I-function conjecturally generates the Lagrangian cone of Gromov-Witten theory for W//G defined by Givental. We prove the conjecture when W//G has a torus action with good properties.

  PublisherOA PDFDOI

Recent grants

• Three problems on Gromov-Witten invariants of algebraic varieties

  NSF · $121k · 2003–2008

• Quasimap Theory and Gromov-Witten Invariants of Complete Intersections

  NSF · $168k · 2016–2019

• Studies in Gromov-Witten Theory

  NSF · $191k · 2007–2011

• Wall-crossings in quasimap theory and applications

  NSF · $159k · 2013–2016

Frequent coauthors

• Bumsig Kim

  30 shared

• Mikhail Kapranov

  7 shared

• Aaron Bertram

  6 shared

• Davesh Maulik

  Massachusetts Institute of Technology

  5 shared

• Matjaž Konvalinka

  5 shared

• Igor Pak

  5 shared

• Duco van Straten

  4 shared

• Victor V. Batyrev

  4 shared