特聘研究員 兼所長 |   李元斌
聯絡資訊
  • ypleemath$\color{red}{@}$gate.sinica.edu.tw
  • +886 2 2368-5999 ext. 736
  • +886 2 2368-9771
研究專長
  • Algebraic Geometry
  • Mathematical Physics
學歷
  • Ph.D. University of California at Berkeley (1994/8 - 1999/5)

經歷
  • Professor of Mathematics University of Utah 2011 - 2020
  • Associate Professor of Mathematics University of Utah 2006 - 2011
  • Visiting Research Mathematician Princeton University 2002-3
  • Assistant Professor of Mathematics University of Utah 2002/8 - 2006/6
  • Junior Fellow IPAM 2001 Fall
  • Hedrick Assistant Professor UCLA 1999 - 2002

獲獎
  • 2018 ICCM best paper award (for Pub. (29)), 2018
  • 2017 ICCM disntinguished paper award (for Pub. (25)), 2017
  • NSF grant DMS-1500601, 2015 ~ 2019
  • NSF grant DMS-1162590, 2012 ~ 2017
  • NSF grant DMS-0901098, 2009 ~2013
  • NSF grant PHY-0652421, 2007
  • NSF grant DMS-0600688, 2006 ~ 2010
  • AMS Centennial Research Fellowship, 2005 ~2007
  • NSF grant DMS-0305895, 2003 ~2006
  • NSF grant DMS-0072547, 2000 ~ 2003

研究簡介

My current research interests are in the general areas of algebraic geometry and mathematical
physics. More specifically I am working on Gromov–Witten theory and its relations
with and applications to birational geometry, Hodge theory, K-theory, symplectic topology,
integrable systems, representation theory, and mirror symmetry.


部分著作目錄
  1. (with H. Fan) "On Gromov-Witten theory of projective bundles" , Michigan Mathematical Journal , 2020.
  2. (with H. Fan) "Towards a quantum Lefschetz hyperplane theorem in all genera" , Geometry & Topology , 23 (1), 493-512, 2019.
  3. (with H.-W. Lin, C.-L. Wang) "Towards A + B theory in conifold transitions" , Journal of Differential Geometry , 110 (3), 495-541, 2018.
  4. (with F. Qu) "A product formula for log Gromov–Witten invariants" , Journal of the Mathematical Society of Japan , 70 (1), 229-242, 2018.
  5. (with H.-W. Lin, C.-L. Wang) "Quantum Cohomology under Birational Maps and Transitions" , String-Math 2015 , 149-168, 2017.
  6. (with N. Priddis, M. Shoemaker) "A proof of the Landau-Ginzburg/Calabi-Yau correspondence via the crepant transformation conjecture" , Annales Scientifiques de l’Ecole Normale Superieure (4) , 49 (6), 1403-1443, 2016.
  7. (with H.-W. Lin, F. Qu, C.-L. Wang) "Invariance of quantum rings under ordinary flops III: A quantum splitting principle" , Cambridge Journal of Mathematics , 4 (3), 333-401, 2016.
  8. (with H.-W. Lin, C.-L.Wang) "Invariance of quantum rings under ordinary flops II: A quantum Leray–Hirsch theorem" , Algebraic geometry , 3 (5), 615-653, 2016.
  9. (with H.-W. Lin, C.-L. Wang) "Invariance of quantum rings under ordinary flops I: Quantum corrections and reduction to local models" , Algebraic geometry , 3 (5), 578-614, 2016.
  10. (with M. Shoemaker) "A Mirror Theorem for the Mirror Quintic" , Geometry & Topology , 18 (3), 1437-1483, 2014.
  11. (with F. Qu) "Orbifold Euler characteristics of universal cotangent line bundles on $\bar{M}_{1,n}$" , Proceedings of the American Mathematical Society , 142 (2), 429-440, 2014.
  12. "Introduction to Gromov–Witten theory and crepant transformation conjecture" , Proceedings of Summer School at Institut Fourier , 2012.
  13. (with R. Pandharipande) "Algebraic cobordism of bundles on varieties" , Journal of the European Mathematical Society , 14 (4), 1081-1101, 2012.
  14. (with H.-W. Lin, C.-L. Wang) "Analytic continuations of quantum cohomology" , proceedings ICCM 2010, AMS/IP Studies in Advanced Mathematics , 51, 2012.
  15. (with Y. Iwao, H.-W. Lin, C.-L. Wang) "Invariance of Gromov–Witten theory under a simple flop" , Journal für die reine und angewandte Mathematik , 663, 67-90, 2012.
  16. (with H.-W. Lin, C.-L. Wang) "Flops, motives and invariance of quantum rings" , Annals of Mathematics , 172 (1), 243-290, 2010.
  17. (with D. Arcara) "Tautological equation in $\bar{M}_{3,1}$ via invariance conjectures" , Canadian Mathematical Bulletin , 52 (2), 161-174, 2009.
  18. (with T. Coates, A. Corti, H.-H. Tseng) "The quantum orbifold cohomology of weighted projective space" , Acta Mathematica , 202 (2), 139-193, 2009.
  19. "Invariance of tautological equations II: Gromov–Witten theory" , Journal of the American Mathematical Society , 22 (2), 331-352, 2009.
  20. (with R.Vakil) "Algebraic structures on the topology of moduli spaces of curves and maps" , Surveys in Differential Geometry , 14, 2009.
  21. (with D. Arcara) "On independence of generators of the tautological rings" , Compositio Mathematica , 144 (6), 1497-1503, 2008.
  22. "Invariance of tautological equations I: conjectures and applications" , Journal of the European Mathematical Society , 10 (2), 399-413, 2008.
  23. (with D. Arcara) "Tautological equations in genus 2 via invariance conjectures" , Bulletin of the Institute of Mathematics Academia Sinica , 2 (1), 1-27, 2007.
  24. "Witten’s conjecture and Virasoro conjecture up to genus two" , Communications in Contemporary Mathematics , 403, 31-42, 2006.
  25. "Notes on axiomatic Gromov–Witten theory and applications" , Algebraic geometry - Seattle 2005 , 1, 309-323, 2005.
  26. (with R. Pandharipande) "A reconstruction theorem in quantum cohomology and quantum K-theory" , American Journal of Mathematics , 126 (6), 1367-1379, 2004.
  27. "Quantum K-Theory I: Foundations" , Duke Mathematical Journal , 121 (3), 389-424, 2004.
  28. (with A. Givental) "Quantum K-theory on flag manifolds, finite-difference Toda lattices and quantum groups" , Inventiones Mathematicae , 151, 193-219, 2003.
  29. (with D. Cox, S. Katz) "Virtual fundamental classes of zero loci" , Communications in Contemporary Mathematics , 276, 157-166, 2001.
  30. "Quantum Lefschetz hyperplane theorem" , Inventiones Mathematicae , 145 (1), 121-149, 2001.
  31. "A formula for Euler characteristics of tautological line bundles on the Deligne-Mumford spaces" , International Mathematics Research Notices (8), 1997.