This course provides a rigorous introduction to the ideas, methods and results of classical statistical mechanics, with an emphasis on presenting the central tools for the probabilistic description of infinite lattice systems. ...
Algebraic K-theory, which to any ring R associates a sequence of groups, can be viewed as a theory of linear algebra over an arbitrary ring. We will study in detail the first two of these groups and some of their applications to other areas of mathematics. ...
In this course we will introduce core concepts of the theory of modular forms and consider several applications of this theory to combinatorics, harmonic analysis, and geometric optimization. ...
The goal of the course is to introduce relativistic quantum field theory as the conceptual and mathematical framework describing fundamental interactions. ...
This course will explain the theory of vanishing cycles and perverse sheaves. We will see how the Hard Lefschetz theorem can be proved using perverse sheaves. If we have more time we will try to see the decomposition theorem and how to categorify certain p ...
We will establish the major results in the representation theory of semisimple Lie algebras over the field of complex numbers, and that of the related algebraic groups. ...
The topics addressed in this course are the structure theory of reductive algebraic groups, their associated Lie algebras, the related finite groups of Lie type, and the representation theory of all of these objects. ...
This course presents geometric constructions of irreducible representations of semi-simple Lie Algebras and their Weyl groups by means of Springer theory. ...
The topics addressed in this course are the structure theory of reductive algebraic groups, their associated Lie algebras, the related finite groups of Lie type, and the representation theory of all of these objects. ...