Simons Foundation Courses

Joint Moments of Characteristic Polynomials and the Riemann Zeta-Function

Explore joint moments of characteristic polynomials in random unitary matrices and their connection to Riemann zeta-function derivatives on the critical line.

• YouTube
• 1 hour
• Self-Paced
• Free Video

The Square of the Riemann Zeta Function Gives Rise to Critical Multiplicative Chaos

Explore the connection between the Riemann zeta function's square and critical multiplicative chaos, revealing deep links between random measures and number theory through recent conjecture proofs.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Optimization Problems for Multiplicative Functions

Explore optimization problems for multiplicative functions in number theory, including explicit bounds and improved uniformity in Halasz's theorem applications.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Factoring Random Integers

Explore advanced number theory as Koukoulopoulos presents breakthrough research on prime factorization patterns, proving Arratia's conjecture about Poisson-Dirichlet distributions.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

Prime Detecting Sieves

Explore advanced mathematical techniques for understanding prime number distribution patterns and global obstructions in number theory with expert insights from ongoing research.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Prime Number Models - Beyond Cramer and Gallagher

Explore advanced probabilistic models for prime numbers, connecting Hardy-Littlewood conjectures, short interval distributions, and Dirichlet L-functions.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

A Refined Random Matrix Model for Function Field L-functions

Explore a refined random matrix model combining Steinhaus multiplicative functions to predict function field L-function statistics and validate theoretical moment calculations.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Moments of One-Level Densities for a Large Orthogonal Family of L-functions

Explore advanced number theory connecting L-function statistics with random matrix theory, verifying Katz-Sarnak conjecture for orthogonal families of holomorphic Hecke newforms.

• YouTube
• 57 minutes
• Self-Paced
• Free Video

Emergent Phenomena Under Pressure - From Hydrogen to Hot Superconductors

Explore quantum phenomena and superconductivity breakthroughs under high-pressure conditions, from hydrogen systems to room-temperature applications in energy technologies.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

Where Did All the Dogs Come From? - Dogs, Ancestors, Breeds and Genomes

Explore canine evolution, genomics and genetics to understand how humans shaped dog breeds, disease susceptibility, and the striking differences in appearance and behavior between breeds.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

Experiments at the Interface of General Relativity and Quantum Mechanics

Explore groundbreaking experiments bridging general relativity and quantum mechanics through clock interferometry, equivalence principle tests, and nano-diamond studies.

• YouTube
• 22 minutes
• Self-Paced
• Free Video

A New Look at Mössbauer Spectroscopy for Fundamental Physics and Nuclear Quantum Optics

Explore novel Mossbauer spectroscopy techniques for detecting new physics interactions at sub-micrometer scales using nuclear sensors and quantum optics advances.

• YouTube
• 20 minutes
• Self-Paced
• Free Video

Testing Atom Charge Neutrality with Atom Interferometry

Explore quantum testing of electron-proton charge equality using atom interferometry, potentially improving sensitivity by orders of magnitude beyond current limits.

• YouTube
• 20 minutes
• Self-Paced
• Free Video

Why Axions Could Be the Next Big Discovery in Physics

Discover why axions could revolutionize physics as compelling dark matter candidates and solutions to quantum chromodynamics problems, with insights into detection experiments.

• YouTube
• 19 minutes
• Self-Paced
• Free Video

CP Violation in Ultracold FrAg

Explore CP violation research using ultracold FrAg molecules to understand why matter exists in the universe through innovative table-top experiments.

• YouTube
• 18 minutes
• Self-Paced
• Free Video