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#Homotopy Theory

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Institute for Advanced Study

Lie Algebras and Homotopy Theory - Jacob Lurie

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Explore connections between Lie algebras and homotopy theory, covering fundamental groups, Whitehead brackets, and Quillen's theorem in this advanced mathematics seminar.
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18 Lesons
1 hour 1 minute
On-Demand
Free-Video
Institute for Advanced Study

Univalence from a Computer Science Point-of-View - Dan Licata

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Explore univalence in computer science with Dan Licata, covering Martin-Löf type theory, computation, and applications in homotopy theory and group structures.
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23 Lesons
56 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

René Thom and Semantic Information - Exploring Mathematical Approaches to Meaning

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Explore René Thom's ideas on semantic information, extending beyond Shannon's statistical theory to topological dynamics and singularity theory applications in biology, linguistics, and philosophy.
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1 Lesons
1 hour 9 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Invariants for Tame Parametrised Chain Complexes

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Explore invariants for tame parametrised chain complexes in applied algebraic topology, focusing on explicit constructions, comprehensive frameworks, and discriminative power in topological data analysis.
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13 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Star Clusters in Clique Complexes and the Vietoris-Rips Complex of Planar Sets

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Explore star clusters in simplicial complexes and their applications to independence complexes and Vietoris-Rips complexes of planar sets, with insights on homotopy information and related conjectures.
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11 Lesons
50 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Vietoris-Rips Thickenings - Problems for Birds and Frogs

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Explore open problems in Vietoris-Rips complexes, connecting diverse mathematical areas. Suitable for both broad theorists and problem-solving specialists in applied algebraic topology.
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1 Lesons
1 hour 18 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Cubespaces and Homotopy Theory

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Delve into advanced mathematical concepts exploring the intersection of cubespaces and homotopy theory, with insights from topological dynamics and ergodic theory applications.
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1 Lesons
53 minutes
On-Demand
Free-Video
IMSA

Wall Finiteness Obstruction for DG Categories II

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Exploration of Wall finiteness obstruction theorem for DG categories, including applications to phantom DG categories and derived categories of algebraic varieties. Discusses extensions to algebras over DG operads.
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14 Lesons
1 hour
On-Demand
Free-Video
Applied Algebraic Topology Network

Wojciech Chachólski - TDA Invariants and Model Categories

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Exploring TDA invariants and model categories in data analysis, focusing on simplification techniques from homotopy theory to extract meaningful summaries while balancing information retention.
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8 Lesons
54 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Basic Homotopy Theory by Samik Basu

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Explore fundamental concepts in homotopy theory, including maps, CW complexes, equivalences, and fibrations. Gain insights into key computations and sequences in this foundational area of topology.
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10 Lesons
56 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

The Transfer in Algebraic K-Theory and THH

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Explore algebraic K-theory transfers, their applications in A-theory, and connections to THH. Gain insights into fundamental questions and trace methods in this advanced mathematics lecture.
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13 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Fields Institute

Artin Reciprocity via Spheres

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Explore Artin reciprocity through spheres, covering functionality, logical construction, global fields, spectra, and K theory in this advanced mathematics lecture.
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11 Lesons
46 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Homotopic Distance and Generalized Motion Planning

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Explore homotopic distance between maps, unifying Lusternik-Schnirelmann category and topological complexity. Learn how Morse-Bott functions and navigation functions apply to generalized motion planning problems.
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1 Lesons
41 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Homotopy Types of Vietoris–Rips Complexes of Metric Gluings

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Explore homotopy types of Vietoris-Rips complexes in metric wedge sums and gluings, with applications to persistent homology of metric graphs and insights into open research directions.
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1 Lesons
1 hour 11 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

A Counter-Example to Hausmann's Conjecture

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Explore a counter-example to Hausmann's conjecture on Vietoris-Rips complexes, challenging long-held beliefs in algebraic topology using persistent homology.
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1 Lesons
53 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Persistent Homotopy Groups of Metric Spaces

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Exploring persistent homotopy groups of metric spaces, blending topology and geometry to capture dataset features beyond persistent homology, with applications and stability properties.
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1 Lesons
1 hour
On-Demand
Free-Video
International Mathematical Union

Motivic Cohomology - Past, Present and Future

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Explore motivic cohomology's evolution, recent developments, and future prospects in algebraic geometry, including cycles with modulus and Chow-Witt theory.
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1 Lesons
45 minutes
On-Demand
Free-Video
ICTP Mathematics

Topology - Lecture 13

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Explore advanced concepts in topology, including complex geometric structures and their properties, in this comprehensive lecture by mathematician Bruno Zimmerman.
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1 Lesons
1 hour 33 minutes
On-Demand
Free-Video
ICTP Mathematics

Topology - Lecture 20

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Explore advanced concepts in topology, including complex mathematical structures and their properties, in this comprehensive lecture by Bruno Zimmerman.
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1 Lesons
1 hour 38 minutes
On-Demand
Free-Video
ICTP Mathematics

Topology - Lecture 12

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Explore advanced concepts in topology, including complex geometric structures and their properties, in this comprehensive lecture by mathematician Bruno Zimmerman.
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1 Lesons
1 hour 40 minutes
On-Demand
Free-Video
ICTP Mathematics

Topology - Lecture 16

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Explore advanced concepts in topology, including complex geometric structures and their properties, in this comprehensive lecture by mathematician Bruno Zimmerman.
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1 Lesons
1 hour 35 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Introduction to Chromatic Homotopy Theory - Lecture 3

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Explore chromatic homotopy theory's advanced concepts and applications in algebraic topology, building on previous lectures to deepen understanding of this complex mathematical field.
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1 Lesons
1 hour 27 minutes
On-Demand
Free-Video
Fields Institute

Motivic Hochschild Homology Over Algebraically Closed Fields

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Explore Hochschild homology in motivic spectra, uncovering torsion classes and connections to Steenrod algebra. Gain insights into algebraic geometry and homotopy theory applications.
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1 Lesons
33 minutes
On-Demand
Free-Video
Fields Institute

Detecting Non-Permutative Elements of K1-Var Using Point Counting

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Explore advanced algebraic geometry techniques for detecting non-permutative elements in K1(Var) through point counting methods, presented by Cornell University's Inna Zakharevich.
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1 Lesons
49 minutes
On-Demand
Free-Video
Fields Institute

Euler Classes, Pairings, and Duality

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Explore Euler classes in modules, their connection to Hochschild homology pairings, and implications for various forms of duality in homotopy theory and arithmetic geometry.
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1 Lesons
45 minutes
On-Demand
Free-Video
Fields Institute

Topological Cyclic Homology and the Fargues-Fontaine Curve

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Explore the connection between localizing invariants and the Fargues--Fontaine curve, with insights on K-theory, topological cyclic homology, and the twistor projective line.
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1 Lesons
48 minutes
On-Demand
Free-Video
Fields Institute

Yang-Baxter Elements and a New Proof of Homological Stability for the Mapping Class Group of Surfaces

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Explores Yang-Baxter elements in monoidal categories, introducing a novel approach to prove homological stability for surface mapping class groups using semi-simplicial sets and bimarked surfaces.
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1 Lesons
50 minutes
On-Demand
Free-Video
Fields Institute

Reflection

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Explore homotopy theory's applications in arithmetic and geometry with David Ayala's insightful conference talk, delving into the concept of reflection in mathematical contexts.
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1 Lesons
49 minutes
On-Demand
Free-Video
Fields Institute

Weights in Homotopy Theory

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Explore the concept of weights in homotopy theory, examining their applications and implications for arithmetic and geometric studies in mathematics.
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1 Lesons
46 minutes
On-Demand
Free-Video
Fields Institute

The Mod -p,v1- Motivic Filtration on the Topological Cyclic Homology of Topological K-Theory

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Explore the mod (p,v1) motivic filtration on topological cyclic homology of K-theory, delving into advanced concepts in homotopy theory and its applications to arithmetic and geometry.
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1 Lesons
25 minutes
On-Demand
Free-Video
Fields Institute

Syntomic Complexes

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Explore syntomic complexes in arithmetic and geometry with Akhil Mathew, delving into advanced mathematical concepts and their applications in homotopy theory.
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1 Lesons
46 minutes
On-Demand
Free-Video
Fields Institute

Slices of ΣnHZ over Q8

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Explore slices of ΣnHZ over Q8, delving into homotopy theory applications in arithmetic and geometry. Gain insights from expert Carissa Slone's research presentation.
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1 Lesons
26 minutes
On-Demand
Free-Video
IMSA

On the Second Homotopy Group of Spaces of Commuting Elements in Lie Groups

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Explore the computation of the second homotopy group of Hom(Z^n, G) spaces, focusing on compact Lie groups. Learn about geometric generators and specific results for simply connected, simple groups.
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1 Lesons
1 hour
On-Demand
Free-Video
International Centre for Theoretical Sciences

Introduction to Chromatic Homotopy Theory - Lecture 2

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Explore chromatic homotopy theory's foundations, techniques, and applications in algebraic topology. Delve into advanced concepts and their significance in modern mathematical research.
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1 Lesons
1 hour 17 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Introduction to Chromatic Homotopy Theory - Lecture 4

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Explore chromatic homotopy theory's advanced concepts and applications in algebraic topology, building on previous lectures to deepen understanding of this complex mathematical field.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Morava E-Theory - Prep 6

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Explore Morava E-Theory in algebraic topology, connecting concepts from commutative algebra and modular representation theory. Gain insights into duality phenomena and classification problems in tensor-triangulated categories.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
IMSA

Eugenia Ellis, Universidad de la República- Algebraic KK-Theory and the KH-Isomorphism Conjecture

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Explore the connection between Davis-Lück homology and equivariant algebraic kk-theory, examining the KH-isomorphism conjecture's assembly map through homotopy theory and adjointness theorems.
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1 Lesons
44 minutes
On-Demand
Free-Video
IMSA

Homotopy Theories of Coalgebras

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Explore homotopy theories of simplicial coalgebras, extending algebraic models for p-adic homotopy theory to include fundamental groups. Discover key ideas and potential G-equivariant analogs.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
IMSA

Equivariant A-Theory & Spaces of Equivariant H-Cobordisms

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Explore equivariant A-theory and h-cobordisms, focusing on Waldhausen's algebraic K-theory of manifolds and its role in classifying manifolds and diffeomorphisms.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
IMSA

How to Enhance Categories and Why - Localization and Homotopical Enhancement

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Exploring alternative techniques for enhancing localized categories using Grothendieck's derivator concept, offering a conceptually clearer approach than infinity-categories or quasicategories.
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1 Lesons
54 minutes
On-Demand
Free-Video
Fields Institute

TQFTs and the Renaissance of the Algebraic Topology of Manifolds

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Explore the resurgence of algebraic topology in manifold studies, focusing on Topological Quantum Field Theories and their impact on modern mathematical research.
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1 Lesons
43 minutes
On-Demand
Free-Video
Fields Institute

Two Problems in Toric Topology

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Explore two key problems in toric topology with Stephen Theriault, delving into advanced mathematical concepts and their implications for the field.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Fields Institute

Bordism of Derived Orbifolds - Lecture 3

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Explore advanced mathematical concepts in bordism theory and derived orbifolds with Stanford University expert Mohammed Abouzaid in this Fields Institute lecture.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Fields Institute

Homotopy Types of Toric Orbifolds from Weyl Polytopes

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Explore homotopy types of toric orbifolds derived from Weyl polytopes in this advanced mathematical talk, delving into complex geometric structures and their topological properties.
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1 Lesons
29 minutes
On-Demand
Free-Video
Fields Institute

Equivariant Formality of Isotropy Actions and Products of Spheres

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Explore equivariant formality in topology, focusing on isotropy actions and sphere products. Gain insights into advanced mathematical concepts and their applications in toric topology.
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1 Lesons
37 minutes
On-Demand
Free-Video
Fields Institute

Commutator Subgroups and Subalgebras in Toric Topology

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Explore commutator subgroups and subalgebras in toric topology with Fedor Vylegzhanin. Gain insights into advanced mathematical concepts and their applications in this specialized field.
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1 Lesons
31 minutes
On-Demand
Free-Video
Fields Institute

Steenrod Operations on Polyhedral Products

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Explore Steenrod operations on polyhedral products in this advanced mathematics talk, delving into toric topology and geometric structures.
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1 Lesons
53 minutes
On-Demand
Free-Video
Fields Institute

Bordism of Manifolds - Lecture 1

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Explore the concept of bordism in manifolds with Stanford's Mohammed Abouzaid, delving into advanced mathematical theories and their applications in topology and geometry.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Fields Institute

On Bar Constructions and Polyhedral Products

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Explore the intricate relationship between bar constructions and polyhedral products in this advanced mathematical talk, delving into toric topology and geometry concepts.
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1 Lesons
47 minutes
On-Demand
Free-Video
Fields Institute

Remarks on the Combinatorial Topology of Moment-Angle Complexes

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Explore combinatorial topology of moment-angle complexes with Sergio Chaves, delving into advanced mathematical concepts and their applications in toric topology and geometry.
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1 Lesons
41 minutes
On-Demand
Free-Video
Fields Institute

Homotopy Rigidity of Quasitoric Manifolds

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Explore homotopy rigidity in quasitoric manifolds, delving into advanced mathematical concepts and their applications in toric topology and geometry.
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1 Lesons
37 minutes
On-Demand
Free-Video
Fields Institute

Polyhedral Products in Motivic Homotopy Theory

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Explore polyhedral products in motivic homotopy theory, delving into advanced mathematical concepts and their applications in algebraic topology and geometry.
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1 Lesons
47 minutes
On-Demand
Free-Video
Fields Institute

Homotopy Types of Moment-Angle Complexes Associated to Almost Linear Resolutions

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Explore homotopy types of moment-angle complexes and their connection to almost linear resolutions in this advanced mathematical talk by Steven Amelotte.
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1 Lesons
50 minutes
On-Demand
Free-Video
Fields Institute

A Generalization of Polyhedral Products

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Explore advanced concepts in algebraic topology, focusing on a novel generalization of polyhedral products and their applications in toric topology and geometry.
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1 Lesons
52 minutes
On-Demand
Free-Video
Fields Institute

Desuspending the BBCG Homotopy Equivalence

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Explore advanced homotopy theory concepts, focusing on desuspending the BBCG homotopy equivalence, with expert Stephen Theriault in this graduate-level mathematics lecture.
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1 Lesons
1 hour
On-Demand
Free-Video
Fields Institute

Stable Splitting Theorem for Polyhedral Products

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Explore stable splitting theorem for polyhedral products in this advanced mathematics lecture, delving into toric topology and geometry concepts.
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1 Lesons
1 hour
On-Demand
Free-Video
Fields Institute

Properties of Polyhedral Products

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Explore properties of polyhedral products in this advanced mathematics lecture, covering key concepts and applications in toric topology and geometry.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Fields Institute

The Davis-Januszkiewicz Construction Reinterpreted and Generalized

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Explore a reinterpretation and generalization of the Davis-Januszkiewicz construction in toric topology, presented by Anthony Bahri from Rider University as part of the Graduate School on Toric Topology.
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1 Lesons
1 hour 21 minutes
On-Demand
Free-Video
Fields Institute

An Introduction to Polyhedral Products

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Explore the foundations of polyhedral products in this graduate-level lecture, covering key concepts and applications in toric topology and geometry.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

Condensed Thoughts - Topological Field Theories and Condensation

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Explore topological field theories, focusing on condensation in TQFTs and its relation to connectivity in homotopy types. Gain insights from recent research discussions.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Poincaré Duality Fibrations and Graph Complexes

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Explore Poincaré duality fibrations and graph complexes in advanced mathematics. Gain insights from Alexander Berglund's conference talk at CIRM's thematic meeting on higher algebra, geometry, and topology.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
NCCR SwissMAP

Rational Homotopy of Embedding Spaces - GrtQ and Unitrivalent Graphs

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Explore rational homotopy of embedding spaces, focusing on grtQ and unitrivalent graphs in this advanced mathematical lecture.
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1 Lesons
40 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

How Algebraic is a Stable Model Category?

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Explore the algebraic nature of stable model categories in this advanced mathematical discussion on chromatic homotopy and K-theory.
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1 Lesons
55 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Equivariant Elliptic Cohomology

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Explore equivariant elliptic cohomology, from motivations to applications in representation theory and global homotopy. Gain insights into elliptic curves, K-theory, and infinity rings.
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17 Lesons
1 hour 8 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Stable Cohomology of Automorphism Groups of Free Groups

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Explore stable cohomology of automorphism groups of free groups. Delve into advanced mathematical concepts with expert Christine Vespa in this in-depth conference talk.
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1 Lesons
1 hour 12 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

2-Categorical Constructions and Multiplicative Equivariant Barratt-Eccles Operad

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Explore (2)-categorical constructions and multiplicative equivariant Barratt theories in this advanced mathematics conference talk by Angélica M. Osorno.
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1 Lesons
59 minutes
On-Demand
Free-Video
Institut Henri Poincaré

Tropical Fukaya Algebras

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Explore multiple cut operations on symplectic manifolds and their impact on curve count-based invariants, focusing on Fukaya algebras and tropical graph representations.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Institut Henri Poincaré

Khovanov Homology and the Cinquefoil

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Explore Khovanov homology's detection of the (2,5) torus knot through advanced Floer homology and recent developments in knot theory.
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1 Lesons
59 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Prismatic Cohomology of Commutative Ring Spectra

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Explore motivic filtrations on trace invariants of commutative ring spectra and their extension to prismatic cohomology, as presented by Arpon Raksit from MIT.
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1 Lesons
1 hour 9 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

A Homotopical Approach to Crystalline Cohomology

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Explore a homotopical approach to crystalline cohomology, focusing on higher homotopies for canonical lifts and easier global definition through gluing.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Stony Brook Mathematics

Nonabelian Mixed Hodge Structures

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Explore nonabelian mixed Hodge structures, their relation to rational homotopy, and applications to character varieties and schematic homotopy types. Examine weights from noncompact bases and parabolic structures.
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1 Lesons
1 hour 38 minutes
On-Demand
Free-Video
Schmid College, Chapman University

Formalization of Infinity Category Theory

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Explore ∞-category theory's formalization, unifying mathematics, computer science, and physics. Learn synthetic reasoning and the Yoneda Lemma in this advanced mathematical seminar.
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1 Lesons
1 hour 51 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Stable Homotopy Groups, Higher Algebra, and the Telescope Conjecture

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Explore stable homotopy groups, spectra, and their applications in topology and geometry. Gain insights into fundamental concepts shaping modern algebraic topology and related fields.
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1 Lesons
1 hour 12 minutes
On-Demand
Free-Video
Banach Center

Cubespaces and Homotopy Theory

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Explore cubespaces and their connection to homotopy theory in this advanced mathematical lecture by Freddie Manners from UC San Diego.
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1 Lesons
53 minutes
On-Demand
Free-Video
BIMSA

Computing Differentials in the Adams Spectral Sequence and the Last Kervaire Invariant Problem

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Explore advanced methods for computing differentials in the Adams spectral sequence and uncover recent progress on the Last Kervaire Invariant Problem in dimension 126.
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1 Lesons
54 minutes
On-Demand
Free-Video
Big Ideas In Dynamics

Thurston's Asymmetric Metric on Teichmüller Space Revisited

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Explore Thurston's asymmetric metric on Teichmüller space and its generalizations to higher-rank Lie groups, examining geometric and dynamical invariants of hyperbolic structures.
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1 Lesons
1 hour
On-Demand
Free-Video
Western Hemisphere Virtual Symplectic Seminar

A Homotopical Description of Deligne-Mumford Compactifications

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Explore homotopical descriptions of Deligne-Mumford compactifications, their relation to GW invariants and Fukaya categories, and implications for symplectic cohomology.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Arthur Bartels: K-Theory of Group Rings

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Exploring the Farrell-Jones Conjecture's prediction of K-theory for group rings, focusing on controlled algebra as a bridge between algebraic formulation and geometric proofs.
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1 Lesons
58 minutes
On-Demand
Free-Video
Global Noncommutative Geometry Seminar

Coarse Homotopy Theory and K-Theory

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Explore coarse homotopy theory and K-theory with Ulrich Bunke, delving into advanced mathematical concepts in noncommutative geometry.
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1 Lesons
59 minutes
On-Demand
Free-Video
Fields Institute

Homotopical Foundations of Quantum Spin Systems

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Explore the mathematical foundations of quantum spin systems through homotopy theory, offering insights into non-commutative geometry and operator algebras in physics.
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1 Lesons
51 minutes
On-Demand
Free-Video
Prague Mathematical Physics Seminar

Category of Quantum L-infinity Algebras

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Explore quantum L-infinity algebras and their categorical structure in this advanced mathematical physics seminar by Martin Zika.
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1 Lesons
1 hour 21 minutes
On-Demand
Free-Video
Prague Mathematical Physics Seminar

Color Kinematics Duality and Homotopy Algebras

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Explore tree-level BCJ color-kinematics duality, double copy, and L-infinity algebras, advancing to loop-level duality and BV-box algebra applications in mathematical physics.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Applied Algebraic Topology Network

Sequential Topological Complexity of Group Homomorphisms

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Delve into advanced algebraic topology concepts, exploring sequential topological complexity of maps and group homomorphisms through detailed mathematical analysis and computations.
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1 Lesons
49 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Homotopy and Singular Homology Groups of Finite Digraphs

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Explore advanced algebraic topology concepts through the computation of homotopy and singular homology groups in finite directed graphs, with applications in data analysis and network science.
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1 Lesons
48 minutes
On-Demand
Free-Video