Institute for Pure & Applied Mathematics (IPAM) Courses

Large Deviations for Triangle Densities

Explore large deviations for triangle densities in graphs, including Borell's inequality, Gaussian noise stability, and applications to quantum ground states approximation.

• YouTube
• 28 minutes
• On-Demand
• Free Video

Volume of P-Zonoids and Inequalities for Determinants

Explore new inequalities for 2-zonoid volumes, potential extensions to p-zonoids, and related determinant inequalities. Delve into Minkowski sums, projections, and support functions in this advanced mathematics lecture.

• YouTube
• 27 minutes
• On-Demand
• Free Video

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

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.

• YouTube
• 24 minutes
• On-Demand
• Free Video

The Brownian Transport Map - IPAM at UCLA

Explore Lipschitz transport maps between probability measures, focusing on the Brownian transport map's construction, properties, and applications to Euclidean functional inequalities.

• YouTube
• 24 minutes
• On-Demand
• Free Video

Topological Properties of Hypersurfaces with Low Entropy - IPAM at UCLA

Explore topological properties of hypersurfaces with low entropy, focusing on Colding-Minicozzi entropy, mean curvature flow, and closed hypersurfaces in this advanced mathematics lecture.

• YouTube
• 22 minutes
• On-Demand
• Free Video

The Log-Minkowski Problem - IPAM at UCLA

Explore the log-Minkowski problem and recent progress in convex geometry, including uniqueness of self-similar solutions and isomorphic resolution, with applications to centro-affine differential geometry.

• YouTube
• 28 minutes
• On-Demand
• Free Video

Singularities and Diffeomorphism - IPAM at UCLA

Explore singularities and diffeomorphism in calculus of variations, covering special cases, classification, and applications in probability and geometry.

• YouTube
• 32 minutes
• On-Demand
• Free Video

Training Quantum Neural Networks with an Unbounded Loss Function - IPAM at UCLA

Explore quantum neural networks, unbounded loss functions, and techniques to overcome barren plateaus in quantum machine learning, with applications in thermal state and Hamiltonian learning.

• YouTube
• 32 minutes
• On-Demand
• Free Video

Quantum Approximate Optimization Algorithm and Local Max-Cut - IPAM at UCLA

Explore quantum optimization algorithms, focusing on QAOA's application to LocalMaxCut. Discover insights on quantum supremacy and the performance comparison between local algorithms and QAOA on various graph instances.

• YouTube
• 28 minutes
• On-Demand
• Free Video

Variational Quantum Architectures for Linear Algebra Applications

Explore variational quantum algorithms for linear algebra applications, including singular value decomposition, linear system solving, and generative models, with focus on NISQ-era implementations and real-world examples.

• YouTube
• 32 minutes
• On-Demand
• Free Video

Classical and Quantum Algorithms for Isogeny Problems

Explore classical and quantum algorithms for isogeny problems in post-quantum cryptography, focusing on computational challenges, path finding in isogeny graphs, and reductions to other problems in elliptic curve cryptography.

• YouTube
• 36 minutes
• On-Demand
• Free Video

Heisenberg-Limited Ground State Energy Estimation for Early Fault-Tolerant Quantum Computers

Explore Heisenberg-limited ground state energy estimation for early fault-tolerant quantum computers, featuring a simplified circuit and classical post-processing for improved efficiency.

• YouTube
• 33 minutes
• On-Demand
• Free Video

Sophia Economou - Problem-Tailored Variational Quantum Algorithms - IPAM at UCLA

Explore problem-tailored variational quantum algorithms, including symmetry-preserving circuits, ADAPT-VQE, and ctrl-VQE, for improved performance in quantum simulations.

• YouTube
• 40 minutes
• On-Demand
• Free Video

Arithmetic Tensor Networks and Integration - IPAM at UCLA

Explore arithmetic tensor networks and their applications in function integration, with insights on exact and approximate contraction methods and their implications for various mathematical problems.

• YouTube
• 32 minutes
• On-Demand
• Free Video

Optimal Scaling Quantum Linear Systems Solver via Discrete Adiabatic Theorem

Explore optimal quantum linear systems solver using discrete adiabatic theorem, achieving linear complexity in condition number and precision, with simplified implementation and constant factor analysis.

• YouTube
• 41 minutes
• On-Demand
• Free Video