In this course we study measurable dynamical systems and especially their long term behavior. This concept has initially emerged in statistical physics but by now is connected with other areas such as  combinatorics, number theory and geometry.  The first part…

A flag variety is a projective algebraic variety with a transitive action of a linear algebraic group.  Flag varieties play an important role in the representation theory of algebraic groups as well as classical algebraic geometry. This course will begin…

During the first semester, the group went through overviews of many specialized mathematical software packages (Mathematica, GAP, Macaulay2, Sage, Sympy, Polymake, Porta, LRS) and general-purpose computer languages (Perl, C++, Python,  Javascript). Students also gave presentations on their own projects. Part…

Besides being of interest in their own right, Central Simple Algebras are a basic tool in algebraic number theory (particularly in their interpretations via Galois cohomology), they arise naturally in algebraic geometry (as obstructions to the existence of universal objects…

A major problem in representation theory has been the determination of a character formula and the dimensions of finite dimensional simple modules over a connected reductive algebraic group G. Lusztig conjectured that the characters could be computed recursively in terms…