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#Polytopes

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Fields Institute

Certain Polytopes Associated to Algebraic Integer Conjugates

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Explore the fascinating world of algebraic number theory in this 40-minute Fields Number Theory Seminar presented by Samprit Ghosh from the University of Calgary. Delve into the intriguing relationship between certain polytopes and algebraic integer conj…
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1 Lesons
40 minutes
On-Demand
Free-Video
Institute for Advanced Study

Spacetime and Quantum Mechanics; Particles and Strings; Polytopes, Binary Geometries and Quiver Categories - Nima Arkani-Hamed

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Explore connections between particle physics and mathematics, revealing how spacetime and quantum mechanics emerge from fundamental mathematical structures in combinatorics, algebra, and geometry.
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22 Lesons
1 hour 18 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Cynthia Vinzant - Log Concave Polynomials and Matroids

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Explore strong log concavity in polynomials, its applications to matroids, and connections to combinatorics and geometry. Learn about recent developments and their implications.
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8 Lesons
58 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Tropical Solutions to Hard Problems in Auction Theory

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Explore tropical mathematics' applications in auction theory, neural networks, and statistics through polytopes, algorithms, and semigroup matrices, unveiling powerful problem-solving techniques.
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10 Lesons
51 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

José Samper Seminar - Higher Chordality

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Explore higher chordality in algebraic topology, covering community algebra, linear resolution, graphs, polytopes, and complex links. Gain insights into advanced mathematical concepts.
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14 Lesons
57 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Structured ML Training via Conditional Gradients

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Explore conditional gradient methods for structured optimization in machine learning, covering applications in traditional and deep learning, with a focus on incorporating polyhedral structures into solutions.
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1 Lesons
24 minutes
On-Demand
Free-Video
International Mathematical Union

Joel Kamnitzer- Perfect Bases in Representation Theory- Three Mountains and Their Springs

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Exploration of perfect bases in representation theory, examining three approaches and their combinatorial implications for tensor product multiplicities in semisimple groups.
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1 Lesons
41 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Polyhedral Geometry of Pivot Rules

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Explore the geometric perspective on pivot rules in linear programming, connecting polyhedra, simplex methods, and arborescences to gain insights into optimization algorithms.
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1 Lesons
30 minutes
On-Demand
Free-Video
Insights into Mathematics

Rational Curvature of a Polytope - Algebraic Topology Lecture 15

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Introduces a new rational definition of polytope curvature, using turn-angle to connect curvature with Euler number. Explores opposite cones and applies Harriot's theorem on spherical triangles.
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1 Lesons
50 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Sums of Weighted Lattice Points of Polytopes

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Explore connections between polytopes and algebraic combinatorics, focusing on sums of weighted lattice points and their computational implications in estimating maximal weighted lattice points.
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1 Lesons
53 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
Fields Institute

Cohomology and Geometric Quantization of Toric Manifolds

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Explore cohomology and geometric quantization in toric manifolds with expert Lisa Jeffrey, delving into advanced mathematical concepts and their applications in toric topology.
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1 Lesons
52 minutes
On-Demand
Free-Video
Fields Institute

Symplectic Quotient Construction of Toric Manifolds

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Explore symplectic quotient construction in toric manifolds with Lisa Jeffrey, delving into advanced mathematical concepts and their applications in toric topology.
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1 Lesons
42 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Realization Spaces of Polytopes and Oriented Matroids

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Explore realization spaces of polytopes and oriented matroids in this advanced mathematical lecture by Arnau Padrol at CIRM's thematic meeting.
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1 Lesons
59 minutes
On-Demand
Free-Video
Institute for Advanced Study

The Realization Space of a Matroid

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Explore the intricacies of matroid realization spaces with Lukas Kühne, delving into advanced mathematical concepts and their applications in combinatorial geometry.
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1 Lesons
18 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Gromov's Rigidity Theorem for Polytopes with Acute Angles

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Explore recent developments in dihedral rigidity, focusing on Gromov's conjecture and Brendle-Wang's alternative smoothing construction for polytopes with acute angles.
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1 Lesons
59 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Scalar Curvature Rigidity of Polytopes

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Explore Riemannian metrics and scalar curvature positivity in differential geometry. Delve into Gromov's comparison principle for polytopes and recent advancements in verifying his conjecture.
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1 Lesons
58 minutes
On-Demand
Free-Video
Uncertainty in Artificial Intelligence

Is the Volume of a Credal Set a Good Measure for Epistemic Uncertainty - UAI 2023 Oral Session 2

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Explore the effectiveness of credal set volume as a measure of epistemic uncertainty in binary and multi-class classification, highlighting implications for machine learning.
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1 Lesons
25 minutes
On-Demand
Free-Video
Centre for Networked Intelligence, IISc

Random Separating Hyperplane Theorem and Learning Polytopes

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Delve into advanced mathematical concepts of hyperplane theorem, polytope learning, and optimization oracles with applications in machine learning's hidden variable problems.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Extension Complexity of Random Polytopes

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Explores extension complexity of random polytopes, discussing results for fixed-dimension convex hulls of random points on unit sphere or ball. Joint work with Kwan and Zhao.
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1 Lesons
46 minutes
On-Demand
Free-Video
ACM SIGPLAN

ReLU Hull Approximation - Fast and Precise Convex Hull Over-Approximation for Neural Network Verification

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Explore a fast, precise approach to over-approximating ReLU function convex hulls in neural network verification, improving efficiency and precision for large-scale networks.
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1 Lesons
18 minutes
On-Demand
Free-Video
Joint Mathematics Meetings

Proving Analytic Inequalities

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Explore advanced mathematical concepts with Avi Wigderson as he delves into proving analytic inequalities, covering Cauchy-Schwarz, Loomis-Whitney, and Young inequalities.
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18 Lesons
54 minutes
On-Demand
Free-Video
Joint Mathematics Meetings

Algebraic Structures on Polytopes

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Explore algebraic structures on polytopes, delving into combinatorics, Hopf monoids, and generalized permutahedra. Gain insights into mathematical applications and current research directions.
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24 Lesons
58 minutes
On-Demand
Free-Video
NCCR SwissMAP

A Tale of Two Polytopes Related to Geodesic Flows on Spheres

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Explore finite dimensional integrability in mathematical physics through geodesic flows on spheres, focusing on two related polytopes.
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1 Lesons
49 minutes
On-Demand
Free-Video
Institute for Advanced Study

Derived Categories of the Permutahedral Varieties

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Delve into the geometric and combinatorial analysis of derived categories in toric varieties, exploring permutahedron's role in matroid theory through convex-geometric approaches.
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1 Lesons
55 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Taxonomy of Infinite Distance Limits in Quantum Gravity Moduli Spaces

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Explore geometric classification of light towers in quantum gravity moduli spaces, examining constraints, evidence, and applications in infinite-distance limits.
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1 Lesons
33 minutes
On-Demand
Free-Video