Activities This Week

In many data-driven applications, the data follows some geometric structure, and the goal is to recover this structure. In many cases, the observed data is noisy and the recovery task is even more challenging. A common assumption is that the data lies on a low dimensional manifold. Estimating a manifold from noisy samples has proven to be a challenging task. Indeed, even after decades of research, there was no (computationally tractable) algorithm that accurately estimates a manifold from noisy samples with a constant level of noise.

In this talk, we will present a method that estimates a manifold and its tangent. Moreover, we establish convergence rates, which are essentially as good as existing convergence rates for function estimation.

נציג את מושג הצביעה הקלאסית של גרף פשוט ונכליל אותו להיפרגרף (כלומר לקבוצה של קודקודים ואוסף כלשהו של תת-קבוצות שלה). ישנן כמה הכללות אפשריות, אנחנו נתמקד בהכללה הבאה: נאמר שצביעה של הקודקודים היא חסרת קונפליקטים אם בכל אחת מקבוצות האוסף יש לפחות קודקוד אחד עם צבע שלא ניתן לאף קודקוד אחר בקבוצה. נראה את הקשר בין המושג הזה לבעיות של השמות תדרים באנטנות סלולריות.

ניתן לראות פרומו חסר כל ערך מתמטי בסרטון

The general structure of absolute Galois groups of fields as profinite groups is still a mystery. Among the very few known properties of such groups are several “Intersection Theorems”, describing subgroups in standard filtrations of absolute Galois groups as the intersection of all normal open subgroups with quotient in a prescribed list of finite groups. These theorems are based on deep cohomological properties of absolute Galois groups. We will present a general “Transfer Theorem” for profinite groups, which explains what lies behind these intersection theorems.

Earlier this year, we discovered a new class of zero-dimensional dynamical systems, which we call “fiberwise essentially minimal”, that are of importance to operator algebras because of the nice properties, in particular K-theoretic classification, of the crossed product. Today, we discuss the Bratteli diagrams associated to these systems, and extend the K-theoretic classification to include a dynamical condition called “strong orbit equivalence”, extending the existing result in the minimal case due to Giordano-Putnam-Skau.