In this talk I will review some mathematical theories of
A-models, including Gromov-Witten theory, FJRW theory and Gauged
Gromov-Witten theory. Then I will describe the project with Tian on the
construction of Gauged Linear Sigma Model which was introduced by Witten
in 1993.

This is the first talk at CRYPTOGRAPHY DAY, a one-day meeting on the Mathematics of Cryptography sponsored by the Alfred P. Sloan Foundation.  It will be at the level of a colloquium talk. All are encouraged/welcome to attend!

For more information:

http://www.math.uci.edu/~asilverb/CryptoDay.html

We finish the discussion of two-step iteration of proper forcing.

A classical problem in Galois theory is a strong variant of
the Inverse Galois Problem: "What finite groups arise as the Galois
group of a finite Galois extension of the rational numbers, if you
impose the additional condition that the extension can only ramify at
finite set of primes?" This question is wide open in almost every
nonabelian case, and one reason is our lack of knowledge about how to
find number fields with prescribed ramification at fixed primes. While
such fields are often constructed to answer arithmetic questions,
there is currently no known way to systematically construct such
extensions in full generality.

However, there are some inspiring programs that are gaining ground on
this front. One method, initiated by Chenevier, is to construct such
number fields using Galois representations and their associated
automorphic representations via the Langlands correspondence. We will
explain the method, show how some recent advances in these subfields
allow us to gain some additional control over the number fields
constructed, and indicate how this brings us closer to our goal. As a
application, we will show how one can use this knowledge to study the
arithmetic of curves over number fields.