I will discuss G-equivariant motivic stable homotopy theory for G finite, and some applications, mostly for G=Z/2. In this case, I will construct a motivic (=algebraic) analogue of Atiyah's real K-theory, and related periodicity theorems (Karoubi-Hornbostel theorems, and a new theorem), and also a solution (in some sense) of the completion problem for Hermitian K-theory. I will also discuss an algebraic (=motivic) version of Landweber's Real cobordism.

This is Shiing-Shen Chern's original work on Chern classes. In this talk, we will discuss three things: 1. Any complex vector bundle has a Hermitian structure. 2. Due to the Hermitian holomorphic structure, the formulas for the canonical connection and its curvature are very simple and easy to calculate. 3. More examples of Chern classes will be computed through Chern-Weil's theory.

In this survey talk I will give an overview of various results and approaches to the boundary regularity problem of holomorphic mappings between domains in $\mathbb C^n$.

Judy and Andrew are going through a bitter divorce. They live thousands of miles apart. They wish to toss a coin over the phone to see who will keep the car. How can they do this without anyone cheating?

If D is a division algebra finite dimensional over its center, then SK_1(D) = { a in D | Nrd(a) = 1 }/[D*,D*]. This is a subtle arithmetic invariant of D which has had ongoing interest and applications in the theory of algebraic groups. We will discuss how valuation theory on D is used to compute SK_1(D) for specific division algebras.

This talk will describe some beautiful work of Patrick Iglesias-Zemmour on diffeology. We will start from the definition of diffeological spaces, with some motivations, give some nice properties of diffeological spaces, and introduce diffeological bundles from the point of view of groupoids. Finally, we will discuss the example of irrational torus from a diffeological viewpoint.

Given a valuation $v$ on a division algebra $D$, there is an associated graded division algebra $\textrm{gr}(D)$, which is often much easier to work with than $D$ itself, but which retains surprisingly much of the structure of $D$. We illustrate this with $SK_1(D)$. If $v$ on the center of $D$ is Henselian and $D$ is tame, then $SK_1(D)$ is isomorphic to $SK_1(\textrm{gr}(D)).$