Speaker: Bruno Benedetti, U. Miami Title: Local constructions of manifolds Abstract: Starting with a tree of tetrahedra, say you are allowed to recursively glue together some two boundary triangles that have nonempty intersection. You may perform this type of move as many times you want. Let us call "Mogami manifolds" the triangulated 3-manifolds (with or without boundary) that can be obtained this way. Mogami, a quantum physicist, conjectured in 1995 that all triangulated 3-balls are Mogami. This conjecture implies an important one in discrete quantum gravity

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?

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

Speaker: Igor Pak, UCLA Title: Counting linear extensions. Abstract: I will survey various known and recent results on counting the number of linear extensions of finite posets. I will emphasize the asymptotic and complexity aspects for special families, where the problem is especially elegant yet remains #P-complete. In the second half of the talk I will turn to posets corresponding to (skew) Young diagrams. This special case is important for many applications in representation theory and algebraic geometry.

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.

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).

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 the n-th eigenfunction) has a universal form: it approaches Gaussian

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. This is joint work with Dmitry Dolgopyat.