Stanford algebraic geometry. Foundations of Algebraic Geometry math216.

Stanford algebraic geometry Harris is famous around the world for his lively textbooks and enthusiastic teaching, as well as for his seminal research contributions. A very MATH 245A TOPICS IN ALGEBRAIC GEOMETRY: COMPLEX ALGEBRAIC SURFACES RAVI VAKIL Goal: We will develop the theory of (complex) algebraic surfaces, with the aim of un-derstanding Enriques’ classification of surfaces. Stanford Algebraic Geometry Seminar POL YGON SP A CES AND MIRR OR SYMMETR Y CIPRIAN S. In the first part, the virtual localization technique is applied to the problem of showing blow-up formulae for virtual invariants on a smooth Algebraic geometry and analytic geometry are two closely related subjects with many important interactions that have spurred major progress in both areas. They are 1. Charles). dimensions, structure sheaf of functions, tangent spaces) have geometric meanings and could also be understood using commutative algebra. You can learn more about Professor Hacon here. Note to reader: the figures, index Department of Mathematics Building 380, Stanford, California 94305 Phone: (650) 725-6284 mathfrontdesk [at] stanford. In the second In this course, we study algebraic geometry over an algebraically closed base field e. List of Attended Conferences . In this talk, we will discuss the twisted invariants for orbifold target spaces. We discuss different approaches for at- Stanford Algebraic Geometry — Seminar — COUNTING JUMPING CURVES OF VECTOR BUNDLES IZZET COSKUN M. Special Stanford Algebraic Geometry/ Number Theory Seminar CANONICAL SUBGROUPS IN p-ADIC FAMILIES OF ABELIAN VARIETIES BRIAN CONRAD University of Michigan Abstract Motivated by problems in the theory of p-adic modular forms, it is important to study how p-power torsion subgroups “deform” in p-adic families of abelian varieties. C. In this talk, we introduce metric algebraic geometry through discussion of Voronoi cells, bottlenecks, offset hypersurfaces, and Monodromy and algebraic stacks: March 5 no seminar (R away) March 12 no seminar planned Mon. Stanford Algebraic Geometry | Seminar | COHOMOLOGY OF ALGEBRAIC VARIETIES PIERRE DELIGNE1 Institute of Advanced Study Monday, February 14 12:20 p. We have an algebraic geometry mailing list, where news will be sporadically sent. Tuesday, October 21, at Stanford (Rm. Stanford Algebraic Geometry — Seminar — AN AMAZING TETRAHEDRON OF EQUIVALENT THEORIES JIM BRYAN University of British Columbia Abstract There are four different theories that look geometrically very different, but surprisingly turn out to be isomorphic. Nonsingularity (“smoothness”) of Noetherian schemes 247 13. On one hand, it involves such classical areas as algebraic geometry and Oct 7, 2009 · Stanford Algebraic Geometry | Seminar | ELLIPTIC K3 SURFACES WITH pn-TORSION SECTIONS CHRISTIAN LIEDTKE Dusseldorf / Stanford Abstract We classify K3 surfaces in positive characteristic p, which come with an elliptic bration and a section of order pn. WAGS: The Western Algebraic Geometry Symposium (I was part of Results for: Algebraic Geometry. Our study leads to a conjecture that describes a highly nontrivial Stanford Algebraic Geometry — Seminar — THE UNEXPECTED POWER OF THE RANK 6 PLUCKER¨ RELATION: A NEW VIEW OF GRASSMANNIANS FROM MATHEMATICAL PHYSICS ALEX KASMAN College of Charleston Abstract Grassmannians are algebraic projective varieties defined by the quadratic polynomial equa-tions called ”the Plu¨cker Instructor: B. Also, I am solely responsible for any Stanford Algebraic Geometry / Algebraic Methods Seminar INTEGRAL STRUCTURES, TORIC GEOMETRY, AND HOMOLOGICAL MIRROR SYMMETRY CHARLES DORAN Washington Abstract We establish the isomorphisms over Z of cohomology / K-theory, global monodromy, and invariant symplectic forms predicted by Kontsevich’s Homological Mirror Symmetry Con- Stanford Algebraic Geometry — Seminar — SYZYGIES AND THE EFFECTIVE CONE OF THE MODULI SPACE OF CURVES GAVRIL FARKAS University of Texas at Austin Abstract One of the fundamental invariants of the moduli space of curves Mg is its cone of effective divisors. Schedule (Spring 2024) The seminar will meet at. In algebraic terms, this means that we can construct a map A1 t!X (the one-dimensional affine space maps to our 18. THE RISING SEA Foundations of Algebraic Geometry math216. The background assumed will depend on the people attending the class. In this talk, we give an elementary proof of Noether–Lefschetz. Click on the title to see the abstract (if available). March 29 (joint with Algebraic Methods seminar) Charles Doran (Columbia/Washington) Integral structure, toric geometry, and homological mirror symmetry: Tues. Published by Princeton University Press. the Gromov-Witten theory of P1 ×C2, 2. These invariants (e. (2024/8) A new paper with X. On the projective space P2, it asks how many curves de ned by homogeneous degree d polynomials have only I am a Szegő Assistant Professor at Stanford University. (2024/6) A new X (as an Azumaya algebra over X X) provide algebraic classes, which su ce to prove the Standard Conjectures for X (joint with F. Click here for the Stanford Algebraic Geometry Seminar, and here for the Berkeley Commutative Algebra and Algebraic Geometry Seminar. 2: Hao Xu (Harvard) Eynard-Orantin theory Stanford Algebraic Geometry | Seminar | A ROLE OF LAPLACE TRANSFORM IN GROMOV-WITTEN THEORY MOTOHICO MULASE Davis Abstract Laplace transformation changes a function de ned on positive integers (or more generally, on positive real numbers) to a complex analytic function. “Supersingular Diagonal Curves and Their Genera”. linear geometry (degree on) Stanford Algebraic Geometry | Seminar | FINITENESS CONJECTURES ABOUT THE PROJECTIVE COORDINATE RINGS OF Xn=G AS n VARIES ANDREW SNOWDEN Stanford Abstract Let X be a complex projective variety with an action of a reductive group G and let Rn be the projective coordinate ring of the space Xn=G of n points on X modulo the action of G, Stanford Algebraic Geometry | Seminar | FORMAL CLASSIFICATION OF IRREGULAR D-MODULES KIRAN KEDLAYA UC San Diego Abstract Consider a vector bundle with connection on a smooth complex algebraic or analytic variety. If one has a nice compacti cation, one can then ask whether or not the connection has regular Stanford Algebraic Geometry | Seminar | TEICHMULLER SPACE AND TOPOLOGICAL FIELD THEORY IN TWO DIMENSIONS EZRA GETZLER Northwestern Abstract A topological eld theory in d dimensions associates to each (d 1)-dimensional closed manifold M an inner-product space V(M), and to each d-dimensional manifold W with it is well-suited for the purposes of non-Archimedean geometry and functional analysis. The heart of the proof involves the use of rational curves on K3 and a degeneration argument. There is also a joint seminar with Berkeley, held four times per year. Intersection numbers against characteristic classes of Stanford Algebraic Geometry — Seminar — LINEAR SYSTEMS OF PLANE CURVES WITH BASE POINTS OF BOUNDED MULTIPLICITY STEPHANIE YANG Michigan Abstract We address the problem of computing the dimension of the space of plane curves of fixed degree and general multiple base points. Show Content. , Millson, J. Abstract/Contents Abstract In this thesis, we examine certain questions relevant to the study of sheaf-theoretic invariants of complex projective surfaces and beyond. Algebraic logic, algebraic number theory, and algebraic topology are all heavily studied, while algebraic geometry and algebraic combinatorics have entire journals devoted to them. Moregenerally, oneexpectsthatthegeometric\positivity" of a line bundle L can be detected on the metrics Algebraic Geometry; Analysis & PDE; Applied Math; Combinatorics; Department Colloquium; Faculty Area Research (FARS) Geometry; Joint Berkeley-Stanford Algebraic Number Theory Seminar; Number Theory; Probability; Representation Theory; Symplectic Geometry Toggle Symplectic Geometry Stanford Algebraic Geometry | Seminar | FORMAL CLASSIFICATION OF IRREGULAR D-MODULES KIRAN KEDLAYA UC San Diego Abstract Consider a vector bundle with connection on a smooth complex algebraic or analytic variety. These results of are based on a rather general study of naive local terms and their behavior under Verdier Fridays 3:30-4:30 in 383N Click on the title to see the abstract (if available). Stanford Algebraic Geometry | Seminar | ASYMPTOTIC OF HURWITZ NUMBERS AND INTERSECTION THEORY ON M g;n DIMITRI ZVONKINE Stanford Abstract We demonstrate a similarity between the asymptotic of the number of quadrangulations (subdivisions into squares) of a genus g surface, rami ed coverings of the sphere by a genus g surface, and the Weil My primary research interest is in algebraic geometry, focusing on moduli problems in algebraic geometry, and on their applications to geometry, topology and to mathematical physics. Stanford Algebraic Geometry — Seminar — STABLE MAPS TO A LOOP GROUP MICHAEL THADDEUS Columbia Abstract Let X be a compact complex manifold, ΩK the space of loops on a compact connected Lie group. In this talk, I will explain a systematic approach to study their cohomology rings, using notably tautological relations of geometric origin. Tu, Leslie. In the first half you will learn the language and The main theme of the talk is the combinatorics of lattice polygons and its relationship to the geometry of the associated toric surfaces. edu O ce hours: MWF, 4-5pm Prerequisites: Math 210A & 210B, and some basic awareness about manifolds Textbook: Algebraic Geometry by Hartshorne (required), Commutative Ring Theory by Matsumura (recommended) Course description: Algebraic geometry was classically concerned with the This volume resulted from the conference A Celebration of Algebraic Geometry, which was held at Harvard University from August 25-28, 2011, in honour of Joe Harris' 60th birthday. There is a place for each of these courses. Conferences in algebraic geometry. This approac h v olv only the basic understanding of the Click here for the Stanford Algebraic Geometry Seminar, and here for the Berkeley Commutative Algebra and Algebraic Geometry Seminar. Ravi Vakil (Stanford) Stabilization of discriminants in the Grothendieck ring: Nov. The distance metric can be the Euclidean metric in the ambient space or a metric intrinsic to the variety. I will illustrate by explaining some examples of con- Stanford Algebraic Geometry — Seminar — QUANTUM COHOMOLOGY OF ISOTROPIC GRASSMANNIANS ANDERS BUCH Aarhus Abstract The (small) quantum cohomology ring of a homogeneous space is a deformation of the classical cohomology ring, which uses the three point, genus zero Gromov-Witten invariants as its structure constants. In anongoingwork, we Counting special lattices inside the "moduli space" of all lattices with extra symmetry leads to interesting invariants e. com December 29, 2015 draft ⃝c 2010–2015 by Ravi Vakil. The Ax--Schanuel theorem . edu (E-mail) Nov 6, 2020 · Two key features of algebraic K-theory are its failure to satisfy \'etale descent, and its motivic filtration in terms of higher Chow groups in the case of smooth schemes over a field (but expected more generally). It also leads to interesting dynamical systems and group theory. Stanford Libraries' official online search tool for books, media, journals, databases, government documents and more. Update: click here for a much later version (really, a distant descendant) The description in the course guide: "Introduces the basic notions and techniques of modern algebraic geometry. NOTES from the conferences I have attended. Bogart and E. “Bott Periodicity and Affine Grassmannians ”. Chen, Quanlin. I did my PHD (2018-2022, MIT) (2024/9) Teaching a topic course on Langlands duality (focusing on type A) , and algebraic geometry course focusing quasi-coherent sheaves (as linearizations / spaces of states). The special ber is reduced and Cohen-Macaulay, and its ir-reducible components form interesting combinatorial patterns. International Press. com. A Math 145: Algebraic Geometry Professor Brian Conrad MWF, 9--9:50am, 380W Sloan Hall . Algebraic structures on the topology of moduli spaces of curves and maps Geometry of Riemann surfaces and their moduli spaces Vakil, R. In these talks, we will discuss their applications to higher-dimensional geometry. Some familiarity with the language of algebraic geometry will be assumed, although we will develop most of the tools as we need them. Occasionally go to Berkeley when you hear about something particularly interesting. 384H. In particular, I will survey the recent solution of Li-Xu's Stable Degeneration Feb 23, 2024 · I will describe some connections between arithmetic geometry of abelian varieties, non-archimedean/tropical geometry, and combinatorics. Ravi Vakil’s The Three Thing advice. Foundations of Algebraic Geometry math216. wordpress. When you are up to it, subscribe to the daily mailing of abstracts of algebraic geometry papers posted to the arXiv. In particular, the Atiyah-Bott localization formula allows one to derive facts about the manifold’s global properties from Stanford Algebraic Geometry | Seminar | FORMAL PSEUDO-DIFFERENTIAL OPERATORS AND r-SPIN NUMBERS HAO XU Harvard Abstract We derive structure theorems about r-spin numbers and formal pseudo-di erential operators, with the goal of gaining a better understanding of Witten’s conjecture (proved by Faber-Shadrin-Zvonkine for the A type singularity and more generally by Stanford Algebraic Geometry | Seminar | COUNTING CURVES ON SURFACES RICHARD THOMAS Imperial College London Abstract I will discuss the counting of holomorphic curves on complex algebraic surfaces via Gromov-Witten theory and via \stable pairs". . Jun 11, 2021 · The classical Noether–Lefschetz theorem says that for a very general surface S of degree ≥ 4 in P^3 over the complex numbers, the restriction map from the divisor class group on P^3 to S is an isomorphism. Speaker. stanford. I co-organize the Stanford algebraic geometry seminar. Relative Proj of a sheaf of graded algebras 4 3. March 30 (at Stanford, 383-N, 3:15-5:45) Joe Harris (Harvard) and Mark de Cataldo References: The posted lecture notes will be rough, so I recommend having another source you like, for example Mumford's Red Book of Varieties and Schemes (the original edition is better, as Springer introduced errors into the second edition by retyping it), and Hartshorne's Algebraic Geometry. When we start looking at vector bundles of a certain (low) rank on X, the natural question that arises is: can we classify them? This is a Stanford Algebraic Geometry — Seminar — AN AMAZING TETRAHEDRON OF EQUIVALENT THEORIES JIM BRYAN University of British Columbia Abstract There are four different theories that look geometrically very different, but surprisingly turn out to be isomorphic. When X is isomorphic to the moduli space M, of stable sheaves on a K3 Chapter 13. For seminar listings from fall 2001, click here. , Lee, Y. Syllabus: The syllabus will evolve depending on the class, but it will roughly cover the following material, in roughly the following order. Stanford Algebraic Geometry | Seminar | SOME RESULTS ON INDEPENDENCE OF ‘ FOR ACTIONS OF CORRESPONDENCES MARTIN OLSSON Berkeley Abstract I will discuss some new results on actions of correspondences and questions of independence of ‘. , Snowden, A. Fri, Mar 5 2021, 12:00pm. Important information on the biregular and birational geometry of a Fano variety is encoded, via Mori theory, in certain Stanford Algebraic Geometry — Seminar — MIRKOVIC-VILONEN CYCLES ON THE AFFINE GRASSMANNIAN JOEL KAMNITZER Berkeley Abstract The geometric Satake correspondence relates representation theory to the geometry of the affine Grassmannian. We use A X in order to construct a triangulated category with an object E x, for every point x in X. Instead, in algebraic geometry we study \textbf{invariants and geometry} of the space of solutions to polynomial equations. 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. 11. Early (out-of-date) version of The Rising Sea: Foundations of Algebraic Geometry (c) 2024 Ravi Vakil. Geometric intuition will be emphasized. Dec. 380-383N) In this talk, we describe some interactions between the algebraic geometry and the combi-natorics of the following setting studied by A. with me, read this. I will describe a proof of this formula Stanford Algebraic Geometry | Seminar | RIGIDITY PROPERTIES OF FANO VARIETIES TOMMASO DE FERNEX Utah Abstract From the point ofview of the Minimal Model Program, Fano varieties constitute the building blocks of uniruled varieties. “Symmetric Homomorphisms of Abelian Varieties”. These notes are inspired by Prof. Then we will show the relations between Large Radius Limit and Lagrangian fibrations of Hyper-Kahler manifolds. That's too hard, so at least what this course is about: why many notions (geometric, arithmetic, algebraic, complex-analytic, ) can be understood in In the first half you will learn the language and dictionary of algebraic geometry, including affine varieties and maps between them, Hilbert basis theorem and Nullstellensatz. Email : sahilkarawade99@gmail. Daniel Kim (Stanford) We will prove the Ax Stanford Algebraic Geometry — Seminar — SYZ FIBRATION FOR HYPER KAHLER MANIFOLDS ANDREY TODOROV Santa Cruz Abstract In the talk first we will discuss the meaning of Large Radius Limit for Hyper-Kahler mani-folds. For more information, please contact Jun Li (jli@math. Tuesday, November 12, at Stanford: Mark Gross (San Diego): Affine structures, log structures, and mirror symmetry (3:00-4:00, Rm. Geometric intuition (from complex and real numbers) could be used to predict behaviors of Metric algebraic geometry is a term proposed for the study of properties of real algebraic varieties that depend on a distance metric. In particular no projective rational or elliptic curves admit a non-trivial map there. 725: Introduction to Algebraic Geometry. This is closely related to the concept of PBS states in string theory. Since such elliptic brations pull back from the universal elliptic Sep 17, 2004 · Stanford Algebraic Geometry — Seminar — TAMELY RAMIFIED COVERS OF THE PROJECTIVE LINE BRIAN OSSERMAN Berkeley Abstract We give new results on existence and non-existence of tamely ramified covers of the projec-tive line. It comes with a surprising mixture of both rigid and flexible behavior. Relative Spec of a (quasicoherent) sheaf of algebras 1 2. BOR CEA Rider Univ ersit y Abstract: The p ossible con gurations, up to orien tation-preserving isometry, for a planar n-gon with prescrib ed length for eac h of its edges, mak e-up a compact space, whic is, in general, smo oth, orien table manifold of The moduli spaces of one-dimensional sheaves on the projective plane have been studied through their connections to enumerative geometry and representation theory. Algebraic Geometry Codes: Advanced Chapters is devoted to the theory of algebraic geometry codes, a subject related to several domains of mathematics. Atiyah pointed out that the space of based holomorphic maps from X to ΩK is finite-dimensional. the fundamental lemma. Schedule (Winter 2024) Monodromy and algebraic stacks: March 5 no seminar (R away) March 12 no seminar planned Mon. Catullo, Ryan, Miguel Machado, and Aaryan Sukhadia. Please help me keep this current. In this talk, we describe some interactions between the algebraic geometry and the combi-natorics of the following setting studied by A. This is a report on work on progress with T. Arithmetic Geometry Preprint Seminar at Stanford Organizers: Linus Hamann, Vaughan McDonald and Zhiyu Zhang. We relate varieties over the complex numbers to complex This is a undergraduate course in classical algebraic geometry. Note to reader: the figures, index, and formatting have yet to be properly dealt with. See the syllabus link for a more detailed discussion. 25: Holiday : Dec. This is a basic course in classical algebraic geometry. Greicius, Quinn. The main tool is the theory of limit linear series, which is better-behaved under degenerations than the theory of admissible Stanford Algebraic Geometry | Seminar | A TROPICAL APPROACH TO EFFECTIVE CONES DIANE MACLAGAN Warwick Abstract Tropical geometry associates a polyhedral complex, called the tropical variety, to a subvariety X of a torus. 4. Schedule (Winter 2024) Stanford Algebraic Geometry | Seminar | Stanford Abstract Given a collection of points in projective space, we consider the question of when the de ning ideal can be generated by the minors of a matrix of linear forms (and the related question Stanford Algebraic Geometry | Seminar | ALGEBRAIC BOUNDS ON ANALYTIC MULTIPLIER IDEALS BRIAN LEHMANN Michigan Abstract A classical theorem of Kodaira states that ample line bundles are characterized by the positivityoftheircurvatureform. There is a fair bit of algebraic geometry at Stanford, and as some of it is in somewhat unexpected places, this page is intended to point out where it is. Because the field is a synthesis of ideas from many different parts of mathematics, it usually requires a Algebraic geometry is a beautiful subject, and it’s usually taught as a mid-level graduate course, so we’ll need to discuss things in this class without a lot of background. Both theories have to be modi ed to avoid giving zero all the time. Griffin Wang on spherical relative Fundamental Lemmas . The tropical variety is a \combinatorial shadow" of X which preserves many invariants of X and of a good compacti cations Y of X. Stanford Algebraic Geometry — Seminar — While the theorem is purely number-theoretic, the proof is almost entirely algebro-geometric; the main idea is to relate the problem of counting number fields to the problem of counting integral points on certain carefully chosen varieties related to Hilbert schemes of points on Stanford Algebraic Geometry — Seminar — geometric meaning to when this dimension is larger than the expected dimension obtained from Riemann-Roch; specifically, the dimension is larger than expected if and only if the system has a multiple (−1)-curve in its base locus. Go to the Western Algebraic Geometry Seminar, a twice-yearly conference. The local dimension is at most the dimension of the tangent space, and nonsingularity251 Math 216: Foundations of algebraic geometry 2009-10 Spring quarter: Wednesday Friday 9:00-10:15 in 380-F (with many exceptions) An updated version of the notes will be gradually posted here, starting roughly September 1, 2010. Later Li and Xu extend this speculation and conjecture that every klt singularity has a canonical Jan 16, 2005 · Stanford Algebraic Geometry — Seminar — ON MODULI SPACES OF STABLE RANK-TWO SHEAVES OVER SOME CALABI-YAU MANIFOLDS WEIPING LI Hong Kong University of Science and Technology Oct 10, 2024 · Around 10 years ago, Donaldson and Sun discovered that metric limits of Ricci positive Kähler–Einstein manifolds are algebraic varieties, and their metric tangent cones also underlie some algebraic structure. For more information, check on google. edu). Later Li and Xu extend this speculation and conjecture that every klt singularity has a canonical Stanford Algebraic Geometry — Seminar — CURVES OF GENUS 2, VECTOR BUNDLES, DUALITIES AND CLASSICAL ALGEBRAIC GEOMETRY QUANG MINH NGUYEN University of Michigan Abstract Let X be a curve of genus 2. com December 30, 2014 draft ⃝c 2010–2015 by Ravi Vakil. The analog algorithm for Abelian integrals of genus 2 Stanford Algebraic Geometry — Seminar — THE PROJECTIVE INVARIANTS OF ORDERED POINTS ON THE LINE BEN HOWARD University of Maryland Abstract One of the classical problems of invariant theory is the study of projective invariants of n-tuples of points on the projective line — which in characteristic zero is the projective Stanford Algebraic Geometry | Seminar | VANISHING THEOREMS FOR LOG CANONICAL PAIRS WITH APPLICATIONS SANDOR KOVACS University of Washington Abstract A conjecture of Shafarevich predicted that any curve mapping to the stack Mg must be hyperbolic. The Zariski tangent space 247 13. Algebraic geometry at Stanford; how to join our mailing list. We prove that the ascending and descending sets for these vector elds Stanford Algebraic Geometry | Seminar | UNIVERSAL FORMULAS FOR COUNTING NODAL CURVES ON SURFACES YU-JONG TZENG Stanford Abstract The problem of counting nodal curves on algebraic surfaces has been studied since the nine-teenth century. ) If you are thinking of doing your Ph. March 30 (at Stanford, 383-N, 3:15-5:45) Joe Harris (Harvard) and Mark de Cataldo (Stonybrook) FOUNDATIONS OF ALGEBRAIC GEOMETRY CLASSES 33 AND 34 RAVI VAKIL CONTENTS 1. special Algebraic geometry is a subject that somehow connects and unies several parts of mathematics, including obviously algebra and geometry, but also number theory, and depending on your point of view many other things, including topology, string theory, etc. In the notes, I have included extra definitions and examples for my understanding. Algebraic Geometry at Stanford. What algebraic geometry is about. Clemens proved there are no rational curves on a general quintic surface in P3. For con Algebraic geometry at Stanford. Arend Bayer (University of Edinburgh) Date. Algebraic sets, Hilbert's Nullstellensatz and varieties over algebraically closed fields. Kirwan, and Cox-Little-O'Shea) are freely electronically available through the library (to those at Stanford). This is joint work with James D. I suspect they may not have Stanford Algebraic Geometry — Seminar — MODULI OF TWISTED SHEAVES AND AZUMAYA ALGEBRAS MAX LIEBLICH M. “On Polynomial Progressions in Finite Fields”. 15. Abstract We construct and describe moduli spaces of Azumaya algebras on a smooth projective sur-face. One can study a vector bundle E on Pn by studying how this decomposition varies when one restricts E to lines. Fano varieties: from derived categories to geometry via stability. We will present a particular example and how a combination of tools and ideas from algebraic geometry The notion of moduli space was invented by Riemann in the 19th century to encode how Riemann surfaces vary in families; today, the study of geometric and homotopy-theoretic aspects of moduli spaces is an important subject with strong ties to algebraic and symplectic geometry. Stanford Algebraic Geometry — Seminar — MARINO-VAFA FORMULA OF ONE-PARTITION HODGE INTEGRALS CHIU-CHU MELISSA LIU Harvard Abstract Marcos Marino and Cumrun Vafa conjectured a remarkable formula of one-partition Hodge integrals based on duality between open Gromov-Witten theory and Chern-Simons theory. I will talk about a general algebraic geometry theory behind this phenomenon. For seminar listings from 2003-2004, click here. Bitz, J, J Echevarria Cuesta, and E Kilgore. Abstract Every vector bundle on P1 decomposes as a direct sum of line bundles. More algebraic aspects of topology study Stanford Algebraic Geometry | Seminar | ELLIPTIC K3 SURFACES WITH pn-TORSION SECTIONS CHRISTIAN LIEDTKE Dusseldorf / Stanford Abstract We classify K3 surfaces in positive characteristic p, which come with an elliptic bration and a section of order pn. Projective morphisms 7 In these two lectures, we will use universal properties to dene two more useful con- Stanford Algebraic Geometry | Seminar | ALGEBRAIC BOUNDS ON ANALYTIC MULTIPLIER IDEALS BRIAN LEHMANN Michigan Abstract A classical theorem of Kodaira states that ample line bundles are characterized by the positivityoftheircurvatureform. 20. When we start looking at vector bundles of a certain (low) rank on X, the natural question that arises is: can we classify them? This is a A theorem of Donaldson and Sun asserts that the metric tangent cone of a smoothable Kähler–Einstein Fano variety underlies some algebraic structure, and they conjecture that the metric tangent cone only depends on the algebraic structure of the singularity. In 1984 Mark Green put forward a very elegant conjecture linking the complexity of the curve in its moduli space to the structure of its equations (syzygies). I. D. There are some available at the bookstore; let me know if and when they run out. As a result, it can be a handy thing to know if you are in a variety of subjects, no- tably number theory, symplectic geometry, Mainly interested in Algebraic Geometry and allied areas . g. L-functions and orbital integrals, and interesting questions e. If one has a nice compacti cation, one can then ask whether or not the connection has regular. Stanford Algebraic Geometry — Seminar — TAMELY RAMIFIED COVERS OF THE PROJECTIVE LINE BRIAN OSSERMAN Berkeley Abstract We give new results on existence and non-existence of tamely ramified covers of the projec-tive line. Families of non-product minimal surfaces with cylindrical tangent The geometry is reflected in the algebra here, because we can actually parameterize this curve using polynomials: if we draw a line of slope tfrom the origin (which is a double zero), then y= tx, so f(x,tx) = t2x2 x3 x2 = x2(t2 x 1), so x= t2 1, which tells us that y= t3 t. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. A systematic treatment and motivation of the theory is emphasized, using concrete examples to illustrate its usefulness. Brugall e, in which we attempt to prove Mar 5, 2021 · Algebraic Geometry. Cofinite and cocompact hyperbolic reflection groups have the following feature: their fundamental Nov. Date 3:00 PM. Brugall e, in which we attempt to prove Math 145: Undergraduate Algebraic Geometry Winter 2017. WAGS: The Western Algebraic Geometry Symposium (I was part of Stanford Algebraic Geometry | Seminar | ASCENDING AND DESCENDING SETS IN COMPLEX STRATIFIED MORSE THEORY MISHA GRINBERG Renaissance Technologies Abstract We present a new construction of gradient-like vector elds in the setting of Morse theory on a complex analytic strati cation. Seminar. Friday Arithmetic Geometry Preprint Seminar at Stanford Organizers: Linus Hamann, Vaughan McDonald and Zhiyu Zhang. In this talk we will highlight some of these connections with an emphasis on recent progress, future directions, and open questions. For the list of my research papers and preprints, please go to Research Outlines. (I tend to update it roughly every month unless someone gives me information directly Stanford Algebraic Geometry | Seminar | PREPERIODIC POINTS OF ALGEBRAIC DYNAMICS AND CALABI-YAU THEOREM YUAN XINYI Clay Mathematical Institute / Columbia Symplectic topology is at the crossroads of several mathematical disciplines such as low-dimensional topology, algebraic geometry, representation theory, Hamiltonian dynamics, integrable systems, mirror symmetry, and string theory. I intend to keep this list vaguely up to date, but I make no guarantees. the Donaldson-Thomas theory of P1 Stanford Algebraic Geometry — Seminar — THE PROJECTIVE INVARIANTS OF ORDERED POINTS ON THE LINE BEN HOWARD University of Maryland Abstract One of the classical problems of invariant theory is the study of projective invariants of n-tuples of points on the projective line — which in characteristic zero is the projective Stanford Algebraic Geometry — Seminar — COSMIC STRING AND FAMILY SEIBERG-WITTEN THEORY ON K3 FIBRATIONS AI-KO LIU Berkeley Abstract Family Seiberg-Witten theory has been developed as a tool to study the enumeration of immersed nodal curves on algebraic surfaces. The topic of the course will be the theory of "moduli spaces" in algebraic geometry. In particular, certain subvarieties of the affine Grassmanian, called Mirkovic-Vilonen cycles, give bases for Stanford Algebraic Geometry — Seminar — TOPOLOGICAL RECURSION RELATIONS BY LOCALIZATION ERIC KATZ Stanford Abstract If a manifold possesses a group action, one can say much about its topology by using equiv-ariant cohomolgy. In particular, we won’t Algebraic geometry is a subject that somehow connects and unies several parts of mathematics, including obviously algebra and geometry, but also number theory, and depending on your The description in the course guide: "Introduces the basic notions and techniques of modern algebraic geometry. We welcome people from number theory, representation theory and algebraic geometry to give talks on topics they find interesting. Stanford Algebraic Geometry Seminar HIRZEBRUCH-RIEMANN-ROCH THEOREM IN QUANTUM COBORDISM THEORY ALEXANDER GIVENTAL Berkeley Abstract Moduli spaces of stable maps in Gromov-Witten theory come equipped not only with virtual fundamental classes but also with virtual tangent bundles. This formula, known as the Riemann hypothesis for Stanford Algebraic Geometry | Seminar | A TROPICAL APPROACH TO RATIONAL CURVES ON HYPERSURFACES ETHAN COTTERILL MSRI / Nantes Abstract H. Brugall e, in which we attempt to prove an analogous statement in tropical Here is a map of Stanford's campus, with parking indicated. Grothendieck's formulation of abstract Galois theory, which builds a bridge between number theory and topology. Room 383-N This book introduces the reader to modern algebraic geometry. Current research areas of the symplectic Gauge-theoretic invariants in algebraic geometry. linear geometry (degree on) Stanford Algebraic Geometry | Seminar | COUNTING CURVES ON SURFACES RICHARD THOMAS Imperial College London Abstract I will discuss the counting of holomorphic curves on complex algebraic surfaces via Gromov-Witten theory and via \stable pairs". Here is my CV. We do not use any Hodge theory, cohomology, or monodromy. The precise topics of what we cover will 18. Stanford Algebraic Geometry | Seminar | Stanford Abstract Given a collection of points in projective space, we consider the question of when the de ning ideal can be generated by the minors of a matrix of linear forms (and the related question There are several types of courses that can go under the name of "introduction to algebraic geometry": complex geometry; the theory of varieties; a non-rigorous examples-based course; algebraic geometry for number theorists (perhaps focusing on elliptic curves); and more. We relate varieties over the complex numbers to complex Algebraic geometry. The shape of this cone is predicted by the Harris-Morrison Slope Conjecture which singles algebraic geometry and linear algebra many ideas from linear algebra can be generalized abstractions duality, subspaces S, S? ideals, varieties, quotient spaces solving equations Gaussian elimination Groebner basis algorithms solving inequalities LP duality real algebraic geometry, p-satz Stanford Algebraic Geometry | Seminar | ORBIT PARAMETRIZATIONS OF DECORATED CURVES [warning: talk is at unusual time] WEI HO Columbia Abstract We discuss parametrizations of geometric data, such as curves with speci ed line bundles or vector bundles, by orbits of representations of algebraic groups. There remain many issues still to be dealt with in the main part of the notes (including many of your corrections and suggestions). We will Upcoming conferences in algebraic geometry Here is a list of upcoming conferences involving algebraic geometry. The main tool is the theory of limit linear series, which is better-behaved under Oct 5, 2009 · Stanford Algebraic Geometry | Seminar | A TROPICAL APPROACH TO RATIONAL CURVES ON HYPERSURFACES ETHAN COTTERILL MSRI / Nantes Abstract H. We will describe the orbifold Stanford Algebraic Geometry | Seminar | FORMAL PSEUDO-DIFFERENTIAL OPERATORS AND r-SPIN NUMBERS HAO XU Harvard Abstract There is a famous conjecture of Witten (proved by Faber-Shadrin-Zvonkine and more gener-ally by Fan-Jarvis-Ruan) that relates Gelfand-Dickey hierarchy to intersection numbers on moduli spaces ofr-spincurves. Algebraic Geometry Seminar. Similarities between Galois theory and the theory of covering spaces are so striking that algebraists use geometric language to talk of field extensions whereas topologists talk of Galois covers. 1. Moregenerally, oneexpectsthatthegeometric\positivity" of a line bundle L can be detected on the metrics Stanford Algebraic Geometry — Seminar — FORMULAS FOR THE ARITHMETIC GEOMETRIC MEAN OF CURVES OF GENUS 3 DAVID LEHAVI Ohio State University Abstract The arithmetic geometric mean algorithm for calculation of elliptic integrals of the first type was introduced by Gauss. Algebraic sets, Hilbert's Nullstellensatz and varieties over algebraically Math 216A: Algebraic Geometry. Location. Conrad, 383CC Sloan Hall, conrad@math. Several examples from the Stanford Algebraic Geometry — Seminar — BIRATIONAL GEOMETRY OF IRREGULAR VARIETIES CHRIS HACON Utah Abstract The purpose of this talk is to illustrate how the Fourier-Mukai transform combined with vanishing and generic vanishing theorems can be used to give surprisingly precise results in the birational classification of irregular varieties. This argument has the additional Jan 19, 2024 · A theorem of Donaldson and Sun asserts that the metric tangent cone of a smoothable Kähler–Einstein Fano variety underlies some algebraic structure, and they conjecture that the metric tangent cone only depends on the algebraic structure of the singularity. Friday, Algebraic geometry. Tuesday, October 26, at Stanford (Rm. WAGS: The Western Algebraic Geometry Symposium (I was part of the group founding the current incarnation in 2001. In the second half, you will learn more about algebraic curves. Sign up for the algebraic geometry mailing list. Organizer: Daniel Kim. edu) or Ravi Vakil (vakil@math. The table of contents (and sketchy introduction) for the notes as of June 15, 2010 The winter quarter course will deliberately be a "second course in algebraic geometry", and I want to move at a pace where I can keep as many people with me as possible, with as complete an understanding as possible. Fulton: Let X be a nonsingular complex algebraic variety and E0 → E1 → ··· → En be a sequence of vector bundles and morphisms over X. These spaces are the algebro-geometric version of the spaces of principal PGLn-bundles and they also have strong connections to Stanford Algebraic Geometry — Seminar — QUANTUM RIEMANN-ROCH FOR ORBIFOLDS HSIAN-HUA TSENG Berkeley Abstract One way of proving the mirror formula for quintic threefold, due to Coates-Givental, is by studying the so-called twisted Gromov-Witten invariants. Past Events. This point of view also allows us to recover A number of branches of mathematics have found algebra such an effective tool that they have spawned algebraic subbranches. Algebraic geometry. Presheaves with transfer. Buch and W. 383-N): Sergey Yuzvinsky (University of Oregon): Differential operators annihilating a polynomial (3:30-4:30 Math 145: Undergraduate Algebraic Geometry Winter 2017. Stanford Algebraic Geometry — Seminar — HODGE-D CONJECTURE FOR K3 AND ABELIAN SURFACES XI CHEN Alberta Abstract We prove that the real regulator map is surjective on a general K3 or Abelian surface. Stepan Kazanin (Stanford) We construct the abelian category of presheaves with transfer [MWV, Chapter 1–2]. m. In the first half you will learn the language and dictionary of algebraic geometry, including affine varieties and maps between them, Hilbert basis theorem and Nullstellensatz. 200-107, click here for a map, and here for the poster): Allen Knutson (Berkeley): Simplicial complexes and B-B decompositions (3:15-4:15) Stanford Algebraic Geometry | Seminar | RELATIVE BEHREND FUNCTIONS DAVESH MAULIK Clay Mathematical Institute / MIT Abstract Given a smooth projective threefold, Donaldson-Thomas invariants encode virtual enumera-tive information about its moduli space of sheaves. com June 11, 2013 draft ⃝c 2010, 2011, 2012, 2013 by Ravi Vakil. 2. A conjecture of Harbourne and Hirschowitz gives geometric AIM / Stanford Abstract We review one application of Algebraic Geometry in String Theory: The construction of physically viable theories. I will explain my related research on a generalization of this toy model to "moduli space” of algebraic varieties, with interesting questions e. Journal Editing Algebraic geometry and analytic geometry are two closely related subjects with many important interactions that have spurred major progress in both areas. Mumford (2nd ed) may be Hyperbolic reflection groups appear in various fields of mathematics such as algebraic geometry, discrete subgroups of Lie groups, geometric group theory, geometric topology, and number theory. Stanford Algebraic Geometry — Seminar — ON MODULI SPACES OF STABLE RANK-TWO SHEAVES OVER SOME CALABI-YAU MANIFOLDS WEIPING LI Hong Kong University of Science and Technology Stanford Algebraic Geometry | Seminar | A TROPICAL APPROACH TO RATIONAL CURVES ON HYPERSURFACES ETHAN COTTERILL MSRI / Nantes Abstract H. Stanford Algebraic Geometry | Seminar | MUSTAFIN VARIETIES DUSTIN CARTWRIGHT Berkeley Abstract A Musta n variety is a degeneration of projective space induced by a point con guration in a Bruhat-Tits building. T. For a principally polarized abelian variety, we show an identity relating the Faltings height and the Néron--Tate height (of a symmetric effective divisor defining the polarization) which involves invariants arising from non Stanford Algebraic Geometry Seminar COUNTING RA TIONAL CUR VES OF ARBITRAR Y SHAPE IN PR OJECTIVE SP A CE ALEKSEY ZINGER Stanford Abstract: I will presen t a metho d for solving virtually ev ery problem of en umerativ e algebraic geom-etry concerning rational curv es in pro jectiv e spaces. Since such elliptic brations pull back from the universal elliptic curve over the Igusa curve, which is the Stanford Algebraic Geometry — Seminar — ON MODULI SPACES OF STABLE RANK-TWO SHEAVES OVER SOME CALABI-YAU MANIFOLDS WEIPING LI Hong Kong University of Science and Technology Determining the structure of the equations of an algebraic curve in its canonical embedding (given by its holomorphic forms) has been a central question in algebraic geometry from the beginning of the subject. Building 380, Stanford, California 94305 Phone: (650) 725-6284 mathfrontdesk [at] stanford. Textbook(s): Arnaud Beauville's Complex algebraic surfaces. Stanford Algebraic Geometry — Seminar — CURVES OF GENUS 2, VECTOR BUNDLES, DUALITIES AND CLASSICAL ALGEBRAIC GEOMETRY QUANG MINH NGUYEN University of Michigan Abstract Let X be a curve of genus 2. Stanford Algebraic Geometry Seminar JET SCHEMES AND BIRATIONAL GEOMETRY LAWRENCE EIN University of Illinois at Chicago Abstract Jet schemes have attracted a great deal of attention recently, because of their central role in the theory of motivic integration. Jan. We will recall the physical requirements of Heterotic string the-ory and describe a precise problem in algebraic geometry to be solved. I will explain A. This gives rise to a degeneracy locus, a subscheme of X. , MATH 216: FOUNDATIONS OF ALGEBRAIC GEOMETRY math216. In this talk I will Stanford Algebraic Geometry — Seminar — DRINFELD MODULAR VARIETIES AND CURVES WITH MANY RATIONAL POINTS MIHRAN PAPIKIAN Stanford Abstract Almost 60 years ago Andre Weil proved a formula for the number of rational points on a smooth projective algebraic curve C of genus g over a finite field Fq. Both books are on reserve at the library. Lewis. See this mathoverflow page for interesting related discussion. This is the first quarter of a course in the theory of schemes. edu (E-mail) Student Algebraic Geometry. Then the resulting \reduced" stable pair theory Specific advice about algebraic geometry at Stanford. the Donaldson-Thomas theory of P1 Algebraic Geometry Seminar 2011-2012; Fridays, 3:00 in 383-N. In the case that X is a closed subscheme of a torus, or equivalently A is a quotient of a Laurent polynomial ring K[x 1 1;:::;x 1 n], the map trop: X Berk ! Rn given by j:j 7! (log(jx 1j);:::;log(jx nj)) is an extension of the tropicalization map on X(K Stanford Algebraic Geometry | Seminar | FREE RESOLUTIONS AND DEGENERACY LOCI STEVEN SAM MIT Abstract I will explain one way to interpret locally free resolutions of degeneracy loci as an enhance-ment for cohomology class formulas. Our point of view is to measure the complexity of In this class, you will be introduced to some of the central ideas in algebraic geometry. czomsnv pxqiiabj snx ilwky dqve czumh rba kvbnbi oajfkf ynkn