Moduli theory | Algebraic varieties
In algebraic geometry, a moduli space of (algebraic) curves is a geometric space (typically a scheme or an algebraic stack) whose points represent isomorphism classes of algebraic curves. It is thus a special case of a moduli space. Depending on the restrictions applied to the classes of algebraic curves considered, the corresponding moduli problem and the moduli space is different. One also distinguishes between fine and coarse moduli spaces for the same moduli problem. The most basic problem is that of moduli of smooth complete curves of a fixed genus. Over the field of complex numbers these correspond precisely to compact Riemann surfaces of the given genus, for which Bernhard Riemann proved the first results about moduli spaces, in particular their dimensions ("number of parameters on which the complex structure depends"). (Wikipedia).
Further Graphs on the Complex Plane (2 of 3: Algebraically verifying Graphs concerning the Moduli)
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From playlist Complex Numbers
Algebraic curves, tropical geometry, and moduli - Sam Payne
Sam Payne Yale University February 11, 2015 Tropical geometry gives a new approach to understanding old questions about algebraic curves and their moduli spaces, synthesizing techniques that range from Berkovich spaces to elementary combinatorics. I will discuss an outline of this method,
From playlist Mathematics
Maxima and Minima for Quadratic and Cubics | Algebraic Calculus One | Wild Egg
Tangents of algebraic curves are best defined purely algebraically, without recourse to limiting arguments! We apply our techniques for finding such tangents to derive some familiar results for quadratic and cubic polynomial functions and their maxima and minima. We compare also with the c
From playlist Algebraic Calculus One
Zinovy Reichstein: The rationality problem for forms of moduli spaces of stable marked curves
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
Moduli of connections on curves: some examples by Frank Loray
20 March 2017 to 25 March 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions between mathematics and theoretical physics, especially
From playlist Complex Geometry
Instability and stratifications of moduli problems in algebraic geometry - Daniel Halpern-Leistner
Daniel Halpern-Leistner Member, School of Mathematics September 23, 2014 More videos on http://video.ias.edu
From playlist Mathematics
Further Graphs on the Complex Plane (1 of 3: Geometrical Representation of Moduli)
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From playlist Complex Numbers
The (Coarse) Moduli Space of (Complex) Elliptic Curves | The Geometry of SL(2,Z), Section 1.3
We discuss complex elliptic curves, and describe their moduli space. Richard Borcherd's videos: Riemann-Roch Introduction: https://www.youtube.com/watch?v=uRfbnJ2a-Bs&ab_channel=RichardE.BORCHERDS Genus 1 Curves: https://www.youtube.com/watch?v=NDy4J_noKi8&ab_channel=RichardE.BORCHERDS
From playlist The Geometry of SL(2,Z)
Orientations for Moduli Spaces in Higher-Dimensional Gauge Theory by Markus Upmeier
DISCUSSION MEETING ANALYTIC AND ALGEBRAIC GEOMETRY DATE:19 March 2018 to 24 March 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore. Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions be
From playlist Analytic and Algebraic Geometry-2018
Joseph Silverman, Moduli problems and moduli spaces in algebraic dynamics
VaNTAGe seminar on June 23, 2020. License: CC-BY-NC-SA. Closed captions provided by Max Weinreich
From playlist Arithmetic dynamics
Geometry of the moduli space of curves – Rahul Pandharipande – ICM2018
Plenary Lecture 3 Geometry of the moduli space of curves Rahul Pandharipande Abstract: The moduli space of curves, first appearing in the work of Riemann in the 19th century, plays an important role in geometry. After an introduction to the moduli space, I will discuss recent directions
From playlist Plenary Lectures
Recursive combinatorial aspects of compactified moduli spaces – Lucia Caporaso – ICM2018
Algebraic and Complex Geometry Invited Lecture 4.3 Recursive combinatorial aspects of compactified moduli spaces Lucia Caporaso Abstract: In recent years an interesting connection has been established between some moduli spaces of algebro-geometric objects (e.g. algebraic stable curves)
From playlist Algebraic & Complex Geometry
Transversality and super-rigidity in Gromov-Witten Theory by Chris Wendl
J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru
From playlist J-Holomorphic Curves and Gromov-Witten Invariants
The Hodge conjecture for moduli spaces of stable sheaves over a nodal curve by Inder Kaur
DISCUSSION MEETING: MODULI OF BUNDLES AND RELATED STRUCTURES ORGANIZERS : Rukmini Dey and Pranav Pandit DATE: 10 February 2020 to 14 February 2020 VENUE: Ramanujan Lecture Hall, ICTS, Bangalore Background: At its core, much of mathematics is concerned with the problem of classifying
From playlist Moduli Of Bundles And Related Structures 2020
Infinite-Dimensional Geometric Invariant Theory and Gauged Gromov–Witten... by Dan Halpern-Leistner
PROGRAM: VORTEX MODULI ORGANIZERS: Nuno Romão (University of Augsburg, Germany) and Sushmita Venugopalan (IMSc, India) DATE & TIME: 06 February 2023 to 17 February 2023 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru For a long time, the vortex equations and their associated self-dual fie
From playlist Vortex Moduli - 2023
Kac polynomials and Lie algebras associated to quivers and curves – Olivier Schiffmann – ICM2018
Lie Theory and Generalizations Invited Lecture 7.1 Kac polynomials and Lie algebras associated to quivers and curves Olivier Schiffmann Abstract: We provide an explicit formula for the following enumerative problem: how many (absolutely) indecomposable vector bundles of a given rank r an
From playlist Lie Theory and Generalizations
Beyond geometric invariant theory 1: Harder-Narasimhan theory by Daniel Halpern-Leistner
DISCUSSION MEETING: MODULI OF BUNDLES AND RELATED STRUCTURES ORGANIZERS : Rukmini Dey and Pranav Pandit DATE: 10 February 2020 to 14 February 2020 VENUE: Ramanujan Lecture Hall, ICTS, Bangalore Background: At its core, much of mathematics is concerned with the problem of classifying
From playlist Moduli Of Bundles And Related Structures 2020
Algebraic geometry 44: Survey of curves
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives an informal survey of complex curves of small genus.
From playlist Algebraic geometry I: Varieties