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#Modular Forms

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University of Chicago Department of Mathematics

Cohomology of Moduli Spaces of Curves

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Dive into the cohomology of moduli spaces of curves with Hannah Larson. Explore tautological rings, compactifications, and the mysteries of non-tautological cohomology groups in algebraic geometry.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
University of Chicago Department of Mathematics

The Ramanujan Conjecture for Modular Forms

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Dive into the Ramanujan conjecture for modular forms, exploring its history and recent developments in a gentle overview suitable for all levels of mathematical background.
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1 Lesons
1 hour
On-Demand
Free-Video
Institute for Advanced Study

The Unbounded Denominators Conjecture - Yunqing Tang

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Explore the unbounded denominators conjecture in modular forms, its implications, and a new proof approach using arithmetic algebraization theorem.
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9 Lesons
1 hour 10 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Théorie des Cordes et Théorie des Nombres : Valeurs Multiples Zêta et Amplitudes Physiques

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Explorez les liens fascinants entre la théorie des nombres et les amplitudes physiques, en mettant l'accent sur l'univaluation et l'invariance modulaire.
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1 Lesons
2 hours 10 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Le dernier théorème de Fermat

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Plongez dans l'histoire fascinante et la résolution du célèbre théorème de Fermat, un défi mathématique qui a intrigué les esprits pendant plus de trois siècles.
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1 Lesons
48 minutes
On-Demand
Free-Video
Simons Institute

Randomness in Number Theory

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Explore randomness in number theory, covering topics like finite fields, graphs, quantum gates, and the Riemann Hypothesis with Princeton's Peter Sarnak.
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11 Lesons
1 hour 12 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Modular Forms by Mahesh Kakde

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Comprehensive exploration of modular forms, covering definitions, properties, and applications. Delves into Eisenstein series, theta functions, and related mathematical concepts for advanced learners in number theory.
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27 Lesons
1 hour 43 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Quadratic Forms and Hermite Constant, Reduction Theory by Radhika Ganapathy

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Explores techniques for computing densest lattice packings, including quadratic forms, Hermite constants, and reduction theory. Covers perfect forms, eutactic lattices, and Voronoi's algorithm for listing perfect forms.
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12 Lesons
1 hour 24 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Computer-Assisted Proofs in the Arithmetic of Quadratic Forms - IPAM at UCLA

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Explore computer-assisted proofs in quadratic forms arithmetic, covering equivalence, representation, local-global principles, and modular forms. Gain insights into complex computations across mathematics.
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14 Lesons
47 minutes
On-Demand
Free-Video
International Mathematical Union

Atsushi Ichino- Theta Lifting and Langlands Functoriality

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Explore theta lifting, seesaw identities, and Langlands functoriality in number theory, focusing on modular forms and local Shimura-Waldspurger correspondence.
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7 Lesons
44 minutes
On-Demand
Free-Video
ICTP Mathematics

Modularity of Some Geometric Objects - Definitions, Reasons and State of the Art

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Explore zeta functions, L-functions, and Galois representations in geometric objects, focusing on plane projective curves and their conjectured relationships with analytic functions.
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10 Lesons
55 minutes
On-Demand
Free-Video
ICTP Mathematics

The Rogers-Ramanujan Identities and the Icosahedron - Lecture 3

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Explore the deep connections between Rogers-Ramanujan identities and the icosahedron, spanning number theory, modular forms, combinatorics, and more. Uncover the beauty and complexity of these mathematical gems.
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14 Lesons
1 hour 24 minutes
On-Demand
Free-Video
ICTP Mathematics

The Rogers-Ramanujan Identities and the Icosahedron - Lecture 2

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Explore connections between Rogers-Ramanujan identities and icosahedron, linking number theory, modular forms, combinatorics, and conformal field theory in an accessible survey for mathematicians.
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13 Lesons
1 hour 45 minutes
On-Demand
Free-Video
ICTP Mathematics

The Rogers-Ramanujan Identities and the Icosahedron - Lecture 1

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Explore the deep connections between the Rogers-Ramanujan identities and the icosahedron, spanning number theory, modular forms, combinatorics, and more in this accessible mathematical lecture.
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19 Lesons
1 hour 17 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Tau of Ramanujan by Eknath Ghate

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Explore Ramanujan's tau-function, its significance in Number Theory, and recent developments. Discover intriguing patterns and open problems in this fascinating mathematical sequence.
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27 Lesons
1 hour 50 minutes
On-Demand
Free-Video
Fields Institute

Quantum Complexity and L-functions

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Explore quantum algorithms for L-functions and zeta functions, examining complexity results, cohomology's role, and applications to modular forms and Mordell-Weil theorem.
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18 Lesons
55 minutes
On-Demand
Free-Video
Fields Institute

Symmetry, Almost

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Explore the beauty of mathematical symmetry and its imperfections, focusing on modular forms and their variants. Discover how altering symmetries can reveal new insights and unexpected beauty.
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11 Lesons
31 minutes
On-Demand
Free-Video
IMSA

Hecke Actions on Loops and Periods of Iterated Shimura Integrals

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Exploration of Hecke actions on loops and periods of iterated Shimura integrals, focusing on SL_2(Z) and modular curves, with insights into mixed modular motives and Galois action.
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1 Lesons
1 hour
On-Demand
Free-Video
Hausdorff Center for Mathematics

Traces of CM Values and Geodesic Cycle Integrals of Modular Functions

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Explores generating series of CM value traces and geodesic cycle integrals of modular functions, covering theta lifts and applications to L-series and cycle integral rationality.
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1 Lesons
46 minutes
On-Demand
Free-Video
ICTP Mathematics

The Rogers-Ramanujan Identities and the Icosahedron - Lecture 4

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Exploración profunda de las identidades Rogers-Ramanujan, su conexión con el icosaedro y sus implicaciones en teoría de números, formas modulares, combinatoria y teoría de campos conformes.
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1 Lesons
1 hour 17 minutes
On-Demand
Free-Video
Fields Institute

Factorization and Modular Forms

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Explore quantum algorithms for factorization and modular forms with Kumar Murty, delving into advanced mathematical concepts and their applications in quantum computing.
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1 Lesons
49 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Modular Forms, Elliptic Polylogarithms and Feynman Integrals

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Explores advanced mathematical concepts in Feynman integrals, focusing on epsilon-form solutions, modular forms, and elliptic polylogarithms, with applications in number theory and physics.
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1 Lesons
1 hour 17 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Symmetric Power Functoriality for Hilbert Modular Forms

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Explore symmetric power functoriality for Hilbert modular forms, comparing with elliptic modular cases in this advanced mathematics lecture by James Newton.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Principle of Quadratic Chabauty and Nonsplit Cartan Modular Curves

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Explore advanced techniques for studying rational points on modular curves, focusing on quadratic Chabauty methods and nonsplit Cartan modular curves in arithmetic geometry.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Rational Points on Modular Curves - Lecture 3

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Explore advanced techniques for studying rational points on modular curves, focusing on geometry, Q-rational points, Chabauty methods, and computational aspects in arithmetic geometry.
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1 Lesons
1 hour 33 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Rational Points on Modular Curves - Lecture 2

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Explore advanced techniques for studying rational points on modular curves, focusing on geometry, Q-rational points, Chabauty methods, and computational aspects in arithmetic geometry.
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1 Lesons
1 hour 35 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Introduction to Modular Forms, Elliptic Curves, and Modular Curves - Lecture 3

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Explores advanced concepts in arithmetic geometry, focusing on modular forms, elliptic curves, and modular curves. Builds on previous lectures to deepen understanding of these fundamental objects.
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1 Lesons
1 hour 30 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Rational Points on Modular Curves by Jan Vonk

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Explore advanced techniques for studying rational points on modular curves, focusing on theoretical and computational aspects in arithmetic geometry.
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1 Lesons
1 hour 34 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Ribet's Lemma in Residually Indistinguishable Case by Mahesh Kakde

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Exploration of Ribet's Lemma in the context of residually indistinguishable cases, delving into advanced concepts in arithmetic geometry and modular curves theory.
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1 Lesons
59 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Iwasawa Theory for Rankin-Selberg L-Function at an Eisenstein Prime

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Explores Iwasawa theory for Rankin-Selberg L-functions at Eisenstein primes, delving into advanced arithmetic geometry concepts and their applications in number theory.
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1 Lesons
31 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Introduction to Modular Forms, Elliptic Curves, and Modular Curves - Lecture 1

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Explore modular forms, elliptic curves, and modular curves in this advanced lecture. Gain insights into arithmetic geometry and the study of rational points on varieties.
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1 Lesons
1 hour 32 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Introduction to Modular Forms, Elliptic Curves, and Modular Curves - Lecture 2

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Explore advanced concepts in arithmetic geometry, focusing on modular forms, elliptic curves, and modular curves. Gain insights into rational points and their significance in number theory.
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1 Lesons
1 hour 40 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Introduction to Modular Forms, Elliptic Curves, and Modular Curves - Lecture 4

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Explore advanced concepts in arithmetic geometry, focusing on modular forms, elliptic curves, and modular curves. Gain insights from expert Eknath Ghate in this in-depth lecture.
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1 Lesons
1 hour 37 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Rational Points on Modular Curves - Lecture 1

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Explore advanced concepts in arithmetic geometry, focusing on rational points on modular curves. Gain insights into theoretical and computational aspects of this fascinating field of mathematics.
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1 Lesons
1 hour 20 minutes
On-Demand
Free-Video
Fields Institute

Quantum Unique Ergodicity for Powerful Level via Shifted Convolution Sum

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Explore advanced mathematical concepts in number theory, focusing on QUE for powerful levels using shifted convolution sum techniques.
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1 Lesons
33 minutes
On-Demand
Free-Video
Fields Institute

Hypergeometric Functions, Galois Representations, and Modular Forms

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Explore connections between hypergeometric functions, Galois representations, and modular forms in advanced number theory and algebraic geometry.
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1 Lesons
39 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Moments of Families of Elliptic Curves

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Explore new developments in higher moment sums of elliptic curve families, their connections to modular forms, and applications to rigid Calabi-Yau threefolds and intermediate Jacobians.
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1 Lesons
50 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Constructing Polylogarithms on Higher-Genus Riemann Surfaces

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Generalization of elliptic polylogarithms to higher-genus Riemann surfaces, exploring homotopy-invariant iterated integrals, modular tensors, and connections to Enriquez-Zerbini polylogarithms and Fay identities.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Modular Regulators and Multiple Modular Values

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Explore recent advancements in computing Goncharov regulator integrals for K_4 classes on modular curves, relating them to multiple modular values and single L-values of modular forms.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Counting Rational Points on Modular Curves of Genus 0 Over Number Fields by Peter Bruin

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Explore techniques for counting rational points on modular curves of genus 0 over number fields, advancing understanding in arithmetic geometry and algebraic number theory.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
Galileo Galilei Institute

Modularity and Monodromy

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Explore the intricate relationship between modularity and monodromy in mathematics, delving into advanced concepts and their applications in number theory and algebraic geometry.
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1 Lesons
1 hour 16 minutes
On-Demand
Free-Video
Galileo Galilei Institute

A Summary of Methods for Solving Differential Equations Involving Automorphic Forms

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Explore advanced techniques for solving differential equations with automorphic forms, enhancing mathematical problem-solving skills in complex analysis and number theory.
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1 Lesons
1 hour
On-Demand
Free-Video
Galileo Galilei Institute

Modular Resurgence for Integrated Correlators at Large N

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Explore modular resurgence in integrated correlators at large N, delving into advanced mathematical concepts and their applications in theoretical physics.
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1 Lesons
1 hour 16 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

The Geometry and Arithmetic of Banana Nano-Manifolds

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Explore the geometry and arithmetic of banana nano-manifolds, focusing on new rigid Calabi-Yau threefolds and their Donaldson-Thomas partition functions, Gromov-Witten potentials, and modular properties.
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1 Lesons
1 hour 19 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Subconvexity of L-functions - Part 1

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Explore advanced concepts in analytic number theory, focusing on subconvexity bounds for L-functions and their applications in mathematics.
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1 Lesons
1 hour 13 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Rings of Siegel-Jacobi Forms of Bounded Relative Index Are Not Finitely Generated

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Explore Siegel-Jacobi forms and their non-finitely generated rings of bounded relative index in this advanced mathematical presentation by Ana Botero.
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1 Lesons
59 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

On Harmonic Weak Maass Forms Associated to Even Integer Weight Newforms

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Explore harmonic weak Maass forms associated with even integer weight newforms, covering modular forms, integral coefficients, and key observations in mathematical theory.
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13 Lesons
51 minutes
On-Demand
Free-Video
NCCR SwissMAP

Quillen Metrics and Applications - Part 3: Gauged Maps, Vortices and Their Moduli

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Explore gauged maps, vortices, and moduli spaces through historical context, applications, and analytical tools in mathematical physics.
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11 Lesons
47 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Brjuno Functions, Hölder Continuity and Modular Forms

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Explore Brjuno functions, Hölder continuity, and modular forms in dynamical systems with Stefano Marmi. Gain insights into cutting-edge research presented at IMPA's international conference celebrating Marcelo Viana.
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1 Lesons
46 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Modular Forms and Differential Equations: Connections and Applications

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Explore connections between modular forms and differential equations, from historical origins to modern applications in mathematics and physics.
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1 Lesons
1 hour 12 minutes
On-Demand
Free-Video
Conference GSI

SL(2, Z)-Equivariant Machine Learning with Modular Forms - Theory and Applications

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Explore SL(2, Z)-equivariant machine learning, delving into modular forms theory and its practical applications in advanced mathematical modeling.
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1 Lesons
23 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Complex Multiplication - Lecture 1

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Explore complex multiplication in mathematics through an in-depth lecture by Jan Vonk, covering fundamental concepts and advanced theories.
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1 Lesons
55 minutes
On-Demand
Free-Video
Centrum Fizyki Teoretycznej PAN

Dispersionless Integrable Equations and Modular Forms

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Explore the connection between dispersionless integrable PDEs and modular forms, focusing on Hirota equations and first-order integrable Lagrangians. Gain insights into advanced mathematical concepts and their applications.
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1 Lesons
1 hour 11 minutes
On-Demand
Free-Video
Centrum Fizyki Teoretycznej PAN

On ODEs Satisfied by Modular Forms

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Explore ODEs satisfied by modular forms, their invariance under Lie groups, and associated algebraic curves. Extend results to Jacobi forms and examine examples from classical modular forms.
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9 Lesons
1 hour 1 minute
On-Demand
Free-Video
BIMSA

Eisenstein Series - An Overview

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Explore Eisenstein series in a concise, self-contained overview, gaining insights into this mathematical concept and its applications.
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1 Lesons
48 minutes
On-Demand
Free-Video
BIMSA

Modularity of Donaldson-Thomas Invariants on Compact Calabi-Yau Threefolds

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Explore Donaldson-Thomas invariants, their connection to BPS indices, and modular behavior in string theory. Gain insights into computational methods and applications to Gopakumar-Vafa invariants and topological string amplitudes.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Iterated Integrals of Modular Forms in String Theory

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Explore iterated integrals of modular forms in string theory, their connection to scattering amplitudes, and the concept of multiple modular values in physics.
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1 Lesons
57 minutes
On-Demand
Free-Video
Galileo Galilei Institute

Modularity in String Theory and Moonshine - Lecture 2

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Explore advanced concepts in string theory, focusing on modularity and its connections to moonshine phenomena in mathematics and theoretical physics.
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1 Lesons
1 hour 28 minutes
On-Demand
Free-Video
Galileo Galilei Institute

Modular Forms and String Theory - Lecture 3

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Explore connections between modular forms and string theory, delving into advanced mathematical concepts and their applications in theoretical physics.
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1 Lesons
1 hour 39 minutes
On-Demand
Free-Video
Galileo Galilei Institute

Modular Forms and String Theory - Lecture 2

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Explore connections between modular forms and string theory, delving into advanced mathematical concepts and their applications in theoretical physics.
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1 Lesons
1 hour 45 minutes
On-Demand
Free-Video
Galileo Galilei Institute

Modular Forms and String Theory - Lecture 1

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Explore the intricate connection between modular forms and string theory in this advanced physics lecture, delving into mathematical foundations and theoretical applications.
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1 Lesons
1 hour 28 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Modularity of Donaldson-Thomas Invariants on Calabi-Yau Threefolds

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Explore Donaldson-Thomas invariants, their mathematical significance, and modular behavior in string theory. Gain insights into BPS indices, wall-crossing phenomena, and topological string amplitudes.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Galileo Galilei Institute

Calabi-Yaus and Curves in Feynman Integrals

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Explore the intricate connection between Calabi-Yau manifolds and Feynman integrals in particle physics, unraveling complex mathematical structures in quantum field theory.
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1 Lesons
53 minutes
On-Demand
Free-Video
Galileo Galilei Institute

Modular Bootstrap for BPS Black Holes

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Explore modular bootstrap techniques for analyzing BPS black holes, uncovering insights into their quantum properties and thermodynamics.
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1 Lesons
1 hour 12 minutes
On-Demand
Free-Video
IPhT-TV

Quantum Cosmology as Automorphic Dynamics

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Explore quantum cosmology through automorphic dynamics, delving into advanced theoretical concepts and their implications for our understanding of the universe's origins and evolution.
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1 Lesons
57 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Introduction to Sphere Packing Problems by Abhinav Kumar

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Explore sphere packing in geometry, covering its history, applications, and recent advances. Learn about lattices, codes, bounds, and energy minimization in various dimensions.
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31 Lesons
1 hour 39 minutes
On-Demand
Free-Video
IMSA

GPPV Invariants and the Spectrum of Singularities

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Explore complex surface singularities, their 3-manifold links, and GPPV invariants. Discover new connections between modular forms and singularity spectra for Brieskorn homology spheres and ADE singularity links.
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1 Lesons
51 minutes
On-Demand
Free-Video
Bill Buchanan OBE

An Interview with Neal Koblitz - Elliptic Curve Cryptography and Beyond

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Renowned mathematician Neal Koblitz discusses his groundbreaking work in elliptic curve cryptography, its impact on modern security, and his insights on the field's evolution and future directions.
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16 Lesons
1 hour 14 minutes
On-Demand
Free-Video
Joint Mathematics Meetings

Symmetry, Almost

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Explore mathematical symmetry, from abstract concepts to modular forms and quantum modular forms, with applications in various fields of mathematics and physics.
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17 Lesons
54 minutes
On-Demand
Free-Video
Conference GSI

A Non-Formal Formula for the Rankin Cohen Deformation Quantization

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Explore the Rankin-Cohen deformation quantization, its connections to modular forms and foliations, and discover a new oscillatory integral formula for Zagier's UDF.
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1 Lesons
26 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Single-valued Integrals and Modular Forms

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Delve into advanced mathematical concepts exploring the relationship between single-valued integrals and modular forms, with applications in analytic number theory and complex analysis.
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1 Lesons
51 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Picard-Fuchs Equations and Modular Forms - Applications and Theory

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Explore the intricate relationship between Picard-Fuchs equations and modular forms, examining their mathematical applications and theoretical foundations in algebraic differential equations.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video