International Centre for Theoretical Sciences Courses

Cosmography Using GW Standard Sirens - Lecture 5

Explore gravitational-wave standard sirens for cosmological distance measurements and mapping the universe's expansion history through advanced observational techniques.

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

Cosmography Using GW Standard Sirens - Lecture 1

Explore gravitational-wave standard sirens for cosmological distance measurements and their role in understanding the expanding universe's geometry and parameters.

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

Examples of Harmonic Maass Forms of Half-Integral Weight

Explore concrete examples of harmonic Maass forms with half-integral weight, examining their properties and applications in modern number theory and modular form theory.

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video

The Partition Function Revisited

Explore the partition function through Ram Murty's mathematical insights at this advanced discussion meeting on harmonic Maass forms and mock modular forms.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Why Are Siegel Modular Forms Relevant for Black Hole Physics?

Explore the surprising connection between Siegel modular forms and black hole physics through expert insights from theoretical physicist Ashoke Sen.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Mock Theta Functions in the Context of Harmonic Maass Forms

Explore mock theta functions through the lens of harmonic Maass forms, uncovering their modular-like properties and mathematical framework in this specialized number theory lecture.

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

Theta Lifts and Holomorphic Projection

Explore theta lifts and holomorphic projection techniques in the context of harmonic Maass forms and mock modular forms, connecting number theory with representation theory.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

Summation Formulas - From Classical Foundations to Harmonic Maass Forms

Explore summation formulas from classical foundations to harmonic Maass forms, bridging traditional mathematical techniques with modern modular form theory.

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

Cycle Integrals of the j-function by Duke, Imamoglu, and Toth

Explore cycle integrals of the j-function through Duke, Imamoglu, and Toth's groundbreaking work in modular forms theory and harmonic Maass forms applications.

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

Hecke Theory of Harmonic Maass Forms

Explore Hecke theory applied to harmonic Maass forms, bridging modular forms and Ramanujan's mock theta functions in this advanced mathematical discussion.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

Introduction to Mock Theta Functions

Discover the mysterious mock theta functions introduced by Ramanujan, exploring their modular-like properties and connections to harmonic Maass forms in modern mathematical research.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

Indefinite Theta Functions

Explore indefinite theta functions and their role in harmonic Maass forms and mock modular forms, connecting Ramanujan's mysterious functions to modern mathematical frameworks.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Generalization of Monster Denominator Identity to Higher Level Using Harmonic Maass Forms

Explore advanced mathematical techniques for generalizing the Monster Denominator Identity to higher levels through harmonic Maass forms and modular function theory.

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

Eichler-Selberg Relations for Traces of Singular Moduli

Explore Eichler-Selberg relations connecting traces of singular moduli in this advanced mathematical lecture by Ken Ono at ICTS.

• YouTube
• 1 hour 15 minutes
• On-Demand
• Free Video

Ramanujan, Modular Forms and Beyond

Explore Ramanujan's groundbreaking work on modular forms and mock theta functions, connecting number theory to modern mathematical applications in physics and geometry.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video