Contact Information: E-mail: ionel "at" math "dot" stanford "dot" edu
Photo Credit: Rod Searcey
Teaching Schedule:
On Sabbatical during the AY 2019-2020.
Research interests
Symplectic topology and geometry, in particular holomorphic
curves and moduli spaces of curves;
Gromov-Witten invariants, enumerative invariants and other gauge
theoretical invariants.
Education
Ph. D., Mathematics, Michigan State University, 1996.
B.S., Mathematics, University "Al. I. Cuza", Iasi, Romania, 1991.
Appointments
2006-present, Professor of Mathematics, Stanford University.
2016-2019, Department Chair, Mathematics Department, Stanford University.
Spring 2018, Member, Mathematical Sciences Research Institute.
Fall 2009, Member, Mathematical Sciences Research Institute.
2004-2006, Professor, University of Wisconsin-Madison.
2004-2006, Associate Professor, Stanford University.
2002-2004, Associate Professor, University of Wisconsin-Madison.
Fall 2001, Member, Institute of Advanced Studies, Princeton.
1998-2002, Assistant Professor, University of Wisconsin-Madison.
1996-1999, CLE Moore Instructor, Massachusetts Institute of Technology.
Fall 1996, Postdoctoral Fellow, Mathematical Sciences Research Institute.
1991-1996, Teaching Assistant, Michigan State University.
1990-1991, Teaching Assistant, University "Al. I. Cuza", Iasi, Romania.
Notable Awards/Honors
AMS Fellow (2020).
Simons Fellow (2015-2016).
Invited speaker, Topology Section, International Congress of Mathematicians (Beijing, 2002).
Plenary speaker, AMS National Meeting (Atlanta, 2005).
Plenary speaker, AMS Sectional Meeting (Madison, 2002).
Alfred P. Sloan Research Fellow (2000-2004).
Significant publications
The Gopakumar-Vafa formula for symplectic manifolds
(with T.H. Parker),
Annals of Math 187 (2018), pp 1-64,
DOI;
arXiv:1306.1516.
GW invariants relative to normal crossing divisors,
Advances in Math. 281 (2015), pp 40-141,
DOI;
arXiv:1103.3977.
Relations in the tautological ring of \(M_g\),
Duke Math. J., Volume 129 (2005), pp 157-186;
DOI.
The symplectic sum formula for Gromov-Witten invariants
(with T.H. Parker), Annals of Math., Volume 159 (2004), pp 935-1025,
DOI;
Corrigendum, June 2015.
Relative Gromov-Witten Invariants
(with T.H. Parker), Annals of Math., Volume 157 (2003), pp 1-52,
DOI.
Topological Recursive Relations in \(H^{2g}(M_{g,n})\)
, Inventiones Math., Volume 148 (2002), pp 627-658,
DOI.
Genus One Enumerative Invariants in \(P^n\) with Fixed j Invariant
,
Duke Math. J., Volume 94 (1998), pp 279-324,
DOI.
Recent Papers/Preprints
A Klein TQFT: the local Real Gromov-Witten theory of curves (with Penka Georgieva),
arXiv:1812.02505.
Relating VFCs on thin compactifications
(with Thomas H. Parker), Mathematische Annalen, Volume 375 (2019), pp. 845-893,
DOI;
arXiv:1807.10326.
Thin compactifications and relative fundamental classes
(with Thomas H. Parker), JSG, Volume 17 (2019), pp 703-752,
DOI;
arXiv:1512.07894.
A natural Gromov-Witten virtual fundamental class (with Thomas H. Parker), preprint,
arXiv:1302.3472.
Selected Recent Talks
International Symplectic Topology Conference, IMPA, Rio de Janeiro, Aug 2019.
Connections for Women Workshop: Enumerative Geometry Beyond Numbers, MSRI, Jan 2018.
Floer Memorial Lecture, Berkeley, Oct 2017.
Symplectic geometry: Celebrating the work of Simon Donaldson, Isaac Newton
Institute, Cambridge, Aug 2017.
Texas Geometry and Topology Conference, Texas Tech University, Feb 2017.
Symplectic Geometry and Topology Conference (in honour of Dusa McDuff), International Centre for Mathematical Sciences, Edinburgh, July 2016.
7th Pacific Rim Conference on Mathematics, Seoul National University, Korea, June
2016.
Perspectives on topology and geometry of 4-manifolds, Dubrovnik, Croatia, June
2016.
Colloquium, MSU, March 2016.
Symplectic Geometry and Topology Workshop, Uppsala University, Sweden, Sept
2015.
Workshop on Conservative Dynamics and Symplectic Geometry, IMPA, Rio de
Janeiro, Aug 2015.
Colloquium, UCLA, Oct 2014.
Gokova Geometry Topology Conference, Gokova, Turkey, May 2014.
Geometry/Topology seminar, MIT, March 2014.
Workshop on Moduli Spaces of Pseudo-holomorphic Curves, mini course (joint with T. Parker), Simons Center for Geometry and Physics, March 2014.
Symplectic Seminar, Simons Center for Geometry and Physics, March 2014.
Workshop on Conservative Dynamics and Symplectic Geometry, IMPA, Rio de
Janeiro, Aug 2013.
Joint Princeton/IAS Symplectic Geometry Seminar, Nov 2013.
Symplectic Geometry and Mathematical Physics Conference, Beijing International Center for Mathematical Research, June 2012.
Symplectic Techniques: The Space of Holomorphic Curves, Graduate lecture series, Program for Women and Mathematics, Princeton, May 2012.
Knots, Contact Geometry and Floer Homology Conference, University of Tokyo, May 2010.