Current Developments in Mathematics

Table of Contents

Trace formula on the Adele Class Space and Weil Positivity

Partial Differential Equations and Monge-Kantorovich Mass Transfer

Quantum Chaos, Symmetry, and Zeta functions, I: Quantum Chaos

Quantum Chaos, Symmetry, and Zeta functions, II: Zeta Functions

Character Formulas for tilting modules over quantum groups at roots of one

Voevodsky's proof of the Milnor Conjecture

Is there finite-time blow-up in 3-D Euler flow?

Problems

Open Problems in Number Theory, collected by Barry Mazur

Open Problems in Geometry and Topology, collected by C. Taubes

The Cauchy problem for nonlinear Schrödinger equation (NLS) with critical nonlinearity

Singularities of Schrödinger’s equation and recurrent bicharacteristic flow

Global minimizers of the Mumford-Shah function

The modified Bers conjecture

The Wave map problem

Geometry of Nodal sets and Multiplicity of Eigenvalues

Questions related to the dimension of Kakeya sets

Some Open Problems in Partial Differential Equations Arising from Fluid Dynamics