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#Discrete Geometry

Showing: 26 courses
Applied Algebraic Topology Network

Convex Sunflower Theorems and Neural Codes

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Explore convex sunflower theorems and neural codes, connecting neuroscience with discrete geometry to understand place cell encoding and cognitive mapping in rat hippocampus.
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19 Lesons
58 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Discrete Charm of Geometry by Alexander Bobenko

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Explore the fascinating world of discrete geometry and its applications in architecture, computer graphics, and physics. Discover structure-preserving discretizations through simple examples and stunning visuals.
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23 Lesons
1 hour 36 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Topological Methods in Discrete Geometry - New Developments

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Explores recent advancements in topological methods for discrete geometry, focusing on configuration spaces in cooperative game theory and their connections to embedding problems in Euclidean spaces.
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1 Lesons
42 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Rips Complexes, Projective Codes, and Zeros of Odd Maps

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Explore connections between Rips complexes, projective codes, and odd map zeros, bridging discrete geometry and topology. New insights into sphere Rips complexes' challenging nature.
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1 Lesons
50 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Discrete Minimizers of Energy Integrals

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Explore the intriguing phenomenon of discrete minimizers in energy integral optimization, its counterintuitive nature, and applications in various fields of mathematics and signal processing.
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1 Lesons
48 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
Simons Institute

Structure of Communication - Richard M. Karp Distinguished Lecture

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Explore communication complexity, its applications, and structural conjectures in theoretical computer science with Shachar Lovett. Gain insights into efficient communication and its connections to various mathematical domains.
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1 Lesons
1 hour
On-Demand
Free-Video
Applied Algebraic Topology Network

Topological Methods in Discrete Geometry

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Explore topological applications in discrete geometry, focusing on mass partitions and Helly-type theorems. Learn about classical results and recent generalizations in these areas.
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1 Lesons
58 minutes
On-Demand
Free-Video
IMSA

Combinatorial Geometry Workshop - Lecture by Dasha Poliakova

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Explore combinatorial geometry in this workshop, delving into advanced concepts and techniques with expert guidance from Dasha Poliakova of SDU Denmark.
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1 Lesons
44 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Dimers and M-curves: Limit Shapes from Riemann Surfaces

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Explore dimer models, M-curves, and limit shapes through algebraic geometry, integrating Riemann surfaces and Schottky uniformization. Gain insights into statistical mechanics and discrete geometry.
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1 Lesons
53 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Incidences and Dimers in Projective Geometry - Statistical Mechanics and Discrete Geometry

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Explore the connection between linear incidence theorems in projective geometry and bipartite graphs on surfaces, incorporating dimer model dynamics to derive dynamic linear incidence theorems.
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1 Lesons
48 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Random Matrix Statistics in the Uniform Spanning Tree

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Explore random matrix statistics in uniform spanning trees, focusing on branch behavior, scaling limits, and connections to Dyson Brownian motion and Loewner evolution.
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1 Lesons
51 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Superport Networks: Generalizing Kirchhoff's Matrix-Tree Theorem

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Exploration of multiport networks, generalizing Kirchhoff's theorem with novel mathematical approaches. Insights into electrical engineering applications and superport network theory.
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1 Lesons
49 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Geometric Objects Associated to Planar Bipartite Graphs

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Explore topological and geometric data associated with planar bipartite graphs, including knots, cluster varieties, and critical varieties, and their interconnections.
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1 Lesons
50 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Planar Site Percolation via Tree Embeddings

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Explore planar site percolation and tree embeddings in infinite graphs. Discover novel proofs for Bernoulli percolation and confirm a 1996 conjecture by Benjamini and Schramm.
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1 Lesons
45 minutes
On-Demand
Free-Video
NCCR SwissMAP

Orthogonal Ring Patterns and Discrete Surfaces

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Explore orthogonal ring patterns and discrete surfaces in integrable systems, focusing on applications in condensed matter physics and quantum field theory.
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1 Lesons
55 minutes
On-Demand
Free-Video
BIMSA

Two Geometric Applications of the Linear Algebra Method

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Explore geometric applications of linear algebra with János Pach, covering discrete geometry, convexity, and combinatorics in this research seminar.
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1 Lesons
1 hour
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

S-embeddings and Discrete Maximal Lorentz Surfaces

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Explore s-embeddings and discrete maximal Lorentz surfaces in this advanced mathematics talk, focusing on isothermic surfaces, mean curvature, and associated families in discrete geometry.
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1 Lesons
50 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Dimers on a Riemann Surface and Compactified Free Field

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Explore dimer models on Riemann surfaces, height function convergence, and connections to compactified free fields. Gain insights into probabilistic methods and discrete complex analysis in statistical mechanics.
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1 Lesons
47 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

On Pfaffians in Spin Models

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Explore Pfaffian relations in spin models, focusing on Ising models on planar graphs and their correlation functions. Discover insights into ferromagnetic spin models and graph simplifications.
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1 Lesons
49 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Bulk Scaling Limits in Free Boundary Schur Process

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Exploring correlation functions and bulk scaling limits in free boundary Schur process, with insights on new deformations of universal distributions in statistical mechanics.
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1 Lesons
52 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Geometry of the Doubly Periodic Aztec Dimer Model

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Explore the geometry of the doubly periodic Aztec diamond dimer model, including arctic curves, amoeba, and local fluctuations in statistical mechanics and discrete geometry.
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1 Lesons
50 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

The Multinomial Dimer Model - Statistical Mechanics and Discrete Geometry

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Explore the multinomial dimer model's limit shape theory, bistochastic gauge, and 3D Aztec diamond applications in statistical mechanics and discrete geometry.
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1 Lesons
48 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Spectrum of the Ising Model

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Explore the correspondence between Ising models and algebro-geometric data, extending Kenyon and Okounkov's work on dimer models and Harnack curves in this advanced mathematical presentation.
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1 Lesons
46 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Minimal Bipartite Dimers and Maximal Riemann Surfaces

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Exploration of critical weights for dimer models on isoradial graphs, extending Kenyon's results using theta functions on maximal Riemann surfaces, with applications to spectral theorems and Laplacians.
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1 Lesons
52 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Causal Set Kinematics: Reconstructing Spacetime Geometry from Random Posets

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Explore causal set quantum gravity, reconstructing spacetime geometry from random posets. Learn dimension estimation, topology, and geometric invariants in discrete orders.
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16 Lesons
45 minutes
On-Demand
Free-Video