Abstract: Iwasawa main conjecture, which is actually a theorem (Mazur & Wiles 84), fulfills the relations between arithmetic objects, p-adic L-functions and complex L-functions. In this talk we sketch how these relations arise and give some consequences.
Boolean Types in Dependent Theories (Joint work with Itay Kaplan and Saharon Shelah)
Abstract: Complete types, seen as ultrafilters, are naturally equivalent to Boolean homomorphisms to {0,1}. The notion of a complete type can thus be generalized in a natural manner to allow assigning a value in an arbitrary Boolean algebra to each formula, and this notion is particularily well behaved when the ambient theory has NIP. I will show that this notion generalizes, in a sense, both complete types and Keisler measures.
Abstract: In this talk we will explore the connection between the two seemingly unrelated concepts appearing in the title. Phase transitions occur when a system undergoes an abrupt change in behaviour as a consequence of a small change in parameters. While phase transitions are evidently observed in the physical world (e.g., water freezing or evaporating), they are also ubiquitous in mathematical problems studied in statistical mechanics, probability, combinatorics and computer science.
Analysis of Boolean functions aims at "hearing the shape" of functions on the discrete cube {-1,1}^n — namely, at understanding what the structure of the (discrete) Fourier transform tells us about the function. In this talk, we focus on the structure of "low-degree" functions on the discrete cube, namely, on functions whose Fourier coefficients are concentrated on "low" frequencies. While such functions look very simple, we are surprisingly far from understanding them well, even in the most basic first-degree case.
Abstract: We present a geometric condition which is sufficient and necessary for the existence of hyperbolic SRB measures on closed Riemannian manifolds.
A common observation in data-driven applications is that data has a low intrinsic dimension, at least locally. Thus, when one wishes to work with data that is not governed by a clear set of equations, but still wishes to perform statistical or other scientific analysis, an optional model is the assumption of an underlying manifold from which the data was sampled. This manifold, however, is not given explicitly but we can obtain samples of it (i.e., the individual data points).
Geva Yashfe: The principal kinematic formula: Euler characteristic and geometry
Abstract: Let C and D be nice domains in R^d. Given some geometric data on each of the domains, the principal kinematic formula computes an integral over the group of rigid motions of R^d: it sums the Euler characteristic of the intersection of C with g.D as g ranges over the group.
