Previous Special Year Seminar

I will give an overview of what is going to be discussed in the seminar during the semester, and start an introduction to the theory. No previous familiarity with geometric Langlands will be assumed.

This seminar is intended to cover background material or serve as a discussion session for the seminar "Yang-Mills theory for mathematicians", which will start on the following week. The first talk will give a brief overview of the concepts of...

This seminar will cover such topics as: Jones-Witten knot invariants, large N duality, knot invariants and Gromov-Witten invariants, topological vertex, Nekrasov's partition function and geometric engineering. The first lecture will give an overview...

In the last eight lectures, we have reduced the proof of the Bloch-Kato to an assertion about motivic cohomology operations. We will prove that this assertion is correct, and so complete the proof of the Bloch-Kato conjecture.

Let F be a presheaf with transfers on the category of smooth affinoid varieties over a non-archemidean field. Suppose that F is overconvergent and homotopy invariant. Then the presheaves H^i(-,F) are also homotopy invariant (where the cohomology is...

Consider an arrangement of nonsingular subvarieties in a nonsingular algebraic variety. We define a compactification of the complement by replacing these subvarieties with a normal crossing divisor. This compactification is obtained by a sequence of...

We will describe some bounds on the multidegrees of complete intersections to have trivial Chow groups in low dimensions.

Let $X\subset \P^N$ be a projective submanifold of dimension $n$ in the complex projective space $\P^N$. Let $U$ be a domain in the parameter space $T$ of complete intersections of codimension $m$ and of a given bidegree $(d_1,\dots,d_m)$ in $\P^N$...

We will classify all unstable motivic operations from bidegree (2n,n) (with coefficients Z) to bidegree (p,q) with coefficients Z/l, l>2. All such operations are polynomials on the elements of the Steenrod Algebra. This work is based upon some...