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! Some of the papers are available from ArXiV.org.

A product formula for log Gromov--Witten invariants, (with F. Qu).
A Mirror Theorem for the Mirror Quintic, (with M. Shoemaker), arXiv:1209.2487.
Invariance of Quantum Rings under Ordinary Flops, (with H.-W. Lin and C.-L. Wang), Part 1 and Part 2.
Introduction to GWT and CTC, my notes from Grenoble Lectures in the summer 2011.
Euler characteristics of universal cotangent line bundles on $\Mbar_{1,n}$ (with F. Qu).
Analytic continuations of quantum cohomology, (with H.-W. Lin and C.-L. Wang), to appear in proceedings ICCM 2010.
Algebraic cobordism of bundles on varieties (with R. Pandharipande) arXiv:1002.1500, to appear in JEMS.
Algebraic structures on the topology of moduli spaces of curves and maps (with R. Vakil), arXiv:0809.1879, to appear in Surveys in Differential Geometry.
Invariance of Gromov--Witten theory under a simple flop (with Y. Iwao, H.-W. Lin and C.-L. Wang), arXiv:0804.3816, to appear in Crelle's.
The quantum orbifold cohomology of weighted projective spaces (with T. Coates, A. Corti, and H.-H. Tseng), math.AG/0608481, Acta Mathematica 202 (2009) no. 2.
Flops, motives and invariance of quantum rings (with H.-W. Lin and C.-L. Wang) (final version 30 June 2006) math.AG/0608370, Annals of Math, 172 (2010) no.1 243-290.
On independence of generators of the tautological rings (with D. Arcara), math.AG/0605488, Compositio Math 144 (2008) no. 6 1497--1503.
Notes on axiomatic Gromov--Witten theory and applications, arXiv:0710.4349, Algebraic geometry---Seattle 2005. Part 1, 309--323, Proc. Sympos. Pure Math., 80, Part 1, Amer. Math. Soc., Providence, RI, 2009.
Invariance of tautological equations II: Gromov--Witten theory, (Appendix with Y. Iwao,) math.AG/0605708, JAMS 22 (2009) no. 2, 331-352.
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, J Euro Math Soc 10 (2008) no. 2, 399-413.
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.
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).
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. PDF.
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

The slides of my talk in WAGS spring 2004 and again in NCTS conference. Note: this has been incorporated into the papers Invariance of tautological equations I and II (see above).

CV and Bibliography

cv.pdf

Research in Utah

Algebraic Geometry Group
Algebraic Geometry Seminar
String Geometry Seminar
Research page of the mathematics department. (outdated!)
OSP at U Conflict of interest form Travel administration

Acknowledgements: The above research is partially supported by

NSF (Links: DMS, Fastlane, research.gov)
AMS Centennial Fellowship (2005-2007).

Y.P.'s homepage

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