Speaker: Spencer Backman, HU
Title: Cone valuations, Gram's relation, and flag-angles

Speaker: Igor Pak, UCLA
Title: Counting linear extensions.
Abstract:

Speaker: Noam Lifshitz, BIU
Title: Sharp thresholds for sparse functions with applications to extremal combinatorics.
Abstract:
The sharp threshold phenomenon is a central topic of research in the analysis of Boolean functions. Here, one aims to give sufficient conditions for a monotone Boolean function $f$ to satisfy $\mu_{p}(f)=o(\mu_{q}(f))$, where $q = p + o(p)$, and $\mu_{p}(f)$ is the probability that $f=1$ on an input with independent coordinates, each taking the value $1$ with probability $p$.

Speaker: Tammy Ziegler, HU
Title: Extending weakly polynomial functions from high rank varieties
Abstract: Let k be a field, V a k-vector space, X in V a subset. Say that f: X —> k is weakly polynomial of degree a if its restriction to any isotropic subspace is a polynomial degree of a. We show that if X is a high rank variety then any weakly polynomial function of degree a is the restriction to X of a polynomial of degree a on V. Joint work with D. Kazhdan.

Speaker: Ohad Klein, BIU
Title: Biased halfspaces, noise sensitivity, and local Chernoff inequalities
Abstract:
Let X be a random variable defined by X=\sum_i a_i x_i where x_i are independent random variables uniformly distributed in \{-1, 1\}, and a_i in R, the reals. Assume Var(X)=1=sum a_{i}^2. We investigate the tail behavior of the variable X, and apply the results to study halfspace functions f:{-1,1}^{n}-->{-1,1} defined by f(x)=1 (\sum_i a_i x_i > t) for some t in R.
A puzzle: Let a = max_{i} |a_{i}|. Is it true that Pr[|X| \leq a] \geq a/10?

Title: On a local version of the fifth Busemann-Petty Problem
Abstract:
In 1956, Busemann and Petty posed a series of questions about symmetric convex bodies, of which only the first one has been solved. Their fifth problem asks the following.
Let K be an origin symmetric convex body in the n-dimensional Euclidean space and let H_x be a hyperplane passing through the origin orthogonal to a unit direction x. Consider a hyperplane G parallel to H_x and supporting to K and let
C(K,x)=vol(K\cap H_x)dist (0, G).

Workshop for graduate students and post-docs

Workshop website Read more about Workshop on Super Strong Approximation in Groups

Title: Nodal statistics of graph eigenfunctions
Abstract: Understanding statistical properties of zeros of Laplacian
eigenfunctions is a program which is attracting much attention from
mathematicians and physicists. We will discuss this program in the
setting of "quantum graphs", self-adjoint differential operators
acting on functions living on a metric graph.
Numerical studies of quantum graphs motivated a conjecture that the
distribution of nodal surplus (a suitably rescaled number of zeros of

Title: Perturbations of non-normal matrices
Abstract: Eigenvalues of Hermitian matrices are stable under perturbations in the sense that the $l_p$ norm of the difference between (ordered)eigenvalues is bounded by the Schatten norm of the perturbation. A similar control does not hold for non-Normal matrices. In the talk, I will discuss

Krieger’s generator theorem shows that any free invertible ergodic measure preserving action (Y,\mu, S) can be modelled by A^Z (equipped with the shift action) provided the natural entropy constraint is satisfied; we call such systems (here it is A^Z) universal. Along with Tom Meyerovitch, we establish general specification like conditions under which Z^d-dynamical systems are universal. These conditions are general enough to prove that
1) A self-homeomorphism with almost weak specification on a compact metric space (answering a question by Quas and Soo)

Abstract: An inhomogeneous Markov chain X_n is a Markov chain whose state spaces and transition kernels change in time. A “local limit theorem” is an asymptotic formula for probabilities of th form
Prob[S_N-z_N\in (a,b)] , S_N=f_1(X_1,X_2)+....+f_N(X_N,X_{N+1})
in the limit N—>infinity. Here z_N is a “suitable” sequence of numbers.
I will describe general sufficient conditions for such results.
If time allows, I will explain why such results are needed for the study of certain problems related to irrational rotations.