Y.-P.'s Research Page
Current Research Area:
Gromov-Witten theory and related fields.
General Research Interests: Algebraic geometry
and mathematical physics, with emphasis placed on Gromov-Witten theory
and its relations with and applications to birational geometry,
moduli of curves, symplectic topology, K-theory, integrable systems,
representation theory, and mirror symmetry.
List of papers (mostly with files or links)
Comments on typos, expositions, and contents etc... are very welcome!
Most are available from ArXiV.org.
- Invariance of Gromov--Witten theory under a simple flop (with Y. Iwao, H.-W. Lin and C.-L. Wang), arXiv:0804.3816.
- The quantum orbifold cohomology of weighted projective spaces (with T. Coates, A. Corti, and H.-H. Tseng), math.AG/0608481, accepted by Acta Mathematica.
- Flops, motives and invariance of quantum rings (with H.-W. Lin and C.-L. Wang) (final version 30 June 2006)
math.AG/0608370,
final version, to appear in Annals of Math.
- On independence of generators of the tautological rings (with D. Arcara), math.AG/0605488, to appear in Compositio Math.
- Notes on axiomatic Gromov--Witten theory and applications,
arXiv:0710.4349, to appear in
Seattle Proceedings.
- Invariance of tautological equations II: Gromov--Witten theory,
(Appendix with Y. Iwao,)
math.AG/0605708,
to appear in JAMS.
New! An exciting consequence of ITE2 has just come out. In math.AG/0612510 by Faber, Shadrin, and Zvonkine, they solved Witten's r-spin conjecture completely. In fact, that was the original motivation of ITE project, which we were not able to carry through....
- Invariance of tautological equations I: conjectures and applications, math.AG/0604318,
to appear in J Euro Math Soc.
- Tautological equations in \Mbar_{3,1} via invariance conjectures
(with D. Arcara).
math.AG/0503184.
updated version.
To appear in Canadian Journal of Mathematics.
- Tautological equations in genus 2 via invariance conjectures
(with D. Arcara),
math.AG/0502488.
updated version.
- Witten's conjecture, Virasoro conjecture, and invariance of tautologicalequations, math.AG/0311100.
- Witten's conjecture and Virasoro conjecture up to genus two,
math.AG/0310442.
To appear in the proceedings of the conference
"Gromov-Witten Theory of Spin Curves and Orbifolds", Contemp. Math., AMS.
- Invariance of genus one tautological relations (temporary title)
(with A. Givental), in preparation.
- Quantum K-Theory II: Computations and open problems, in preparation.
- Frobenius manifolds, Gromov--Witten theory, and Virasoro constraints, (with R. Pandharipande), a book in preparation,
Part1.ps,
Part2.ps (partial),
(Part 3 not yet available).
PDF file optimized for 2-to-1 printing.
- Orbifold Euler characteristics of universal cotangent line bundles on
$\overline{M}_{1,n}$, preprint,
math.AG/0005217.
- A reconstruction theorem in quantum cohomology and quantum K-theory,
(with R. Pandharipande),
math.AG/0104084.
Updated PDF file.
Amer. J. Math., 126 (2004), no. 6, 1367--1379.
- Quantum K-theory on flag manifolds, finite difference Toda lattices
and quantum groups (with A. Givental), Invent. Math. 151,
193-219, 2003.
math.AG/0108105,
Link to the published version.
- Quantum K-Theory I: Foundations,
math.AG/0105014.
Duke Math. J. 121 (2004), no. 3, 389-424,
Link.
- Virtual Fundamental Classes of Zero Loci, (with D. Cox and
S. Katz), in "Advances in algebraic geometry motivated by physics"
(Lowell, MA, 2000), 157--166, Contemp.
Math., 276, Amer. Math. Soc., Providence, RI, 2001.
math.AG/0006116.
- Quantum Lefschetz hyperplane theorem, Invent. Math. 145 (2001), no. 1,
121--149.
math.AG/0003128.
Link to the published version.
- A formula for Euler characteristics of tautological line bundles on
the Deligne-Mumford spaces, IMRN 1997 No. 8.
PS file
- Quantum K-theory, PhD thesis, UC Berkeley, 1999.
- The quadrupole moment of Delta and Hyperion calculated on the
constituent quark shell model in large oscillator basis,
(with W.-C. Chang), B.S. thesis, communicated in the annual
meeting of Taiwanese physical society, 1991.
Slides of talks
CV and Bibliography
cv.pdf
Research in Utah
Acknowledgements:
The above research is partially supported by
Y.-P.'s homepage
