Let G be an infinite connected graph. For each vertex of G we decide randomly and independently: with probability p we paint it blue and with probability 1-p we paint it yellow. Now, consider the subgraph of blue vertices: does it contain an infinite connected component?
There is a critical probability p_c(G), such that if p>p_c then almost surely there is a blue infinite connected component and if pp_c or p<p_c.
We will focus on planar graphs, specifically on the triangular
Abstract: This talk will describe joint work with Aravind Asok
and Jean Fasel using the methods of homotopy theory to construct new
examples of
algebraic vector bundles. I will describe a natural conjecture
which, if
true, implies that over the complex numbers the classification
of algebraic
vector bundles over smooth affine varieties admitting an
algebraic cell
decomposition coincides with the classification of topological
complex vector bundles.
Abstract:
The “geometrization" of mechanics (whether classical, relativistic or quantum) is almost as old as modern differential geometry, and it nowadays textbook material.
The formulation of a mathematically-sound theory for the mechanics of continuum media is still a subject of ongoing research. In this lecture I will present a geometric formulation of continuum mechanics, starting with the definition of the fundamental physical observables, e.g., force, deformation, stress and traction. The outcome of this formulation is a generalization of Newton’s "F=ma” equation for continuous media.
10:00-11:00 We will have a special lecture on string diagrams by Shaul Barkan
11:00-13:00 Asaf Horev will continue his talk about ambidexterity and duality
A Gaussian stationary function (GSF) is a random f: R --> R whose
distribution is shift-invariant and all its finite marginals have
centered multi-normal distribution. It is a simple and popular model
for noise, for which the mean number of zeroes was computed already
in the 1940's by Kac and Rice. However, it is far more complicated
to estimate the probability of a significant deficiency or abundance
in the number of zeroes in a long interval (compared to the expectation).
We do so for a specific family of GSFs with additional smoothness and absolutely
Title: a random Schroedinger operator stemming from reinforced process
Abstract:
We will explain the relationship between a toy model to Anderson localization, called the H^{2|2} model (according to Zirnbauer) and edge reinforced random walk.
The latter is a random walk in which, at each step, the walker prefers traversing previously visited edges, with a bias proportional to the number of times the edge was traversed. Recent study on this random walk showed that it is equivalent to Zirnbauer's model and we will show some consequences once this equivalence is established.
Title: Asymptotics for Chebyshev Polynomials of Infinite Gap Sets on the Real Line
Abstract: The Chebyshev Polynomials of a compact subset, e, of the complex plane are the monic polynomials minimizing the sup over e. We prove Szego--Widom asymptotics for the Chebyshev Polynomials of a compact subset of R which is regular for potential theory and obeys the Parreau--Widom and DCT conditions. We give indications why these sufficient conditions may also be necessary.
Abstract:
Given a self-adjoint bounded operator, its spectrum is a compact subset of the real numbers. The space of compact subsets of the real numbers is naturally equipped with the Hausdorff metric. Let $T$ be a topological (metric) space and $(A_t)$ be a family of self-adjoint, bounded operators. In the talk, we study the (Hölder-)continuity of the map assigning to each $t\in T$ the spectrum of the operator $A_t$.
