Homotopy Theory

Karol Szumilo

Oct 02, 13:0 - 14:30

MC 107

We will introduce the Univalence Axiom and discuss a few of its immediate consequences such as existence of types that are not sets, function extensionality or preservation of n-types by dependent products.

Geometry and Topology

Martin Frankland

Oct 06, 15:30 - 16:30

MC 107

The classical Adams spectral sequence can be computed via higher order operations in mod p cohomology. Baues and Jibladze carried out computations of the differential $d_2$ using the algebra of secondary operations. Baues and Blanc described an algebro-combinatorial structure which encodes enough information about $n^{th}$ order operations to compute the differential $d_n$. In joint work with Baues, we specialize that work to the case $n=3$ and describe a more concrete algebraic structure which suffices to compute the differential $d_3$.

Analysis Seminar

Ilya Kossovskiy

Oct 07, 14:30 - 15:30

MC 107

Study of equivalences and symmetries of real submanifolds in complex space goes back to the classical work of Poincare and Cartan and was deeply developed in later work of Tanaka and Chern and Moser. This work initiated far going research in the area (since 1970's till present), which is dedicated to questions of regularity of mappings between real submanifolds in complex space, unique jet determination of mappings, solution of the equivalence problem, and study of automorphism groups of real submanifolds.
Current state of the art and methods involved provide satisfactory (and sometimes complete) solution for the above mentioned problems in nondegenerate settings. However, very little is known for more degenerate situations, i.e., when real submanifolds under consideration admit certain singularities of the CR-structure (such as non-constancy of the CR-dimension or that of the CR-orbit dimension).
The recent CR (Cauchey-Riemann Manifolds) -- DS (Dynamical Systems) technique, developed in our joint work with Shafikov and Lamel, suggests to replace a real submanifold with a CR-singularity by appropriate complex dynamical systems. This technique has recently hepled to solve a number of long-standing problems in CR-geometry, related to regularity of CR-mappings.
In this talk, we give an overview of the technique and the results obtained recently by using it.
We also discuss a possible development in this direction, in particular, new sectorial extension phenomena for CR-mappings.