Lecture 1

Speaker: Otis Chodosh

Time/place: Surge 284 3:40~4:30

Title:Properties of Allen--Cahn min-max constructions on 3-manifolds

Abstract:

I will describe recent joint work with C. Mantoulidis in which we study the properties of bounded Morse index solutions to the Allen--Cahn equation on 3-manifolds. One consequence of our work is that a generic Riemannian 3-manifold contains an embedded minimal surface with Morse index p, for each positive integer p.

Lecture 2

Speaker:  Ved Datar

Time/place: Surge 284 4:40~5:30

Title: Hermitian-Yang-Mills connections on collapsing K3 surfaces

Abstract:

Let $X$ be an elliptically fibered K3 surface with a fixed $SU(n)$ bundle $\mathcal{E}$. I will talk about degenerations of connections on $\mathcal{E}$ that are Hermitian-Yang-Mills with respect to a collapsing family of Ricci flat metrics. This can be thought of as a vector bundle analog of the degeneration of Ricci flat metrics studied by Gross-Wilson and Gross-Tosatti-Zhang. I will show that under some mild conditions on the bundle, the restriction of the connections to a generic elliptic fiber converges to a flat connection. I will also talk about some ongoing work on strengthening this result. This is based on joint work with Adam Jacob and Yuguang Zhang.

Event on Elections and Voting, with Panels on the Technology, Law, & Policy of Election Hacking, 1:30 - 7:30 pm

The Technology of Voting: Risks & Opportunities
Josh Benaloh (Microsoft Research)
Alex Halderman (University of Michigan)
Hovav Shacham (UC San Diego)
Panel moderated by Alice Silverberg (UC Irvine), 3:30 pm - 4:40 pm

Keynote Speaker: James Carville 6:30 - 7:30 pm

More information: https://cpri.uci.edu/can-adversaries-hack-our-elections-can-we-stop-them...

FREE to UCI students, faculty, and staff.  Register at: https://scout.eee.uci.edu/s/CPRI-March13

First, I will present the Laplacian smoothing gradient descent proposed recently by Prof. Stan Osher. We show that when applied to a variety of machine learning models including softmax regression, convolutional neural nets, generative adversarial nets, and deep reinforcement learning, this very simple surrogate of gradient descent can dramatically reduce the variance and improve the accuracy of the generalization. The new algorithm, (which depends on one nonnegative parameter) when applied to non-convex minimization, tends to avoid sharp local minima. Instead it seeks somewhat flatter local(and often global) minima. The method only involves preconditioning the gradient by the inverse of a tri-diagonal matrix that is positive definite. The motivation comes from the theory of Hamilton-Jacobi partial differential equations. This theory demonstrates that the new algorithm is almost the same as doing gradient descent on a new function which (a) has the same global minima as the original function and (b) is "more convex". Second, I will talk about modeling, simulation, and experiments of the micro-encapsulation of droplets. This is a work joint with Professors Andrea Bertozzi, Dino Di Carlo, and Stan Osher’s groups.

A major project in set theory aims to explore the connection between large cardinals and so-called generic absoluteness principles, which assert that forcing notions from a certain class cannot change the truth value of (projective, for instance) statements about the real numbers. For example, in the 80s Kunen showed that absoluteness to ccc forcing extensions is equiconsistent with a weakly compact cardinal. More recently, Schindler showed that absoluteness to proper forcing extensions is equiconsistent with a remarkable cardinal. (Remarkable cardinals will be defined in the talk.) Schindler's proof does not resemble Kunen's, however, using almost-disjoint coding instead of Kunen's innovative method of coding along branchless trees. We show how to reconcile these two proofs, giving a new proof of Schindler's theorem that generalizes Kunen's methods and suggests further investigation of non-thin trees.