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#Topological Invariants

Showing: 28 courses
University of Chicago Department of Mathematics

Symmetries, Anomalies and Anomaly Inflow in Physics and Mathematics

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Explore symmetries in physics, quantum effects, and their mathematical connections in this insightful colloquium by Jeff Harvey on "Symmetries, Anomalies and Anomaly Inflow".
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1 Lesons
55 minutes
On-Demand
Free-Video
Institute for Advanced Study

The Shapes of Spaces and the Nuclear Force - Gregory Moore

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Explores the interplay between physics and mathematics, focusing on topological concepts and their applications in understanding fundamental forces and the structure of space.
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23 Lesons
41 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Marian Mrozek - Combinatorial vs. Classical Dynamics: Recurrence

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Explore combinatorial dynamics in data science, its ties to classical dynamics, and applications in computer-assisted proofs. Learn about topological invariants and recent developments in recurrent behavior analysis.
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15 Lesons
50 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Intrinsic Topological Transforms via the Distance Kernel Embedding

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Explore topological transforms for abstract metric spaces using distance kernel embedding, combining persistent homology with Euclidean embeddings for enhanced shape analysis and discrimination.
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8 Lesons
32 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Sheaves as Computable and Stable Topological Invariants for Datasets

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Explores sheaf theory in topological data analysis, connecting level-sets persistence with derived sheaves. Presents functorial equivalences, stability theorems, and barcode decompositions for continuous data analysis.
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14 Lesons
23 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Tomoo Yokoyama - Generalizations of Morse Graph of Flows and Reeb Graph of Hamiltonian Flows

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Generalizations of Morse and Reeb graphs for flows, exploring connections between dynamical systems, topological structures, and abstract orbit spaces. Insights into Conley theory and topological invariants.
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14 Lesons
28 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Takashi Owada - Limit Theorems for Topological Invariants of the Dynamic Multi-Parameter Simplicial Complex

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Explore topological invariants in dynamic multi-parameter simplicial complexes, covering connectivity, probability, and limiting processes in applied algebraic topology.
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15 Lesons
28 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

An Application of Neighborhoods in Directed Graphs in the Classification of Binary Dynamics

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Explore graph theory applications in classifying binary dynamics, focusing on vertex neighborhoods and their use in analyzing neuronal network activity, with insights from the Blue Brain Project.
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19 Lesons
55 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Persistent Stiefel-Whitney Classes

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Explore persistent Stiefel-Whitney classes in topological data analysis, extending beyond homology groups to estimate vector bundle structures from finite samples using a persistent approach.
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1 Lesons
1 hour
On-Demand
Free-Video
IMSA

Topological Invariants of Compact Singular Varieties

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Explore topological invariants of compact singular varieties with José Seade from UNAM. Gain insights into advanced mathematical concepts and their applications in algebraic geometry.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
IMSA

Extensions in MHM and Hain's Biextension Line Bundle - Part 1

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Explore complex manifolds, biextension line bundles, and normal functions in algebraic geometry. Discover formulas for Q-line bundle extensions and their topological invariants.
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1 Lesons
49 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Topological and Combinatorial Models of Directed Path Spaces

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Explore topological and combinatorial models for directed path spaces in concurrency theory, focusing on methods to analyze execution paths and state spaces in computer science.
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1 Lesons
1 hour 25 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Topological Invariants Arising in Geometry by Jaya N Iyer

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Explore topological invariants in geometry with Jaya N Iyer. This talk delves into advanced mathematical concepts, offering insights for researchers and enthusiasts in the field.
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1 Lesons
35 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Chern-Simons Field Theory Invariants by Pichai Ramadevi

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Explore knots, links, and three-manifolds through Chern-Simons field theory. Discover recent developments in knot-quiver correspondence and new Zhat invariants for three-manifolds.
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1 Lesons
1 hour 34 minutes
On-Demand
Free-Video
ICTP-SAIFR

Unification of Topological Invariants and Topological Markers

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Explore topological invariants and markers in quantum materials, unifying concepts through wrapping numbers and quantum metrics. Apply to 1D and 2D systems.
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12 Lesons
42 minutes
On-Demand
Free-Video
Dublin Institute for Advanced Studies DIAS

Learning 4-Dimensional Knot Invariants from the Jones Polynomial

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Explore machine learning techniques in knot theory, focusing on learning 4D topological invariants from the Jones polynomial and their implications for understanding knot structures.
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1 Lesons
1 hour 48 minutes
On-Demand
Free-Video
Wolfram

Using Graph Rewriting to Study Discrete Lattice Systems - Wolfram Student Podcast Episode 3

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Explore graph rewriting techniques for studying topological invariants in finite lattice systems and their applications to physical phenomena.
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1 Lesons
35 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

Flops and Hilbert Scheme of Space Curve Singularities

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Explore pagoda flop transitions and their application in deriving explicit results for topological invariants of Hilbert schemes of space curve singularities.
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1 Lesons
1 hour 22 minutes
On-Demand
Free-Video
Global Noncommutative Geometry Seminar

Axion Insulators and Their Topological Invariants

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Explore axion insulators and their topological invariants with Bernardo Uribe, delving into advanced concepts in noncommutative geometry and condensed matter physics.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Topological Invariants of Gapped States and 't Hooft Anomalies

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Explore topological invariants of gapped ground-states in lattice systems, their interpretation as obstructions to gauging, and the role of locality in infinite-volume systems with rapidly decaying interactions.
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1 Lesons
1 hour
On-Demand
Free-Video
BIMSA

Operator Algebras, Bi-Unitary Connections and Tensor Networks - Lecture 4

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Explore tensor categories as quantum symmetries, using Jones subfactor theory and bi-unitary connections to study 2D topological order and tensor networks.
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1 Lesons
1 hour 43 minutes
On-Demand
Free-Video
BIMSA

Operator Algebras, Bi-Unitary Connections and Tensor Networks - Lecture 2

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Explore tensor categories as quantum symmetries, using Jones subfactor theory and bi-unitary connections to study 2D topological order and tensor networks.
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1 Lesons
1 hour 42 minutes
On-Demand
Free-Video
BIMSA

Operator Algebras, Bi-Unitary Connections and Tensor Networks - Lecture 1

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Explore tensor categories as quantum symmetries, using Jones subfactor theory and bi-unitary connections to study 2D topological order and tensor networks.
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1 Lesons
1 hour 36 minutes
On-Demand
Free-Video
Centre for Quantum Technologies

Topology in Time-Evolving Quantum Systems

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Delve into quantum topology's dynamic nature, exploring how symmetry changes affect topological invariants in non-equilibrium systems through experimental studies with ultracold atomic BEC in 1D lattices.
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1 Lesons
57 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Topology and the Electromagnetic Responses of Quantum Materials

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Explore electromagnetic responses in quantum materials, focusing on topological insulators, Weyl semimetals, and quantized effects. Gain insights into Berry phases, anomalous Hall effect, and circular photogalvanic effect.
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28 Lesons
30 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

TQFTs from Non-Semisimple Modular Categories and Modified Traces - Marco de Renzi

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Explore non-semisimple TQFTs and modified traces in topology, focusing on construction methods, invariants, and mapping class group representations derived from modular categories.
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1 Lesons
1 hour 9 minutes
On-Demand
Free-Video
Bogolyubov Institute for Theoretical Physics

Методи виявлення топологічних інваріантів у кристалічних ізоляторах

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Дослідіть методи виявлення та аналізу топологічних інваріантів у кристалічних ізоляторах через поглиблений теоретичний семінар для фізиків-дослідників та аспірантів.
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1 Lesons
1 hour 41 minutes
On-Demand
Free-Video
Joint Mathematics Meetings

Smooth Invariants of Four-dimensional Manifolds and Quantum Field Theory

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Explore the intersection of smooth 4D manifold invariants and quantum field theory, focusing on Yang-Mills theory, instantons, and topological invariants in this advanced mathematics lecture.
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24 Lesons
48 minutes
On-Demand
Free-Video