Hausdorff Center for Mathematics Courses

Stephan Stieberger - Single Valued Multiple Zeta Values and String Amplitudes

Explores the connection between real and complex iterated integrals in mathematics and their applications to open and closed string scattering amplitudes in physics, using single-valued projections.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Modular Graph Functions and Non Holomorphic Modular Forms

Explore non-holomorphic modular forms in string theory, their properties, and connections to mixed motives and L-functions. Gain insights into advanced mathematical concepts in physics.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

6j-Symbols for SL(2,C) Group and Feynman Diagrams

Explore 6j-symbols for SL(2,C) group using Feynman diagrams, deriving Racah coefficients for infinite-dimensional unitary principal series representations and expressing results as complex integrals or Mellin-Barnes type sums.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

Graphical Hyperlogarithms

Explore graphical hyperlogarithms, a generalization of iterated integrals related to cell zeta values. Learn about their graphical representation and coaction formula in subquotient graphs.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

The Galois Group of the Category of Mixed Hodge Tate Structures

Explore the Galois group of mixed Hodge-Tate structures, focusing on Tannakian formalism and the canonical description of the Hopf algebra in relation to graded comodules.

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

Michael Hoffman - Multiple Zeta Values and Alternating MZVs Arising From a Combinatorial Problem

Exploration of multiple zeta values and alternating MZVs stemming from a combinatorial problem, discussing formulas involving Euler polynomials and relations among alternating multiple zeta values.

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

Raf Bocklandt: Deforming Dimers

Explore deformation theory of dimer models, their relation to mirror symmetry for Riemann surfaces, and various aspects illustrated with examples.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

Automorphisms of Manifolds and the Farrell Jones Conjectures

Explores recent extensions of the Farrell-Jones Conjecture to Waldhausen's algebraic K-theory of spaces, examining implications for high-dimensional, closed, aspherical manifolds and their automorphism groups.

• YouTube
• 1 hour
• On-Demand
• Free Video

Algebraic vs. Topological K-Theory

Explore the comparison between algebraic and topological K-theory, focusing on specific rings and functional analytic applications in algebra, geometry, and number theory.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Algebraic vs Topological K-Theory - Lecture 1

Explore K-theory's applications in algebra, geometry, and number theory, comparing algebraic and topological K-theory for functional analytic rings and continuous function rings.

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

On Excision in Algebraic K-Theory

Explore advanced algebraic K-theory concepts, focusing on Suslin's excision theorem for Tor-unital rings and its extension to connective ring spectra and localizing invariants.

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

Motivic Eisenstein Cohomology, P-Adic Interpolation and Applications

Explore motivic Eisenstein classes, p-adic interpolation, and their applications in arithmetic, including explicit reciprocity law for Rankin-convolutions.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Algebraic K-Theory and Descent for Blow-Ups - Lecture 1

Explore algebraic K-theory and descent for blow-ups, focusing on pro-descent for infinitesimal thickenings and its implications for Weibel's conjecture on negative K-groups.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

Arthur Bartels: K-Theory of Group Rings

Exploring the Farrell-Jones Conjecture's prediction of K-theory for group rings, focusing on controlled algebra as a bridge between algebraic formulation and geometric proofs.

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

Maurice Herlihy: Applying Combinatorial Topology to Byzantine Tasks

Explore combinatorial topology's application to Byzantine tasks in distributed systems, focusing on fault-tolerant algorithms and consensus protocols.

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