She is the first woman to be awarded with an Abel, and she was recognized specifically for "pioneering achievements in geometric partial differential equations, gauge theory
and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics."
She was honored again in 2007 for her gauge theory
work with the Leroy P.
Fellow mathematicians celebrate Donaldson's 35 years (and counting) contributions to geometry with papers on such matters as the Atiyah-Floer conjecture: a formulation, a strategy of proof, and generalizations; remarks on Nahm's equations; conjectures on counting associative three-folds in G2-manifolds; introduction to a provisional mathematical definition of Coulomb branches of three-dimensional N = 4 gauge theories; the Dirichlet problem for the complex homogenous Monge-Ampere equation; Donaldson theory in non-Kahlerian geometry; and two lectures on gauge theory
and Khovanov homology.
In Section 2 we explain why the theory of HTSC should have effective description in terms of a SO(5) gauge theory
. In Sections 2.1 and 2.2, we define the order parameters and symmetry generators of the microscopic theory underlying HTSC and explain how the SO(5) symmetry arises from these structures.
The phase space of a (continuum) gauge theory
is a space of connections on a (finite dimensional) principal bundle P with structure group G and with base M.
An Elementary Primer For Gauge Theory
. World Scientific, Singapore, 1983.
Practitioners recount the course of the sibling sciences since then, discussing such matters as symmetries and dynamical symmetries in nuclei, chiral symmetry in subatomic physics, exotic nuclei far from the stability line, large underground detectors for proton decay and neutrino physics, and lattice gauge theory
and the origin of mass.
In the quiver gauge theory
and brane tiling literature, Zn denotes a Pyramid Partition Function (cluster variable) associated to a certain cascade of Seiberg dualities (mutation sequence).
Superspace methods in string theory, supergravity and gauge theory
. Lectures at the XXXVII Winter School in Theoretical Physics "New Developments in Fundamental Interactions Theories", Karpacz, Poland, Feb.