Scientific

Accessibility is a fundamental tool when working with partially hyperbolic systems. For instance, in the 1970s it was used as a tool to show certain systems were transitive, and in the 1990s it was used to establish stable ergodicity. We will review the general notion and how it applies in these settings. We will also review the result from 2003 by Dolgopyat and Wilkinson on the C^1 density of stably transitive systems.

I will construct an infinite-dimensional analog of the HaPPY code as a growing series of stabilizer codes defined respective to their Hilbert spaces. These Hilbert spaces are related by isometries that will be defined during this talk. I will analyze its system in various aspects and discuss its implications in AdS/CFT. Our result hints that the relevance of quantum error correction in quantum gravity may not be limited to the CFT context.

For other events in this series see the quanTA events website.

A broad class of convex geometry problems deals with questions on retrieval of information about (convex) sets from data about different types of their projections, sections, or both. Examples of such assumptions are volume estimates, rigidity of structure, symmetry conditions etc.

In this talk, we will discuss known results and recent developments regarding the dual notions of point-projections and non-central sections of convex bodies. In particular, we provide a partial affirmative answer to the question on a shape recognition posed by A. Kurusa, and discuss a generalization of V. Klee's theorem for polyhedra.

We'll show how a simple idea from probability theory on the recurrence of random walks can be used in many important dynamical and geometric situations, building on work of Eskin-Margulis and others. No prior knowledge of probability theory, random walks, or geometry is required. If time permits, as an unrelated "dessert" of sorts, we'll give a brief proof of the Hopf ratio ergodic theorem using the Birkhoff ergodic theorem for flows.

The distinguishing number of a graph is the smallest number of colors necessary to color the vertices so that no nontrivial automorphism preserves the color classes. If a graph can be distinguished with two colors, the distinguishing cost is the smallest possible size of a color class over all 2-distinguishing colorings. In this talk I will present the long-sought-after (at least by me, :-) ) cost of 2-distinguishing hypercubes. We will begin the talk with definitions and intuitive examples of distinguishing and of cost, cover a bit of history, and work our way to a new technique using binary matrices. Then will we be able to state and understand the new results on hypercubes.