Past Events
The mod p cohomology of locally symmetric spaces for definite unitary groups at infinite level is expected to realize the mod p local Langlands correspondence for GL_n. In particular, one expects the (component at p) of the associated Galois representation to be determined by cohomology as a…
We define Teichmuller space for a genus $g>1$ surface as the quotient of all complex structures by the group of isotopies. We show how this presentation can be used to endow Teichmuller space with a canonical smooth structure, making it into a $6g-6$ dimensional manifold.
As we all know, Gromov has two lawn-related pet peeves: everyone and their dog taking shortcuts on his lawn, and the excessively long time it takes to mow his lawn. Naturally, he’s been seeking the optimal lawn topography to mow as little as possible, while still ensuring no one takes any…
Our speaker this week is John Anderson (this meeting is the last of the quarter).
Abstract: Hyperbolic pde's arise frequently in physics. In this talk, I will describe some of the types of problems that arise in the study of hyperbolic pde's, with a particular focus on…
Let X be an integral affine or projective scheme over a perfect field of an arbitrary characteristic. Then, X admits a resolution. That is, there exists a smooth scheme Y and a projective birational morphism from Y onto X.
The synchronous discussion…
Abstract: A holomorphic function in a neighborhood of z=0 is algebraic if it satisfies a polynomial equation with coefficients in Q[z]. An example of such a function is the square root of 1-4z. The power series expansion of this function turns out to have coefficients which are all integers, and…
In this talk, we develop algorithms for numerical computation, based on ideas from competitive games and statistical inference.
In the first part, we propose competitive gradient descent (CGD) as a natural generalization of gradient descent to saddle point problems and general sum games…
Minimizing harmonic maps (i.e., minimizers of the Dirichlet integral) with prescribed boundary conditions are known to be smooth outside a singular set of codimension 3. I will present an extension of Almgren and Lieb’s linear law on the bound of the singular set. Next, I will investigate how…