Institute for Advanced Study Courses

Exceptional Splitting of Reductions of Abelian Surfaces With Real Multiplication - Yunqing Tang

Explore real multiplication in abelian surfaces, focusing on exceptional splitting of reductions. Delve into simple reduction, finite extension, and density zero concepts with insights on special devices and intersection numbers.

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

A Derived Hecke Algebra in the Context of the Mod P Langlands Program - Rachel Ollivier

Explore derived Hecke algebras in mod p Langlands program, covering super singular modules, involution, trace maps, and twisted duals with Rachel Ollivier.

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

Weinstein Manifolds Through Skeletal Topology - Laura Starkston

Explore skeletal topology's role in understanding Weinstein manifolds, focusing on arboreal singularities, Fukaya categories, and stratification of skeletons in symplectic geometry.

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

New Experimental Directions for Fundamental Physics II - Peter Graham

Explore cutting-edge experimental approaches in fundamental physics, focusing on innovative techniques and their potential to advance our understanding of particle physics beyond the LHC.

• YouTube
• 1 hour 36 minutes
• Self-Paced
• Free Video

New Physics at the LHC and Beyond I - Liantao Wang

Explore cutting-edge particle physics research at the LHC, including luminosity, hadron colliders, and factorization. Gain insights into new physics prospects and theoretical advancements in the field.

• YouTube
• 1 hour 31 minutes
• Self-Paced
• Free Video

New Approaches to the Hierarchy Problem I - Nathaniel Craig

Explore innovative approaches to the hierarchy problem in particle physics, focusing on technical and direct naturalness, effective field theory, and their implications for the Standard Model.

• YouTube
• 1 hour 34 minutes
• Self-Paced
• Free Video

Extraordinary Physics with Millisecond Pulsars - Scott Ransom

Explore millisecond pulsars' role in detecting gravitational waves, testing general relativity, and understanding dense matter, using advanced timing observations and cutting-edge telescopes.

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

The Polynomial Method and the Restriction Problem - Larry Guth

Explore the polynomial method and restriction problem in mathematics, featuring insights on visualizing concepts, analyzing proofs, and examining algebraic potential.

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

Math in the Real World - More Than Just a Numbers Game

Explore how mathematics shapes product lifecycles and impacts modern careers, with insights from industry leaders on its role in R&D, manufacturing, marketing, and supply chain.

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

Sovereign Power, Death, and Monuments - Zainab Bahrani

Explores ancient Mesopotamian monuments, examining their timeless significance in relation to law, sovereign power, and biopolitics through archaeological analysis and critical theory perspectives.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Theoretical physicist Robbert Dijkgraaf explores how physicists are striving for the long-sought unification of quantum mechanics and general relativity, with string theory being a leading contender.

• World Science U
• Self-Paced
• Free Online Course

Topological Bound for Tropical Varieties

Delve into advanced tropical geometry concepts, exploring non-planar tropical curves, topological bounds, and Floor composition methods for understanding Betti numbers in various dimensions.

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

Beyond the g-Conjecture in Combinatorial Mathematics

Delve into McMullen's g-conjecture, its historical significance, and recent breakthroughs in combinatorics, including the 2020 proof involving anisotropy of quadratic forms in characteristic 2.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Three Proofs of the Reverse Khovanskii-Teissier Inequality

Delve into three distinct mathematical approaches proving the reverse Khovanskii-Teissier inequality, exploring analytic, algebraic, and convex geometric perspectives in advanced geometry.

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

Invariants of Lattice Polytopes and Matroids

Delve into advanced mathematical concepts exploring invariants of lattice polytopes, subdivisions, and their connections to Ehrhart theory, Hodge theory, and matroid theory enrichments.

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