Bio

For a bio, please see my homepage: http://math.stanford.edu/~vakil/

Academic Appointments

  • Professor, Mathematics

Administrative Appointments

  • multiple, multiple (see my homepage http://math.stanford.edu/~vakil/ for more information) (2001 - Present)

Boards, Advisory Committees, Professional Organizations

  • multiple, multiple (see my homepage http://math.stanford.edu/~vakil/ for details) (2015 - Present)

Contact

  • Academic
    rvakil@stanford.edu
    University - Faculty Department: Mathematics Position: Professor
    • 450 JANE STANFORD WAY, BLDG. 380
    • STANFORD,  California  94305 
    (650) 725-4066 (fax)

Additional Info

Links

Current Research and Scholarly Interests

Algebraic geometry and related subjects. For a complete publication list, see my publication page http://math.stanford.edu/~vakil/preprints.html rather than the list here.

2025-26 Courses

Stanford Advisees

All Publications

  • Low-degree Hurwitz stacks in the Grothendieck ring COMPOSITIO MATHEMATICA Landesman, A., Vakil, R., Wood, M. 2024; 160 (8)

    View details for DOI 10.1112/S0010437X24007206

    View details for Web of Science ID 001309505500001

  • NUMERICAL SCHUBERT CALCULUS VIA THE LITTLEWOOD-RICHARDSON HOMOTOPY ALGORITHM MATHEMATICS OF COMPUTATION Leykin, A., del Campo, A., Sottile, F., Vakil, R., Verschelde, J. 2021; 90 (329): 1407–33

    View details for DOI 10.1090/mcom/3579

    View details for Web of Science ID 000631281700014

  • MOTIVIC HILBERT ZETA FUNCTIONS OF CURVES ARE RATIONAL JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU Bejleri, D., Ranganathan, D., Vakil, R. 2020; 19 (3): 947–64

    View details for DOI 10.1017/S1474748018000269

    View details for Web of Science ID 000530572700009

  • DISCRIMINANTS IN THE GROTHENDIECK RING (vol 164, pg 1139, 2015) DUKE MATHEMATICAL JOURNAL Vakil, R., Wood, M. 2020; 169 (4): 799–800

    View details for DOI 10.1215/00127094-2020-0001

    View details for Web of Science ID 000519534900005

  • Formal pseudodifferential operators and Witten's r-spin numbers JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK Liu, K., Vakil, R., Xu, H. 2017; 728: 1–33

    View details for DOI 10.1515/crelle-2014-0102

    View details for Web of Science ID 000404720100001

  • REUs with Limited Faculty Involvement, "Underrepresented" Subjects in the Undergraduate Curriculum, and the Culture of Mathematics Rubinstein, Y. A., Vakil, R. edited by Peterson, M. A., Rubinstein, Y. A. WORLD SCIENTIFIC PUBL CO PTE LTD. 2016: 53–72

    View details for Web of Science ID 000382055100005

  • DISCRIMINANTS IN THE GROTHENDIECK RING DUKE MATHEMATICAL JOURNAL Vakil, R., Wood, M. M. 2015; 164 (6): 1139-1185

    View details for DOI 10.1215/00127094-2877184

    View details for Web of Science ID 000353931900004

  • The Chow ring of the moduli space of curves of genus six ALGEBRAIC GEOMETRY Penev, N., Vakil, R. 2015; 2 (1): 123–36

    View details for DOI 10.14231/AG-2015-006

    View details for Web of Science ID 000218560100006

  • Mnev-Sturmfels universality for schemes A celebration of algebraic geometry Lee, S., Vakil, R. American Mathematical Society. 2013: 457-468
  • Algebraic geometry and the ongoing unification of mathematics European Mathematics Society Newsletter Vakil, R. 2013; 89: 24-30
  • The geometry of eight points in projective space: representation theory, Lie theory and dualities PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY Howard, B., Millson, J., Snowden, A., Vakil, R. 2012; 105: 1215-1244

    View details for DOI 10.1112/plms/pds016

    View details for Web of Science ID 000312644200004

  • THE IDEAL OF RELATIONS FOR THE RING OF INVARIANTS OF n POINTS ON THE LINE: INTEGRALITY RESULTS COMMUNICATIONS IN ALGEBRA Howard, B., Millson, J., Snowden, A., Vakil, R. 2012; 40 (10): 3884-3902

    View details for DOI 10.1080/00927872.2011.598594

    View details for Web of Science ID 000309120100025

  • The ideal of relations for the ring of invariants of n points on the line JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY Howard, B., Millson, J., Snowden, A., Vakil, R. 2012; 14 (1): 1-60

    View details for DOI 10.4171/JEMS/295

    View details for Web of Science ID 000300201000001

  • The Moduli Space of Curves, Double Hurwitz Numbers, and Faber's Intersection Number Conjecture ANNALS OF COMBINATORICS Goulden, I. P., Jackson, D. M., Vakil, R. 2011; 15 (3): 381-436

    View details for DOI 10.1007/s00026-011-0102-9

    View details for Web of Science ID 000297147400001

  • The Mathematics of Doodling AMERICAN MATHEMATICAL MONTHLY Vakil, R. 2011; 118 (2): 116-129

    View details for DOI 10.4169/amer.math.monthly.118.02.116

    View details for Web of Science ID 000287175500002

  • Universal covering spaces and fundamental groups in algebraic geometry as schemes JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX Vakil, R., Wickelgren, K. 2011; 23 (2): 489-526

    View details for Web of Science ID 000308577200012

  • Solving Schubert problems with Littlewood-Richardson homotopies International Symposium on Symbolic and Algebraic C omputation Sottile, F., Vakil, R., Verschelde, J. 2010: 179-186
  • MathOverflow Notices of the American Mathematical Society Geraschenko, A., Morrison, S., Vakil, R. 2010: 701
  • A short proof of the lambda(g)-conjecture without Gromov-Witten theory: Hurwitz theory and the moduli of curves JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK Goulden, I. P., Jackson, D. M., Vakil, R. 2009; 637: 175-191

    View details for DOI 10.1515/CRELLE.2009.094

    View details for Web of Science ID 000273634700008

  • pi(p), the Value of pi in l(p) AMERICAN MATHEMATICAL MONTHLY Keller, J. B., Vakil, R. 2009; 116 (10): 931-935

    View details for DOI 10.4169/000298909X477069

    View details for Web of Science ID 000207893100008

  • The relations among invariants of points on the projective line COMPTES RENDUS MATHEMATIQUE Howard, B., Millson, J., Snowden, A., Vakil, R. 2009; 347 (19-20): 1177-1182

    View details for DOI 10.1016/j.crma.2009.07.013

    View details for Web of Science ID 000271128200014

  • THE EQUATIONS FOR THE MODULI SPACE OF n POINTS ON THE LINE DUKE MATHEMATICAL JOURNAL Howard, B., Millson, J., Snowden, A., Vakil, R. 2009; 146 (2): 175-226

    View details for DOI 10.1215/00127094-2008-063

    View details for Web of Science ID 000262586100001

  • Geometric positivity in the cohomology of homogeneous spaces and generalized Schubert calculus AMS Summer Research Institute on Algebraic Geometry Coskun, I., Vakil, R. AMER MATHEMATICAL SOC. 2009: 77–124

    View details for Web of Science ID 000265595600004

  • Algebraic structures on the topology of moduli spaces of curves and maps Geometry of Riemann surfaces and their moduli spaces Vakil, R., Lee, Y. International Press. 2009: 197-216
  • A description of the outer automorphism of S-6, and the invariants of six points in projective space JOURNAL OF COMBINATORIAL THEORY SERIES A Howard, B., Millson, J., Snowden, A., Vakil, R. 2008; 115 (7): 1296-1303

    View details for DOI 10.1016/j.jcta.2008.01.004

    View details for Web of Science ID 000259664900015

  • Intersections of Schubert varieties and other permutation array schemes Workshop on Algorithms in Algebraic Geometry Billey, S., Vakil, R. SPRINGER. 2008: 21–54

    View details for Web of Science ID 000255928900003

  • A new description of the outer automorphism of S_6, and the invariants of six points in projective space J. Comb. Theory Ser. A Vakil, R., Howard, B., Millson, J., Snowden, A. 2008; 115 (7): 1296-1303
  • The moduli space of curves and Gromov-Witten theory CIME Summer School on Enumerative Invariants in Algebraic Geometry and String Theory Vakil, R. SPRINGER-VERLAG BERLIN. 2008: 143–198

    View details for Web of Science ID 000259296900004

  • A desingularization of the main component of the moduli space of genus-one stable maps into P-n GEOMETRY & TOPOLOGY Vakil, R., Zinger, A. 2008; 12: 1-95

    View details for DOI 10.2140/gt.2008.12.1

    View details for Web of Science ID 000253770900001

  • Absolute Galois Acts Faithfully on the Components of the Moduli Space of Surfaces: A Belyi-Type Theorem in Higher Dimension INTERNATIONAL MATHEMATICS RESEARCH NOTICES Easton, R. W., Vakil, R. 2007

    View details for DOI 10.1093/imrn/rnm080

    View details for Web of Science ID 000206288300079

  • A natural smooth compactification of the space of elliptic curves in projective space ELECTRONIC RESEARCH ANNOUNCEMENTS OF THE AMERICAN MATHEMATICAL SOCIETY Vakil, R., Zinger, A. 2007; 13: 53-59

    View details for Web of Science ID 000249398400001

  • A geometric Littlewood-Richardson rule ANNALS OF MATHEMATICS Vakil, R. 2006; 164 (2): 371-422

    View details for Web of Science ID 000243500300001

  • Schubert induction ANNALS OF MATHEMATICS Vakil, R. 2006; 164 (2): 489-512

    View details for Web of Science ID 000243500300003

  • Murphy's law in algebraic geometry: Badly-behaved deformation spaces INVENTIONES MATHEMATICAE Vakil, R. 2006; 164 (3): 569-590

    View details for DOI 10.1007/s00222-005-0481-9

    View details for Web of Science ID 000237190900002

  • Towards the geometry of double Hurwitz numbers ADVANCES IN MATHEMATICS Goulden, I. P., Jackson, D. M., Vakil, R. 2005; 198 (1): 43-92

    View details for DOI 10.1016/j.aim.2005.01.008

    View details for Web of Science ID 000233780400005

  • Relative virtual localization and vanishing of tautological classes on moduli spaces of curves DUKE MATHEMATICAL JOURNAL Graber, T., Vakil, R. 2005; 130 (1): 1-37

    View details for Web of Science ID 000236628600001

  • The affine stratification number and the moduli space of curves CRM Workshop on Algebraic Structures and Moduli Spaces Roth, M., Vakil, R. AMER MATHEMATICAL SOC. 2004: 213–227

    View details for Web of Science ID 000225222500010

  • Hodge integrals and Hurwitz numbers via virtual localization COMPOSITIO MATHEMATICA Graber, T., Vakil, R. 2003; 135 (1): 25-36

    View details for Web of Science ID 000179943400002

  • The moduli space of curves and its tautological ring Notices of the American Mathematical Society Vakil, R. 2003; 50 (6): 647-658
  • The Gromov-Witten potential of a point, Hurwitz numbers, and Hodge integrals PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY Goulden, I. P., Jackson, D. M., Vakil, R. 2001; 83: 563-581

    View details for Web of Science ID 000172208200003

  • Twelve points on the projective line, branched covers, and rational elliptic fibrations MATHEMATISCHE ANNALEN Vakil, R. 2001; 320 (1): 33-54

    View details for DOI 10.1007/PL00004469

    View details for Web of Science ID 000169028600003

  • Recursions for characteristic numbers of genus one plane curves ARKIV FOR MATEMATIK Vakil, R. 2001; 39 (1): 157-180

    View details for DOI 10.1007/BF02388797

    View details for Web of Science ID 000174336800009

  • Genus 0 and 1 Hurwitz numbers: Recursions, formulas, and graph-theoretic interpretations TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY Vakil, R. 2001; 353 (10): 4025-4038

    View details for Web of Science ID 000169831900008

  • A tool for stable reduction of curves on surfaces Advances in Algebraic Geometry Motivated by Mathematical Physics Vakil, R. 2001: 145-154
  • On the tautological ring of \overline{M}_{g,n} Gokova Geometry-Topology Conference Vakil, R., Graber, T. International Press. 2001
  • The enumerative geometry of rational and elliptic curves in projective space JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK Vakil, R. 2000; 529: 101-153

    View details for Web of Science ID 000166061900003

  • Counting curves on rational surfaces MANUSCRIPTA MATHEMATICA Vakil, R. 2000; 102 (1): 53-84

    View details for DOI 10.1007/s002291020053

    View details for Web of Science ID 000088174700004

  • The characteristic numbers of quartic plane curves CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES Vakil, R. 1999; 51 (5): 1089-1120

    View details for DOI 10.4153/CJM-1999-048-1

    View details for Web of Science ID 000083512700010

  • On the Steenrod length of real projective spaces: finding longest chains in certain directed graphs DISCRETE MATHEMATICS Vakil, R. 1999; 204 (1-3): 415-425

    View details for DOI 10.1016/S0012-365X(98)00383-5

    View details for Web of Science ID 000081062400024

  • On Conway's recursive sequence DISCRETE MATHEMATICS Kubo, T., Vakil, R. 1996; 152 (1-3): 225-252

    View details for DOI 10.1016/0012-365X(94)00303-Z

    View details for Web of Science ID A1996UM57600018

https://orcid.org/0000-0001-8506-270X