Vakil, Ravi - Department of Mathematics, Stanford University

• MATH 121 PROBLEM SET 5 This set is due at noon on Friday March 2 in Jason Lo's mailbox.
• MATH 216: FOUNDATIONS OF ALGEBRAIC math216.wordpress.com
• MATH 210A: MODERN ALGEBRA Lectures: Tuesdays and Thursdays 1112:15 in Room 380W.
• SECRET RESEARCH SUMMARY FOR RECOMMENDERS Dear Joe, Bill, Johan, and Rahul ---
• MODERN ALGEBRA (MATH 210) MIDTERM SOLUTIONS POKMAN CHEUNG
• A TOOL FOR STABLE REDUCTION OF CURVES ON Abstract. In the study of the geometry of curves on surfaces, the following
• Polya Seminar November 30, 2009 1. (1985 -A1) Determine, with proof, the number of ordered triples (A1, A2, A3)
• GOLDEN MEAN EVERYWHERE?
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 3 This set is due Monday, October 31. It covers classes 5, 6, and 7. Read all of these
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 1 This set is due Monday, October 17. It covers classes 1 and 2. Hand in five of these
• THE CHARACTERISTIC NUMBERS OF QUARTIC PLANE CURVES Abstract. The characteristic numbers of smooth plane quartics are computed using intersec
• THE AFFINE STRATIFICATION NUMBER AND THE MODULI SPACE OF CURVES
• INTRO TO ALGEBRAIC GEOMETRY, PROBLEM SET 5 Due Thursday October 21 in class (no lates). Hand in seven of the following
• MODERN ALGEBRA (MATH 210) THANKSGIVING LEFTOVERS: PROOF OF TUESDAY'S THEOREM
• A SHORT PROOF OF THE # g CONJECTURE WITHOUT GROMOVWITTEN THEORY: HURWITZ THEORY AND THE MODULI OF CURVES
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 11 This set is due Thursday, February 9, in Jarod Alper's mailbox. It covers (roughly)
• A DOITYOURSELF PROOF OF THE n = 3 CASE OF FERMAT'S LAST THEOREM
• Towards the geometry of double Hurwitz I. P. Goulden, D. M. Jackson and R. Vakil
• MATH 210A PROBLEM SET 4 This problem set will be due on Friday, October 15, 2010 by 3 pm in Jeremy Miller's
• MODERN ALGEBRA (MATH 210) PROBLEM SET 3 1 The following problems appeared on recent quals. They aren't to be handed in; they
• THE AFFINE STRATIFICATION NUMBER AND THE MODULI SPACE OF CURVES
• PROBLEMSOLVING MASTERCLASS WEEK 6 1. Let p be an odd prime and let Z p denote (the field of) integers modulo p. How many
• PUTNAM PROBLEMSOLVING SEMINAR WEEK 1: INDUCTION AND PIGEONHOLE
• MODERN ALGEBRA (MATH 210) PROBLEM SETS 1 AND 2 Problem Set 1. (due Friday, Oct. 8 at noon at Jarod Alper's door, 380--J)
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 14 This set is due Thursday, March 2, in Jarod Alper's mailbox. It covers (roughly)
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 3 This set is due at noon on Friday October 19. You can hand it in to Jarod Alper
• SCHUBERT INDUCTION ABSTRACT. We describe a Schubert induction theorem, a tool for analyzing intersections
• MATH 216: FOUNDATIONS OF ALGEBRAIC math216.wordpress.com
• ``YOU CAN'T GET THERE FROM HERE'': WHY YOU CAN'T TRISECT AN ANGLE, DOUBLE THE CUBE, OR SQUARE THE
• MATH 210 PROBLEM SET 3 This problem set is due on Friday, February 9 at Jarod Alper's office door.
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 18 This set is due Thursday, May 4. You can hand it in to Rob Easton, in class or via his
• ABSOLUTE GALOIS ACTS FAITHFULLY ON THE COMPONENTS OF THE MODULI SPACE OF SURFACES: A BELYITYPE THEOREM
• PROBLEMSOLVING MASTERCLASS WEEK # (SOMEWHERE BETWEEN 3 AND 4)
• PROSPECTUS: ``WILLIAM LOWELL PUTNAM MATHEMATICAL COMPETITION: PROBLEMS, SOLUTIONS,
• MODERN ALGEBRA (MATH 210) PROBLEM SET 4 From the text: 5.27--5.31. If you use results of earlier exercises (see 5.29), make sure to
• POLYA PROBLEM-SOLVING SEMINAR WEEK 3: RECURRENCES
• THE MODULI SPACE OF CURVES AND GROMOV-WITTEN ABSTRACT. The goal of this article is to motivate and describe how Gromov-Witten the-
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 9 This set is due Tuesday, January 24, in Jarod Alper's mailbox. It covers (roughly)
• PUTNAM PROBLEM-SOLVING SEMINAR WEEK 2: NUMBER THEORY
• MODERN ALGEBRA (MATH 210) THANKSGIVING LEFTOVERS: PROOF OF TUESDAY'S THEOREM
• MODERN ALGEBRA (MATH 210) PROBLEM SET 4 1. Let G be a group of order 7. Show that Aut(H) is abelian of order 6.
• MATH 216: FOUNDATIONS OF ALGEBRAIC math216.wordpress.com
• A TOOL FOR STABLE REDUCTION OF CURVES ON Abstract. In the study of the geometry of curves on surfaces, the following
• THE MODULI SPACE OF CURVES AND GROMOVWITTEN ABSTRACT. The goal of this article is to motivate and describe how GromovWitten the
• MURPHY'S LAW IN ALGEBRAIC GEOMETRY: BADLYBEHAVED DEFORMATION SPACES
• GENUS 0 AND 1 HURWITZ NUMBERS: RECURSIONS, FORMULAS, AND GRAPHTHEORETIC INTERPRETATIONS
• RECURSIONS FOR CHARACTERISTIC NUMBERS OF GENUS ONE PLANE CURVES
• A GEOMETRIC LITTLEWOODRICHARDSON RULE ABSTRACT. We describe a geometric LittlewoodRichardson rule, interpreted as deform
• THE MODULI SPACE OF CURVES, DOUBLE HURWITZ NUMBERS, AND FABER'S INTERSECTION NUMBER CONJECTURE
• SCHUBERTINDUCTION ABSTRACT. We describe a Schubert induction theorem, a tool for analyzing intersections
• SOME AMUSING PROBLEMS RELATED TO ALGEBRAIC Here are some problems to pique your interest; we will solve (or mostly solve)
• FOUNDATIONS OF ALGEBRAIC GEOMETRY CLASS 1 1. Welcome 1
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 12 This set covers classes 17 through 29.
• MATH 216 HANDOUT: CURVES (PART TWO) Because I'm far behind on looking at your problem sets, I won't yet assign problems,
• This appendix explains how to perform practical computations in the deformation theory of (essentially finite type) affine schemes with isolated
• MODERN ALGEBRA (MATH 210) PROBLEM SET 3 This set is due Friday, Oct. 22 at noon at Jarod Alper's door, 380J.
• INTRO TO ALGEBRAIC GEOMETRY, PROBLEM SET 6 Due Thursday October 28 in class (no lates). Hand in seven of the following
• FOUNDATIONS OF ALGEBRAIC GEOMETRY CLASS 21 1. Nonsingularity ("smoothness") of Noetherian schemes 1
• MODERN ALGEBRA (MATH 210) PROBLEM SET 6 1. If is prime, show that the automorphism group of the group is isomorphic to
• THE GEOMETRY OF SPACES OF EIGHT POINTS IN PROJECTIVE SPACE (DUALITIES, REPRESENTATION
• SCHUBERT INDUCTION ABSTRACT. We describe a Schubert induction theorem, a tool for analyzing intersections
• THE MODULI SPACE OF CURVES AND GROMOVWITTEN ABSTRACT. The goal of this article is to motivate and describe how GromovWitten the
• 18.034 PROBLEM SET 2 Due February 18 in class. No lates will be accepted. Discussion is encouraged,
• A GEOMETRIC LITTLEWOODRICHARDSON RULE ABSTRACT. We describe an explicit geometric LittlewoodRichardson rule, interpreted as
• PUTNAM PROBLEMSOLVINGSEMINARWEEK 5: INEQUALITIES
• INTRO TO ALGEBRAIC GEOMETRY, PROBLEM SET 3 Due Thursday October 7 in class. No lates will be accepted, so AnaMaria will
• INTRO TO ALGEBRAIC GEOMETRY, PROBLEM SET 1 Due Tuesday September 21 in class. No lates will be accepted, so AnaMaria
• INTRO TO ALGEBRAIC GEOMETRY, PROBLEM SET 8 Due Thursday November 11 at my o#ce (2271) by noon. You're strongly en
• THE MODULI SPACE OF CURVES AND GROMOVWITTEN ABSTRACT. The goal of this article is to motivate and describe how GromovWitten the
• INTERSECTIONS OF SCHUBERT VARIETIES AND OTHER PERMUTATION ARRAY SCHEMES
• MODERN ALGEBRA (MATH 210) PROBLEM SET 5 1. Suppose G is a finite group. Let S be the subset of G consisting of all elements whose
• 18.034 PROBLEM SET 11 This problem set is not for credit; do not hand it in! It is intended to give you a
• INTERSECTIONS OF SCHUBERT VARIETIES AND OTHER PERMUTATION ARRAY SCHEMES
• Proceedings of 7 th Gokova GeometryTopology Conference,
• PROBLEMSOLVING MASTERCLASS WEEK 2 1. Triangle ABC has an area 1. Points E, F, G lie, respectively, on sides BC, CA, AB such
• A DOITYOURSELF PROOF OF THE n = 3 CASE OF FERMAT'S LAST THEOREM
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 13 This set is due Thursday, February 23, in Jarod Alper's mailbox. It covers (roughly)
• THE GROMOV-WITTEN POTENTIAL OF A POINT, HURWITZ NUMBERS, AND HODGE INTEGRALS
• GEOMETRIC POSITIVITY IN THE COHOMOLOGY OF HOMOGENEOUS SPACES AND GENERALIZED SCHUBERT CALCULUS
• THE MODULI SPACE OF CURVES, DOUBLE HURWITZ NUMBERS, AND FABER'S INTERSECTION NUMBER CONJECTURE
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 10 This set is due Thursday, February 2, in Jarod Alper's mailbox. It covers (roughly)
• 18.034 PROBLEM SET 5 Due March 17 in class. No lates will be accepted. Discussion is encouraged,
• A DOITYOURSELF PROOF OF THE n = 3 CASE OF FERMAT'S LAST THEOREM
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 8 This set is due at noon on Friday November 30. You can hand it in to Jarod Alper
• MATH 216 PROBLEM SET 2 This set is due at noon on Friday October 9. Hand it in to Jack Hall (jhall@math) in
• MODERN ALGEBRA (MATH 210) MIDTERM SOLUTIONS POKMAN CHEUNG
• MURPHY'S LAW IN ALGEBRAIC GEOMETRY: BADLY-BEHAVED DEFORMATION SPACES
• Problems for Polya Seminar October 26, 2009 1. Suppose that a, b, c are positive numbers. Prove that
• MATH 210 PROBLEM SET 3 This problem set is due on Friday, February 9 at Jarod Alper's office door.
• TOWARDS THE GEOMETRY OF DOUBLE HURWITZ NUMBERS I. P. GOULDEN, D. M. JACKSON AND R. VAKIL
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 16 This set is due Thursday, March 16, in Jarod Alper's mailbox. It covers (roughly)
• PROBLEM-SOLVING MASTERCLASS WEEK 7 1. Find the smallest term in the sequence {an} where a1 = 199319941995
• RECURSIONS FOR CHARACTERISTIC NUMBERS OF GENUS ONE PLANE CURVES
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 14 This set is due Thursday, March 2, in Jarod Alper's mailbox. It covers (roughly)
• DEFORMATION THEORY AND MODULI IN ALGEBRAIC GEOMETRY CHAPTER 2 ROUGH DRAFT
• 18.034 PROBLEM SET 1 Due February 11 in class. No lates will be accepted. Discussion is encouraged,
• THE FUNDAMENTAL THEOREM OF GALOIS THEORY Important Theorem. If E=k is a finite extension, then the following statements are
• A Desingularization of the Main Component of the Moduli Space of GenusOne Stable Maps into P n
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 6 This set is due Wednesday, November 30. It covers (roughly) classes 13 and 14.
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 15 This set is due Thursday, March 9, in Jarod Alper's mailbox. It covers (roughly)
• MATH 216: FOUNDATIONS OF ALGEBRAIC September 10, 2010.
• MODERN ALGEBRA (MATH 210) PROBLEM SET 5 1. Suppose G is a finite group. Let S be the subset of G consisting of all elements whose
• PUTNAM PROBLEMSOLVING SEMINAR WEEK 7: GENERAL PROBLEMSOLVING
• SOME AMUSING PROBLEMS RELATED TO ALGEBRAIC Here are some problems to pique your interest; we will solve (or mostly solve)
• MODERN ALGEBRA (MATH 210) EXAM PRACTICE PROBLEMS AND GALOIS THEORY PRACTICE PROBLEMS
• MODERN ALGEBRA (MATH 210) PROBLEM SET 3 1. (a) Must any finite integral domain be a field? (b) (The field F 4 .) Ex. 3.14 (p. 125). Ex.
• PUTNAM PROBLEMSOLVINGSEMINARWEEK 7: PROBLEMS PROBLEMSPROBLEMS
• INFORMATION ABOUT HONORS CALCULUS, 18.014 Lectures: Ravi Vakil, vakil@math.mit.edu, office 2-271. T Th 1, F
• MATH 216: FOUNDATIONS OF ALGEBRAIC math216.wordpress.com
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 12 This set is due Thursday, February 16, in Jarod Alper's mailbox. It covers (roughly)
• PROPERTIES OF GEOMETRIC FIBERS 1. INTRODUCTION
• POLYA PROBLEM-SOLVING SEMINAR WEEK 7: MISCELLANEOUS PROBLEMS, AND PROBLEM-SOLVING
• Proceedings of Symposia in Pure Mathematics Geometric positivity in the cohomology of homogeneous spaces and
• 18.014 UNIT II: THE INTEGRAL Friday, Sept. 15.
• A natural smooth compactification of the space of elliptic curves in projective space via blowing up the space of stable maps
• INTRO TO ALGEBRAIC GEOMETRY, PROBLEM SET 10 Due Tuesday November 30 in class; this will possibly be extended. You're
• INTERSECTIONS OF SCHUBERT VARIETIES AND OTHER PERMUTATION ARRAY SCHEMES
• A Beginner's Guide to Jet Bundles from the Point of View of Algebraic Geometry
• 18.034 PROBLEM SET 4 Hand in seven of the following problems. Due March 3 in class. No lates will be
• 18.034 PROBLEM SET 7 Due April 7 in class. No lates will be accepted. Discussion is encouraged, with
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 7 This set is due Wednesday, December 7. It covers (roughly) classes 15 and 16.
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 1 This set is due at noon on Friday October 5. You can hand it in to Jarod Alper
• A SHORT PROOF OF THE # g CONJECTURE WITHOUT GROMOVWITTEN THEORY: HURWITZ THEORY AND THE MODULI OF CURVES
• PROBLEMSOLVING MASTERCLASS WEEK 1 1. A game starts with four heaps of beans, containing 3, 4, 5 and 6 beans. The two players
• INTRO TO ALGEBRAIC GEOMETRY, PROBLEM SET 2 Due Tuesday September 28 in class. No lates will be accepted, so AnaMaria will
• PUTNAM PROBLEMSOLVINGSEMINARWEEK 6: The Rules. These are way too many problems to consider. Just pick a few problems you
• HODGE INTEGRALS AND HURWITZ NUMBERS VIA VIRTUAL LOCALIZATION
• THE MODULI SPACE OF CURVES, DOUBLE HURWITZ NUMBERS, AND FABER'S INTERSECTION NUMBER CONJECTURE
• A NATURAL SMOOTH COMPACTIFICATION OF THE SPACE OF ELLIPTIC CURVES IN PROJECTIVE SPACE
• PUTNAM PROBLEMSOLVING SEMINAR WEEK 3: The Rules. These are way too many problems to consider in this evening session alone.
• A DESCRIPTION OF THE OUTER AUTOMORPHISM OF S6, AND THE INVARIANTS OF SIX POINTS IN PROJECTIVE SPACE
• MATH 216 PROBLEM SET 14: QUASICOHERENT SHEAVES (LINE BUNDLES; QUASICOHERENT SHEAVES ON PROJECTIVE
• MATH 216 PROBLEM SET 3 This set is due at noon on Friday October 16. Hand it in to Jack Hall (jhall@math) in
• MATH 121 PROBLEM SET 3 This set is due at noon on Friday February 16 in Jason Lo's mailbox.
• 18.024 (HONORS MULTIVARIABLE Lecture: T, Th 1, F 2, 2147, Ravi Vakil (vakil@math, 2271). Office hours
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 17 This set is due Thursday, April 20. You can hand it in to Rob Easton, in class or via
• A DESCRIPTION OF THE OUTER AUTOMORPHISM OF S 6 , AND THE INVARIANTS OF SIX POINTS IN PROJECTIVE SPACE
• ABSOLUTE GALOIS ACTS FAITHFULLY ON THE COMPONENTS OF THE MODULI SPACE OF SURFACES: A BELYITYPE THEOREM
• PROBLEMSOLVING MASTERCLASS WEEK 7 We'll end with an ``allstar'' session of seven problems.
• Responses to Third Referee Report for "Equations for the moduli space of n points on the line"
• UNIVERSAL COVERING SPACES AND FUNDAMENTAL GROUPS IN ALGEBRAIC GEOMETRY AS SCHEMES
• PUTNAM PROBLEM-SOLVING SEMINAR WEEK 7: GENERAL PROBLEM-SOLVING
• MODERN ALGEBRA (MATH 210) PROBLEM SET 7 1. Are the following ideals prime in C[x, y]? (a) (x, y -1), (b) (x, y2
• PROBLEM-SOLVING MASTERCLASS WEEK 5 1. An m n checkerboard is colored randomly: each square is independently assigned
• PROBLEM-SOLVING MASTERCLASS WEEK 5 1. If a and b are positive integers, show that if (a + 1)/b + b/a is an integer then it equals
• The William Lowell Putnam Mathematical Competition
• FOUNDATIONS OF ALGEBRAIC GEOMETRY CLASS 37 1. Motivation and game plan 1
• MATH 216 PROBLEM SET 6 This set is due at noon on Friday, November 6. Hand it in to Jack Hall (jhall@math)
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 19 This set is due Thursday, May 18. You can hand it in to Rob Easton, in class or via
• A NONPROJECTIVE THREEFOLD A. KNUTSON, AS TOLD TO R. VAKIL
• TOWARDS THE GEOMETRY OF DOUBLE HURWITZ NUMBERS I. P. GOULDEN, D. M. JACKSON AND R. VAKIL
• PROBLEMSOLVING MASTERCLASS WEEK 7 1. Find the smallest term in the sequence {a n } where a 1 = 1993 1994 1995 , a n+1 = a n /2 if a n
• INTRO TO ALGEBRAIC GEOMETRY, PROBLEM SET 9 Due Thursday November 18 in class. Hand in five of the following problems,
• MODERN ALGEBRA (MATH 210) PROBLEM SET 7 1. Prove that Q ( ) = Q (x). You may use the fact that is transcendental.
• MATH 210 PROBLEM SET 4 This problem set is due on Friday, February 23 at Jarod Alper's office door.
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 6 This set is due at noon on Friday November 9. You can hand it in to Jarod Alper
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 17 This set is due Thursday, April 20. You can hand it in to Rob Easton, in class or via
• MATH 216: FOUNDATIONS OF ALGEBRAIC math216.wordpress.com
• Problems for Polya Seminar November 2, 2009 1. Suppose that f : [0, 1] [0, 1] is continuous. Prove that there exists a num-
• MATH 210A PROBLEM SET 2 This problem set will be due on Friday, October 1, 2010 by 3 pm in Jeremy Miller's
• POLYA PROBLEM-SOLVING SEMINAR WEEK 5: INVARIANTS AND MONOVARIANTS
• 18.034 PROBLEM SET 3 Solve eight of the following problems. Due February 25 in class. No lates will be
• A GEOMETRIC LITTLEWOOD-RICHARDSON RULE ABSTRACT. We describe a geometric Littlewood-Richardson rule, interpreted as deform-
• MATH 216 PROBLEM SET 15: RELATIVE SPEC AND PROJ AND PROJECTIVE MORPHISMS; AND INTRODUCTION TO CECH
• POLYA PROBLEM-SOLVING SEMINAR WEEK 2: NUMBER THEORY
• PROBLEM-SOLVING MASTERCLASS WEEK 4 1. Let p(z) be a polynomial of degree n, all of whose zeros have absolute value 1 in the
• MATH 216: FOUNDATIONS OF ALGEBRAIC math216.wordpress.com
• INTRO TO ALGEBRAIC GEOMETRY, PROBLEM SET 7 Due Thursday November 4 in class (no lates). Hand in six of the following
• Columbus April 5, 2003 Why the golden mean?
• ALGEBRAIC STRUCTURES ON THE TOPOLOGY OF MODULI SPACES OF CURVES AND MAPS
• PUTNAM PROBLEMSOLVING SEMINAR WEEK 4: NUMBER THEORY
• Transcendence of e and 1. If F is in C [X] with degree n, define
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 5 This set is due Monday, November 14. It covers (roughly) classes 10, 11, and 12.
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 2 This set is due Monday, October 24. It covers classes 3 and 4. Read all of these prob
• M g IS IRREDUCIBLE April 1998: The original note was from some time in 1996. I've
• PUTNAM PROBLEMSOLVING SEMINAR WEEK 5: The Rules. These are way too many problems to consider in this evening session alone.
• PUTNAM PROBLEMSOLVING SEMINAR WEEK 6: ALGEBRAIC TECHNIQUES
• PROBLEMSOLVING MASTERCLASS WEEK 2 1. If 2n + 1 and 3n + 1 are both perfect squares, show that n is divisible by 40. (Steph
• INTRO TO ALGEBRAIC GEOMETRY, PROBLEM SET 5 Due Thursday October 21 in class (no lates). Hand in seven of the following
• WHICH PARTS OF ROTMAN HAVE WE COVERED IN MATH 210? Here is a list of what I think we've covered in Rotman, and what we covered outside of
• AN EXAMPLE OF A NICE VARIETY WHOSE RING OF GLOBAL SECTIONS IS NOT FINITELY GENERATED
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 12 This set is due Thursday, February 16, in Jarod Alper's mailbox. It covers (roughly)
• PUTNAM PROBLEMSOLVING SEMINAR WEEK 1: INDUCTION AND PIGEONHOLE
• UNIVERSAL COVERING SPACES AND FUNDAMENTAL GROUPS IN ALGEBRAIC GEOMETRY AS SCHEMES
• THE MODULI SPACE OF CURVES AND ITS TAUTOLOGICAL The moduli space of curves has proven itself a central object in geometry. The past
• THE GROMOVWITTEN POTENTIAL OF A POINT, HURWITZ NUMBERS, AND HODGE INTEGRALS
• PROBLEM-SOLVING MASTERCLASS WEEK 6 1. Show that for any positive integer n, there is an integer N such that the product
• MODERN ALGEBRA (MATH 210) PROBLEM SET 8 1. Describe the set of integers of the form a2
• Solution to the Mathieu-12 Puzzle Jaehyun Park
• THE EQUATIONS FOR THE MODULI SPACE OF n POINTS ON THE LINE BENJAMIN HOWARD, JOHN MILLSON, ANDREW SNOWDEN AND RAVI VAKIL
• MATH 210 PROBLEM SET 7 This problem set is due on Friday, March 16 at Jarod Alper's office door.
• PROBLEM-SOLVING MASTERCLASS WEEK 6 1. Let p be an odd prime and let Zp denote (the field of) integers modulo p. How many
• PROBLEM-SOLVING MASTERCLASS WEEK 2 1. Evaluate
• MODERN ALGEBRA (MATH 210) THANKSGIVING LEFTOVERS: PROOF OF TUESDAY'S THEOREM
• Murphy's Law for the Hilbert scheme (and the Chow variety, and moduli spaces of surfaces of general type, and stable maps, and nodal and cuspidal
• Problems for Polya Seminar November 9, 2009 1. What are the last two digits of 31234
• Proceedings of 7th Geometry-Topology Conference,
• MATH 210A PROBLEM SET 6 This problem set will be due on Monday, November 1, 2010 by 3 pm in Jeremy Miller's
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 1 This set is due Monday, October 17. It covers classes 1 and 2. Hand in five of these
• Columbus April 5, 2003 Why the golden mean?
• MATH 216: FOUNDATIONS OF ALGEBRAIC math216.wordpress.com
• ABSOLUTE GALOIS ACTS FAITHFULLY ON THE COMPONENTS OF THE MODULI SPACE OF SURFACES: A BELYI-TYPE THEOREM
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 3 This set is due Monday, October 31. It covers classes 5, 6, and 7. Read all of these
• MODERN ALGEBRA (MATH 210) PROBLEM SET 2 From the text: 2.69, 2.76, 2.98, 2.103. (For the last, and for future reference, read and
• A SHORT PROOF OF THE # g CONJECTURE WITHOUT GROMOVWITTEN THEORY: HURWITZ THEORY AND THE MODULI OF CURVES
• RELATIVE VIRTUAL LOCALIZATION AND VANISHING OF TAUTOLOGICAL CLASSES ON MODULI SPACES OF CURVES
• INTRO TO ALGEBRAIC GEOMETRY, PROBLEM SET 6 Due Thursday October 28 in class (no lates). Hand in seven of the following
• A GEOMETRIC LITTLEWOODRICHARDSON RULE 1. Introduction 1
• 1. Introduction 1 2. Algebraic geometry 1
• ABSOLUTE GALOIS ACTS FAITHFULLY ON THE COMPONENTS OF THE MODULI SPACE OF SURFACES: A BELYI-TYPE THEOREM
• THE MODULI SPACE OF n POINTS ON THE LINE IS CUT OUT BY SIMPLE QUADRICS WHEN n IS NOT SIX
• BABY ALGEBRAIC GEOMETRY SEMINAR: AN ALGEBRAIC PROOF OF RIEMANNROCH
• A DESCRIPTION OF THE OUTER AUTOMORPHISM OF S 6 , AND THE INVARIANTS OF SIX POINTS IN PROJECTIVE SPACE
• PUTNAM PROBLEMSOLVING SEMINAR WEEK 2: GENERATING FUNCTIONS
• A DOITYOURSELF PROOF OF THE n = 3 CASE OF FERMAT'S LAST THEOREM
• MURPHY'S LAW IN ALGEBRAIC GEOMETRY: BADLYBEHAVED DEFORMATION SPACES
• 30 NOVEMBER 2000. Abstract. The Hilbert scheme of closed and open subschemes of the line.
• RELATIVE VIRTUAL LOCALIZATION AND VANISHING OF TAUTOLOGICAL CLASSES ON MODULI SPACES OF CURVES
• FOUNDATIONS OF ALGEBRAIC GEOMETRY BONUS HANDOUT: PROOFS OF ``HARTOGS'' AND KRULL
• 18.024 (HONORS MULTIVARIABLE Lecture: T, Th 1, F 2, 2--147, Ravi Vakil (vakil@math, 2--271). O#ce hours
• TWELVE POINTS ON THE PROJECTIVE LINE, BRANCHED COVERS, AND RATIONAL ELLIPTIC FIBRATIONS
• PUTNAM PROBLEMSOLVINGSEMINARWEEK 2: NUMBERTHEORY
• MATH 216 PROBLEM SET 11: DIMENSION AND NONSINGULARITY
• MATH 216: FOUNDATIONS OF ALGEBRAIC August 26, 2010.
• INTRO TO ALGEBRAIC GEOMETRY, PROBLEM SET 3 Due Thursday October 7 in class. No lates will be accepted, so Ana-Maria will
• MATH 216 PROBLEM SET 17: CURVES (PART ONE) This set is due by the end of the day on Wednesday, May 12. E-mail me the list of
• 30 NOVEMBER 2000. Abstract. The Hilbert scheme of closed and open subschemes of the line.
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 7 This set is due Wednesday, December 7. It covers (roughly) classes 15 and 16.
• MATH 210A PROBLEM SET 1 This problem set will be due on Friday September 24 at a time and location to be an-
• MODERN ALGEBRA (MATH 210) PROBLEM SET 3 This set is due Friday, Oct. 22 at noon at Jarod Alper's door, 380--J.
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 4 This set is due Monday, November 7. It covers (roughly) classes 8 and 9. Read all of
• ABSOLUTE GALOIS ACTS FAITHFULLY ON THE COMPONENTS OF THE MODULI SPACE OF SURFACES: A BELYITYPE THEOREM
• RELATIVE VIRTUAL LOCALIZATION AND VANISHING OF TAUTOLOGICAL CLASSES ON MODULI SPACES OF CURVES
• INTRO TO ALGEBRAIC GEOMETRY, PROBLEM SET 11 Due Thursday December 9 in class. Hand in 6 of these problems. Ask someone
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 6 This set is due Wednesday, November 30. It covers (roughly) classes 13 and 14.
• MATH 216: FOUNDATIONS OF ALGEBRAIC June 15, 2010.
• Columbus April 4, 2003 The Mathematics of Doodling
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• MATH 216 PROBLEM SET 9 This set is due at noon on Friday, December 4. Hand it in to Jack Hall (jhall@math)
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• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 2 This set is due at noon on Friday October 12. You can hand it in to Jarod Alper
• FOUNDATIONS OF ALGEBRAIC GEOMETRY PROBLEM SET 4 This set is due at noon on Friday October 26. You can hand it in to Jarod Alper
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• 18.034 PROBLEM SET 4 Hand in seven of the following problems. Due March 3 in class. No lates will be
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• 18.034 PROBLEM SET 6 Due March 31 in class. No lates will be accepted. Discussion is encouraged,
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