Transgressions and Flows
Dienstag, 8.3.16, 10:15-11:15, Raum 127, Eckerstr. 1
Transgressions and Flows
Mittwoch, 9.3.16, 10:15-11:15, Raum 127, Eckerstr. 1
Geometric measure theory
Mittwoch, 9.3.16, 13:15-14:15, Raum 127, Eckerstr. 1
Transgressions and Flows
Donnerstag, 10.3.16, 10:15-11:15, Raum 127, Eckerstr. 1
Etale motivic cohomology
Freitag, 11.3.16, 10:15-11:15, Raum 404, Eckerstr. 1
We discuss structure theorems and duality\nresults for etale integral motivic cohomology\nof smooth projective varieties over algebraically closed,\nfinite, and local fields.\n\n
Introduction to Geometric Complexity Theory
Montag, 14.3.16, 10:15-11:15, Raum 404, Eckerstr. 1
This is the first talk in a series of 5 talks on Geometric Complexity Theory and is intended to be an introduction, accessible by a broad audience. Master students are very welcome!\n\nComplexity theory studies how fast computational problems can be solved. In algebraic complexity theory, the study is limited to the problem of evaluating polynomials and the complexity is measured by counting arithmetic operations. We give an introduction that leads up to the central "Determinant versus Permanent" problem, which can be seen as an algebraic analogue of P versus NP.
Algebraic Complexity Theory
Dienstag, 15.3.16, 10:15-11:15, Raum 404, Eckerstr. 1
Complexity theory studies how fast computational problems can be solved. In algebraic complexity theory, the study is limited to the problem of evaluating polynomials and the complexity is measured by counting arithmetic operations. We give an introduction that leads up to the central "Determinant versus Permanent" problem, which can be seen as an algebraic analogue of P versus NP.
Group actions and non-negative sectional curvature
Dienstag, 15.3.16, 14:15-15:15, Raum 404, Eckerstr. 1
The construction of manifolds of non-negative (or positive) sectional\ncurvature is intimately tied to Lie group actions on manifolds. Some classical\nexamples are symmetric spaces, space forms and homogeneous spaces. In this talk\nwe will see the history of constructing examples using group actions and their\nimportance for non-negative curvature. While there are obstructions like\nGromov's Betti number theorem, the gap between obstructions and known examples\nremains quite wide. We will look at some recent ideas to produce examples of\nnew topological types. We will also mention some open problems along the way.
Actions and Representation Theory of Affine Reductive Groups
Mittwoch, 16.3.16, 10:15-11:15, Raum 404, Eckerstr. 1
We will recall several classical results about actions of algebraic groups on varieties and the representation theory of reductive groups. We restrict ourselves to the case of an algebraically closed field of characteristic zero, because the theory is most tame in this case.
Geometric Complexity Theory
Donnerstag, 17.3.16, 10:15-11:15, Raum 404, Eckerstr. 1
The GCT program rephrases rephrases the Determinant versus Permanent problem as a geometric question: To a homogeneous polynomial of degree d, we associate its orbit under linear substitution of the variables and take the closure of this orbit in the space of all homogeneous d-forms. For certain d-forms (i.e. the determinant and the permanent) the question becomes whether one such orbit closure is contained in the other. We focus on how the representation theory of the general linear group might help to answer this question. For the most part, however, we present problems and questions that are still open.
The Boundary of Orbit Closures of Homogeneous Forms
Freitag, 18.3.16, 10:15-11:15, Raum 404, Eckerstr. 1
Arguably, the boundary of an orbit closure (i.e. the complement of the orbit in its closure) presents the greatest challenge in understanding its geometry. This boundary is always a divisor of the orbit closure and\na modest goal is to determine its number of irreducible components. We present an approach to this problem using geometric invariant theory which led to some recent work characterizing the boundary of the 3 by 3 determinant. We explain the problems that arise already in the 4 by 4\ncase and hope for fruitful comments from the audience.