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#Theoretical Mathematics

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Krista King

How to Solve Partial Derivatives

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Learn to calculate and interpret partial derivatives for multivariable functions, including first-order, second-order, and mixed partial derivatives, with clear explanations and examples.
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12 Lesons
35 minutes
On-Demand
Free-Video
Banach Center

Theoretical and Numerical Approach to Lyapunov Exponents of Skew-Product Semiflows

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Explore Lyapunov exponents in skew-product semiflows through theoretical and numerical approaches, enhancing understanding of dynamical systems.
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1 Lesons
25 minutes
On-Demand
Free-Video
Fields Institute

Fourier Uniqueness and Non-Uniqueness Pairs

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Explore Fourier uniqueness and non-uniqueness pairs in this advanced mathematics lecture, delving into complex analysis and function spaces.
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1 Lesons
55 minutes
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Free-Video
Michael Penn

What Mathematicians Mean When We Use Super as a Prefix

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Explore the mathematical meaning of "super" as a prefix, delving into its applications and significance in various mathematical contexts.
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1 Lesons
22 minutes
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Free-Video
Michael Penn

Some Example Calculations in the Heisenberg Vertex Algebra

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Explore in-depth calculations within the Heisenberg vertex algebra, demonstrating advanced mathematical concepts and techniques in this specialized field of study.
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1 Lesons
21 minutes
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Free-Video
Michael Penn

Vertex Algebras - The Non-Negative Products

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Explore the structure of non-negative products in vertex algebras, delving into advanced mathematical concepts and their applications in algebraic theory.
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1 Lesons
24 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Entropy and C^0 Stability of Hypersurfaces - IPAM at UCLA

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Explore entropy's role in hypersurface complexity, focusing on sphere rigidity, stability properties, and generalizations in higher dimensions. Gain insights into cutting-edge research in geometric analysis.
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10 Lesons
24 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Alexander Volberg: The Probability of Buffon Needle to Land Near Cantor Set

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Explore the probability of Buffon's needle landing near Cantor sets, delving into unexpected connections with various mathematical fields and theories.
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13 Lesons
53 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Landscape Function and Its Relations With Eigenvectors of a Schrödinger Operator

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Explore landscape functions and their connections to Schrodinger operator eigenvectors, covering effective potentials, energy computations, and exponential decay in various contexts.
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9 Lesons
44 minutes
On-Demand
Free-Video
International Mathematical Union

Variety of Fractional Laplacians

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Explore various types of fractional Laplacians, their properties, and applications in mathematical analysis through proofs, comparisons, and counterexamples.
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9 Lesons
42 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Conics in a Second by Bernd Sturmfels

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Explore conics through historical and modern perspectives, from pentagon construction to applied algebraic geometry, with insights on Newton's method and enumerative geometry.
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13 Lesons
35 minutes
On-Demand
Free-Video
ICTP Mathematics

Determinantal Point Processes - II

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Exploration of determinantal point processes, covering theorems, Young graphs, Markov chains, and related mathematical concepts with applications in random matrix theory.
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11 Lesons
57 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Grothendieck Inequality by Gadadhar Misra

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Explore the Grothendieck inequality, its consequences, and related concepts in mathematics. Learn about max cut problems, cut norms, and proofs, including Kirvine's approach to this fundamental inequality.
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26 Lesons
1 hour 8 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

On the MLC Conjecture by Misha Lyubich

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Explore the MLC Conjecture with Misha Lyubich in this interactive lecture, offering insights into complex dynamics and opportunities for audience engagement.
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1 Lesons
47 minutes
On-Demand
Free-Video
IMSA

Quantum Toric Geometry II - Non-Commutative Geometric Invariant Theory

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Explore quantum geometric invariant theory, extending classical GIT to non-commutative cases. Gain insights into cutting-edge research in quantum toric geometry.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
IMSA

Geometric Recursion for Combinatorial Teichmüller Spaces and Applications

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Explores geometric recursion in combinatorial Teichmüller spaces, covering Mirzakhani-McShane identity, Topological Recursion, and discrete versions, with applications to Witten-Kontsevich theorem and Norbury's polynomials.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
International Mathematical Union

Homotopy Patterns in Group Theory

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Explore homotopy patterns in group theory, delving into advanced mathematical concepts and their applications in topology and algebra.
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1 Lesons
43 minutes
On-Demand
Free-Video
International Mathematical Union

Formation of Singularities in Nonlinear Dispersive PDEs

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Explore the formation of singularities in nonlinear dispersive partial differential equations with mathematician Galina Perelman in this insightful lecture on advanced mathematical concepts.
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1 Lesons
44 minutes
On-Demand
Free-Video
International Mathematical Union

Surfaces via Spinors and Soliton Equations

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Explore Weierstrass representation of surfaces, its relation to Willmore functional, and application to Davey-Stewartson II equation solutions with unique singularity patterns.
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1 Lesons
44 minutes
On-Demand
Free-Video
International Mathematical Union

Michel van den Bergh- Noncommutative Crepant Resolutions

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Explore noncommutative crepant resolutions in algebraic geometry with Michel van den Bergh, delving into advanced mathematical concepts and their applications.
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1 Lesons
1 hour
On-Demand
Free-Video
International Mathematical Union

The Liouville Quantum Gravity Metric

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Explore the construction and properties of the Liouville quantum gravity metric, a distance function for random fractal surfaces, and delve into related open problems in this mathematical presentation.
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1 Lesons
42 minutes
On-Demand
Free-Video
International Mathematical Union

Yiannis Sakellaridis- Spherical Varieties, Functoriality, and Quantization

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Explore spherical varieties, functoriality, and quantization in algebraic geometry and representation theory with Yiannis Sakellaridis' advanced mathematical lecture.
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1 Lesons
44 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Guido De Philippis - PDE Constrained Measures III

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Explore advanced concepts in PDE-constrained measures with Guido De Philippis, delving into complex mathematical theories and applications in this advanced lecture.
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1 Lesons
35 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Roger Heath-Brown: The Determinant Method I

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Explore rational points on algebraic varieties, their counting methods, and related phenomena in this advanced mathematics lecture by renowned number theorist Roger Heath-Brown.
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1 Lesons
53 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Ilya Molchanov - Random Sets Generated by Translates of a Convex Body

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Explores K-hulls and K-strongly convex sets, analyzing facial structures and applying theory to random point samples. Discusses convergence of f-vectors and related probabilistic results.
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1 Lesons
30 minutes
On-Demand
Free-Video
ICTP Mathematics

An Introduction to Higher Teichmuller Theory - D. Canary

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Explore higher Teichmuller Theory, delving into advanced mathematical concepts and their applications in geometry and topology. Gain insights from expert D. Canary in this comprehensive lecture.
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1 Lesons
1 hour 11 minutes
On-Demand
Free-Video
ICTP Mathematics

Knot Homology and Sheaves on the Hilbert Scheme of Points on the Plane - A. Oblomkov

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Explore advanced mathematical concepts connecting knot theory, homology, and algebraic geometry on the Hilbert scheme of points in the plane.
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1 Lesons
53 minutes
On-Demand
Free-Video
ICTP Mathematics

On the Robustness of Intermingled Basins - Rual Ures

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Explore the mathematical concept of intermingled basins and their robustness in dynamical systems, focusing on recent developments and applications in this field.
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1 Lesons
40 minutes
On-Demand
Free-Video
ICTP Mathematics

Measure and Smooth Rigidity of Lattice Actions in Low Dimensions - Federico Rodriguez-Hertz

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Explore measure and smooth rigidity of lattice actions in low dimensions with Federico Rodriguez-Hertz, delving into advanced mathematical concepts and their applications.
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1 Lesons
43 minutes
On-Demand
Free-Video
ICTP Mathematics

Chiral Algebras from Three Dimensions

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Explore the fascinating connection between chiral algebras and three-dimensional physics in this advanced mathematical lecture by renowned physicist Sergei Gukov.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
ICTP Mathematics

Bounds on the Number of Generators of Prime Ideals

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Explore prime ideals and their generators, focusing on mathematical bounds and theoretical implications in algebraic geometry and commutative algebra.
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1 Lesons
35 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

The Zappa-Szép Product of a Fell Bundle and a Groupoid

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Explore the mathematical concept of Zappa-Szép products, focusing on their application to Fell bundles and groupoids. Gain insights into advanced algebraic structures and their properties.
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1 Lesons
41 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Groupoid Models for Groupoid Correspondences and C*-Algebras

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Explore groupoid models for correspondences and C*-algebras, delving into advanced mathematical concepts and their applications in algebraic structures.
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1 Lesons
58 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Crossed Products as Compact Quantum Metric Spaces

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Explore quantum metric spaces through crossed products, delving into advanced mathematical concepts and their applications in quantum theory.
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1 Lesons
34 minutes
On-Demand
Free-Video
Fields Institute

CM Values of Higher Automorphic Green Functions

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Explore higher automorphic Green functions and their CM values in this advanced mathematics lecture, focusing on theta series, representation theory, geometry, and arithmetic.
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1 Lesons
1 hour 17 minutes
On-Demand
Free-Video
Fields Institute

Challenges in Discrete Geometry - Part I- Convex Polytopes

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Explore convex polytopes, from Euler's formula to modern combinatorial results. Discover connections to other mathematical areas and intriguing open problems in discrete geometry.
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1 Lesons
48 minutes
On-Demand
Free-Video
Fields Institute

Generalized Kac-Moody Superalgebras and Root Groupoid

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Explore advanced algebraic structures with Vera Serganova as she delves into Generalized Kac-Moody Superalgebras and Root Groupoid, offering insights for mathematicians and theoretical physicists.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
Fields Institute

Irregular Triads in 3-Uniform Hypergraphs

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Explore irregular triads in 3-uniform hypergraphs, delving into advanced concepts in model theory and combinatorics with Caroline Terry from Ohio State University.
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1 Lesons
1 hour 15 minutes
On-Demand
Free-Video
Fields Institute

A Harder-Narasimhan Stratification of the B+dR-Grassmannian

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Explore the B+dR-Grassmannian's Harder-Narasimhan stratification in this advanced mathematics lecture by Eva Viehmann, delving into complex algebraic geometry concepts.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Fields Institute

Cyclic Cohomology and Higher Invariants of Elliptic Differential Operators

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Explore advanced mathematical concepts in cyclic cohomology and their applications to elliptic differential operators, focusing on higher invariants and recent developments.
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1 Lesons
55 minutes
On-Demand
Free-Video
ICTP Mathematics

Symbolic Powers of Ideals - Part 3

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Explore advanced concepts in tight closure theory, focusing on symbolic powers of ideals and their applications in algebraic geometry and commutative algebra.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
ICTP Mathematics

Briancon-Skoda Theorems - Part 2

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Explore advanced concepts in tight closure theory, focusing on Briancon-Skoda theorems and their applications in algebraic geometry and commutative algebra.
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1 Lesons
51 minutes
On-Demand
Free-Video
ICTP Mathematics

Briancon-Skoda Theorems - Part 1

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Explore the Briancon-Skoda Theorems in this graduate-level mathematics lecture, delving into tight closure of ideals and their applications in algebraic geometry.
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1 Lesons
52 minutes
On-Demand
Free-Video
QuantumTopology

On Representations of Virtual Braid Group and Groups of Virtual Links

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Explore representations of virtual braid groups and virtual link groups, delving into their properties, structures, and connections to quantum topology.
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1 Lesons
44 minutes
On-Demand
Free-Video
QuantumTopology

On the Hurwitz Existence Problem for Branched Covers Between Surfaces

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Explore the Hurwitz existence problem for branched covers between surfaces, delving into mathematical concepts and theories related to topology and surface geometry.
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1 Lesons
42 minutes
On-Demand
Free-Video
QuantumTopology

Turaev Viro Invariants and Complexity of Virtual 3-Manifolds

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Explore Turaev-Viro invariants and their application in determining complexity of virtual 3-manifolds, advancing understanding in quantum topology and geometric structures.
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1 Lesons
46 minutes
On-Demand
Free-Video
QuantumTopology

Cocyclic Invariants of Knots

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Explore cocyclic invariants of knots, delving into advanced mathematical concepts and their applications in quantum topology.
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1 Lesons
1 hour 30 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Marzieh Forough: Lifts of Completely Positive Maps

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Explore the mathematical concept of lifts in completely positive maps, delving into advanced topics in quantum information theory and operator algebras.
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1 Lesons
48 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Some Remarks on Prismatic Cohomology of Rigid Spaces

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Explore advanced mathematical concepts with Peter Scholze as he delves into prismatic cohomology of rigid spaces, offering insights and observations on this complex topic.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Resolution of Singularities and the McKay Correspondence by Yukari Ito

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Explore resolution of singularities and McKay correspondence in algebraic geometry with Yukari Ito's insightful lecture, part of the inaugural Asian-Oceanian Women in Mathematics meeting.
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1 Lesons
32 minutes
On-Demand
Free-Video
IMSA

The Z-P-Equivariant Steenrod Algebra and Its Applications

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Explore recent advancements in Z/p-equivariant Steenrod algebra, including calculations of its dual with constant coefficients and applications to constructing Z/p-equivariant spectrum BPR at odd primes.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Hausdorff Center for Mathematics

Jason Miller- Conformal Removability of SLEκ for κ∈[4,8)

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Explores conformal removability of SLEκ curves, focusing on κ=4. Presents new conditions for conformal removability and discusses applications to SLEκ for κ∈(4,8). No prior SLE or LQG knowledge required.
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1 Lesons
44 minutes
On-Demand
Free-Video
IMSA

Josef Svoboda, University of Miami - Q-Series Invariants and Abelian Covers

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Explore q-series invariants of plumbed 3-manifolds, examining their behavior under abelian covers and deriving formulas for Seifert manifolds, with applications to vanishing results.
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1 Lesons
49 minutes
On-Demand
Free-Video
Fields Institute

Smooth Cartan Subalgebras and Lie Groupoid Twists

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Explore smooth Cartan subalgebras and Lie groupoid twists in this advanced mathematics talk by Anna Duwenig, delving into operator algebras and group actions.
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1 Lesons
50 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Universes in Set and Type Theory

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Explore universes in set and type theory, examining their foundations, structures, and applications in mathematical logic and computer science.
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1 Lesons
53 minutes
On-Demand
Free-Video
IMSA

On the Spectral Problem of a Three Term Difference Operator

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Explore the spectral problem of quantum mechanical operators in complex Planck's constant scenarios, focusing on toric Calabi-Yau threefolds and their implications.
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12 Lesons
53 minutes
On-Demand
Free-Video
IMSA

Poisson and Quantum Algebras of SL(n) Monodromies and Groupoid Action

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Explore Poisson and quantum algebras of SL(n) monodromies, delving into advanced mathematical concepts and their applications in theoretical physics and geometry.
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1 Lesons
1 hour 9 minutes
On-Demand
Free-Video
IMSA

Quantum Toric Geometry, Generalized Geometries & O-Minimality Conference

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Explore advanced mathematical concepts in quantum toric geometry, generalized geometries, and o-minimality with expert Carlos A. Ruiz from UNAM in this conference presentation.
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1 Lesons
52 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Categorical Landau Paradigm and the SymTFT - IPAM at UCLA

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Explore advanced concepts in quantum physics with Oxford researcher Sakura Schafer-Nameki, focusing on the Categorical Landau Paradigm and SymTFT in relation to quantum error correction and gravity.
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1 Lesons
53 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Introduction to Discrete Integrable Systems - Part 1

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Explore discrete integrable systems with Sanjay Ramassamy, covering fundamental concepts and applications in geometry and statistical mechanics. Gain insights into this advanced mathematical field.
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1 Lesons
1 hour 17 minutes
On-Demand
Free-Video
Insights into Mathematics

Inclusion-Exclusion via Multisets - Data Structures in Mathematics Math Foundations

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Explore inclusion/exclusion via multisets, expanding to integral multisets with negative multiplicities. Learn a conceptual approach to this fundamental Set Theory theorem and its applications.
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5 Lesons
48 minutes
On-Demand
Free-Video
IEEE

Indistinguishability Obfuscation from Well Founded Assumptions - Part 3

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Explore advanced cryptographic concepts like indistinguishability obfuscation, learning parity with noise, and structured seed PRGs. Delve into degree-2.5 integer PRGs and their applications in cryptography.
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18 Lesons
54 minutes
On-Demand
Free-Video
TheIACR

Statistical Concurrent Non-Malleable Zero Knowledge from One-Way Functions

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Explore advanced cryptographic concepts: statistical concurrent non-malleable zero-knowledge proofs derived from one-way functions in this concise theoretical presentation.
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1 Lesons
23 minutes
On-Demand
Free-Video