An exact AdS/CFT duality

• Gaberdiel

Counting Calabi-Yau black holes with (mock) modular forms

• Pioline

A shifted convolution problem arriving from physics

• Klinger-Logan

Endoscopy in the relative Langlands program

• Leslie

Gauge-String Duality and Arithmetic

• Gopakumar

A problem of number theory with surprising numerical aspects

• Zagier

Designing Gravity via Symmetric Product Orbifolds

• Castro

Quantum Jacobi forms, partial theta functions, q‑series, and applications

• Folsom

Towards a classification of orthogonal hypergeometric polynomials

• Sahi

Indefinite theta series for N-gons and other figures

• Kudla

An introduction to the categorical Langlands program

• Emerton

Amplitudes for mathematicians

• Brown

I will try to give a brief overview of the landscape of the areas of physics which now go under the name of `amplitudes', and how they connect with mathematics and especially number theory. After that I can either focus on the mathematics which underlies Feynman integrals (locally symmetric spaces) or string perturbation theory (moduli spaces of curves), depending on the audience's preference.

Relative Langlands duality

• Gan

Hypergroup moonshine

• Gannon

Resurgent analysis of generalised Eisenstein series in string theory

• Treilis

Borel-Serre type compactifications for loop groups

• Patnaik

Topics in iterated integrals

• Schlotterer

A Multiplicity One Theorem for General Spin Groups

• Emory

Higher-genus analogues of polylogarithms

• Zerbini