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.
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
Abstract: We will discuss the question: for a random walk in a random environment, when should one expect a central limit theorem, i.e. that after appropriate scaling, the random walk converges to Brownian motion? The answer will turn out to involve the spectral theory of unbounded operators. All notions will be defined in the talk. Joint work with Balint Toth.
I will present an overview of some recent progress on the study of the nodal sets of Steklov eigenfunctions. In particular, I will discuss sharp estimates on the nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces with boundary obtained in my joint
work with D. Sher and J. Toth.
Abstract: Consider a random matrix with i.i.d. normal entries. Since its distribution is invariant under rotations, any normalized eigenvector is uniformly distributed over the unit sphere. For a general distribution of the entries, this is no longer true. Yet, if the size of the matrix is large, the eigenvectors are distributed approximately uniformly. This property, called delocalization, can be quantified in various senses. In these lectures, we will discuss recent results on delocalization for general random matrices.
20 years ago Weiss constructed a collection of non-trivial translation invariant probability measures on the space of entire functions using tools from dynamical systems. In this talk, we will present another elementary construction of such a measure, and give upper and lower bounds for the possible growth of entire functions in the support of such measures.
On the Asymptotic behavior of a log gas in the bulk scaling limit in the presence of a varying external potential.
T.Bothner, P.Deift, A.Its and I.Krasovsky
Abstract: We study the partition function Z of a Coulomb gas of particles with an external potential 2v applied to the
particles in an interval of length L. When v is infinite, Z describes the gap probability for GUE eigenvalues in the bulk scaling limit,
and has been well-studied for many years. Here we study the the behavior of Z in the full (v,L) plane.
Abstract: Consider a random matrix with i.i.d. normal entries. Since its distribution is invariant under rotations, any normalized eigenvector is uniformly distributed over the unit sphere. For a general distribution of the entries, this is no longer true. Yet, if the size of the matrix is large, the eigenvectors are distributed approximately uniformly. This property, called delocalization, can be quantified in various senses. In these lectures, we will discuss recent results on delocalization for general random matrices.
