The contraction of a Lie group G to a subgroup K is a Lie group, often simpler than G itself, that approximates G to first order near K.
We’ll see how to construct the Dynkin diagram for a simple Lie algebra. Two Lie algebras are isomorphic if and only if their Dynkin diagrams are, so classifying the Dynkin diagrams is the main ingredient for the classification theorem.
We show that the examples of asymptotically cylindrical Calabi-Yau manifolds recently obtained by Haskins-Hein-Nordstrom admit a full polyhomogeneous expansion at infinity.
It is the mandate of the Elliott classification programme to classify separable simple unital nuclear C*-algebras by invariants consisting of K-theory and tracial states.
This talk is the first of several covering Barto's simpler proof of a dichotomy for conservative templates (originally due to Bulatov). We will first cover the preliminary notions and notations. Then we will show the correctness of the reduction to minimal absorbing subuniverses algorithm.
I will discuss conjectures, theorems, and experiments concerning the moments of zeta functions associated to hyperelliptic curves over finite fields. This is joint work with Kevin Wu.
What's a moduli space? How do you get a moduli space? How come I don't have any moduli spaces? Fundamentally, they are new spaces containing all the information of more complicated spaces, but in a manner (hopefully) easier to work with. Some, such as the moduli space of curves, have connections to combinatorics, topology, and algebraic geometry.
A paper of Gulick from 1966 contains some good mathematics, but it also contains an error. It claims that for a Banach algebra $A$, the intersection of the Jacobson radical of $A^{**}$ with $A$ is precisely the radical of $A$.
Attaining strong bounds on the least quadratic nonresidue (mod p) is a classical problem, with a history stretching back to Gauss. The approach which has led to the best results uses character sums, objects which are ubiquitous in analytic number theory.
This talk is the second of several covering Barto’s simpler proof of a dichotomy for con- servative templates (originally due to Bulatov).