Bio
For a bio, please see my homepage: http://math.stanford.edu/~vakil/
Academic Appointments
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Professor, Mathematics
Administrative Appointments
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multiple, multiple (see my homepage http://math.stanford.edu/~vakil/ for more information) (2001 - Present)
Boards, Advisory Committees, Professional Organizations
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multiple, multiple (see my homepage http://math.stanford.edu/~vakil/ for details) (2015 - Present)
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.
2024-25 Courses
- Topics in Algebraic Geometry
MATH 245A (Aut) -
Independent Studies (1)
- Advanced Reading and Research
MATH 360 (Aut, Win, Spr)
- Advanced Reading and Research
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Prior Year Courses
2023-24 Courses
- Groups and Rings
MATH 120 (Aut) - Introduction to Algebraic Geometry
MATH 216A (Aut) - Introduction to Algebraic Geometry
MATH 216B (Win)
2022-23 Courses
- Introduction to Algebraic Geometry
MATH 216B (Win) - Introduction to Algebraic Geometry
MATH 216C (Spr)
2021-22 Courses
- Topics in Algebraic Geometry
MATH 245A (Win) - Topics in Algebraic Geometry
MATH 245C (Spr)
- Groups and Rings
All Publications
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MOTIVIC HILBERT ZETA FUNCTIONS OF CURVES ARE RATIONAL
JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU
2020; 19 (3): 947–64
View details for DOI 10.1017/S1474748018000269
View details for Web of Science ID 000530572700009
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DISCRIMINANTS IN THE GROTHENDIECK RING (vol 164, pg 1139, 2015)
DUKE MATHEMATICAL JOURNAL
2020; 169 (4): 799–800
View details for DOI 10.1215/00127094-2020-0001
View details for Web of Science ID 000519534900005
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Formal pseudodifferential operators and Witten's r-spin numbers
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
2017; 728: 1–33
View details for DOI 10.1515/crelle-2014-0102
View details for Web of Science ID 000404720100001
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REUs with Limited Faculty Involvement, "Underrepresented" Subjects in the Undergraduate Curriculum, and the Culture of Mathematics
WORLD SCIENTIFIC PUBL CO PTE LTD. 2016: 53–72
View details for Web of Science ID 000382055100005
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DISCRIMINANTS IN THE GROTHENDIECK RING
DUKE MATHEMATICAL JOURNAL
2015; 164 (6): 1139-1185
View details for DOI 10.1215/00127094-2877184
View details for Web of Science ID 000353931900004
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The Chow ring of the moduli space of curves of genus six
ALGEBRAIC GEOMETRY
2015; 2 (1): 123–36
View details for DOI 10.14231/AG-2015-006
View details for Web of Science ID 000218560100006
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The geometry of eight points in projective space: representation theory, Lie theory and dualities
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY
2012; 105: 1215-1244
View details for DOI 10.1112/plms/pds016
View details for Web of Science ID 000312644200004
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THE IDEAL OF RELATIONS FOR THE RING OF INVARIANTS OF n POINTS ON THE LINE: INTEGRALITY RESULTS
COMMUNICATIONS IN ALGEBRA
2012; 40 (10): 3884-3902
View details for DOI 10.1080/00927872.2011.598594
View details for Web of Science ID 000309120100025
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The ideal of relations for the ring of invariants of n points on the line
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
2012; 14 (1): 1-60
View details for DOI 10.4171/JEMS/295
View details for Web of Science ID 000300201000001
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The Moduli Space of Curves, Double Hurwitz Numbers, and Faber's Intersection Number Conjecture
ANNALS OF COMBINATORICS
2011; 15 (3): 381-436
View details for DOI 10.1007/s00026-011-0102-9
View details for Web of Science ID 000297147400001
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The Mathematics of Doodling
AMERICAN MATHEMATICAL MONTHLY
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
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Universal covering spaces and fundamental groups in algebraic geometry as schemes
JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX
2011; 23 (2): 489-526
View details for Web of Science ID 000308577200012
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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
2009; 637: 175-191
View details for DOI 10.1515/CRELLE.2009.094
View details for Web of Science ID 000273634700008
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pi(p), the Value of pi in l(p)
AMERICAN MATHEMATICAL MONTHLY
2009; 116 (10): 931-935
View details for DOI 10.4169/000298909X477069
View details for Web of Science ID 000207893100008
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The relations among invariants of points on the projective line
COMPTES RENDUS MATHEMATIQUE
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
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THE EQUATIONS FOR THE MODULI SPACE OF n POINTS ON THE LINE
DUKE MATHEMATICAL JOURNAL
2009; 146 (2): 175-226
View details for DOI 10.1215/00127094-2008-063
View details for Web of Science ID 000262586100001
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Geometric positivity in the cohomology of homogeneous spaces and generalized Schubert calculus
AMS Summer Research Institute on Algebraic Geometry
AMER MATHEMATICAL SOC. 2009: 77–124
View details for Web of Science ID 000265595600004
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A description of the outer automorphism of S-6, and the invariants of six points in projective space
JOURNAL OF COMBINATORIAL THEORY SERIES A
2008; 115 (7): 1296-1303
View details for DOI 10.1016/j.jcta.2008.01.004
View details for Web of Science ID 000259664900015
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Intersections of Schubert varieties and other permutation array schemes
Workshop on Algorithms in Algebraic Geometry
SPRINGER. 2008: 21–54
View details for Web of Science ID 000255928900003
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The moduli space of curves and Gromov-Witten theory
CIME Summer School on Enumerative Invariants in Algebraic Geometry and String Theory
SPRINGER-VERLAG BERLIN. 2008: 143–198
View details for Web of Science ID 000259296900004
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A desingularization of the main component of the moduli space of genus-one stable maps into P-n
GEOMETRY & TOPOLOGY
2008; 12: 1-95
View details for DOI 10.2140/gt.2008.12.1
View details for Web of Science ID 000253770900001
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Absolute Galois Acts Faithfully on the Components of the Moduli Space of Surfaces: A Belyi-Type Theorem in Higher Dimension
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
2007
View details for DOI 10.1093/imrn/rnm080
View details for Web of Science ID 000206288300079
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A natural smooth compactification of the space of elliptic curves in projective space
ELECTRONIC RESEARCH ANNOUNCEMENTS OF THE AMERICAN MATHEMATICAL SOCIETY
2007; 13: 53-59
View details for Web of Science ID 000249398400001
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A geometric Littlewood-Richardson rule
ANNALS OF MATHEMATICS
2006; 164 (2): 371-422
View details for Web of Science ID 000243500300001
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Schubert induction
ANNALS OF MATHEMATICS
2006; 164 (2): 489-512
View details for Web of Science ID 000243500300003
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Murphy's law in algebraic geometry: Badly-behaved deformation spaces
INVENTIONES MATHEMATICAE
2006; 164 (3): 569-590
View details for DOI 10.1007/s00222-005-0481-9
View details for Web of Science ID 000237190900002
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Towards the geometry of double Hurwitz numbers
ADVANCES IN MATHEMATICS
2005; 198 (1): 43-92
View details for DOI 10.1016/j.aim.2005.01.008
View details for Web of Science ID 000233780400005
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Relative virtual localization and vanishing of tautological classes on moduli spaces of curves
DUKE MATHEMATICAL JOURNAL
2005; 130 (1): 1-37
View details for Web of Science ID 000236628600001
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The affine stratification number and the moduli space of curves
CRM Workshop on Algebraic Structures and Moduli Spaces
AMER MATHEMATICAL SOC. 2004: 213–227
View details for Web of Science ID 000225222500010
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Hodge integrals and Hurwitz numbers via virtual localization
COMPOSITIO MATHEMATICA
2003; 135 (1): 25-36
View details for Web of Science ID 000179943400002
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The Gromov-Witten potential of a point, Hurwitz numbers, and Hodge integrals
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY
2001; 83: 563-581
View details for Web of Science ID 000172208200003
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Genus 0 and 1 Hurwitz numbers: Recursions, formulas, and graph-theoretic interpretations
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
2001; 353 (10): 4025-4038
View details for Web of Science ID 000169831900008