Activities This Week

Celebrating Michael Lin’s 80th birthday. Place: Ben-Gurion university of the Negev. Room -103 in building 14 Mendel building (across from Aroma branch on the west side of the campus). Time: Tuesday 31/5/2022 between 10:30-16:30.

Schedule:

10:00 - 10:30 Coffee 10:30 - 11:20 Omri Sarig (Weizmann institute) 11:40 - 13:00 Jon Aaronson (Tel-Aviv University) 13:00 - 14:30 Lunch (the lunch will take place in room -101 of the math building) 14:30 - 15:20 Eli Glasner (Tel-Aviv University, joint with Colloquium) 15:30 - 16:20 Ariel Yadin (Ben Gurion University)

Organizers: Yair Glasner, Tom Meyerovitch, and Guy Cohen Zoom broadcasting LINK Meeting ID: 820 8565 9434 The conference website: https://sites.google.com/view/michael-lins-80th-birthday/home

Lobachevsky started to work on computing volumes of hyperbolic polytopes long before the first model of the hyperbolic space was found. He discovered an extraordinary formula for the volume of an orthoscheme via a special function called dilogarithm.

We will discuss a generalization of the formula of Lobachevsky to higher dimensions. For reasons I do not fully understand, a mild modification of this formula leads to the proof of a conjecture of Goncharov about the depth of multiple polylogarithms. Moreover, the same construction leads to a functional equation for polylogarithms generalizing known equations of Abel, Kummer, and Goncharov.

Guided by these observations, I will define cluster polylogarithms on a cluster variety.

Consider a dynamical system (X,T) consisting of a compact set X in the Euclidean space and a transformation T on X. Takens-type time-delay embedding theorems state that for a generic real-valued observable h on X, one can reconstruct uniquely the initial state x of the system from a sequence of values of h(x), h(Tx), …, h(T^{k-1} x), provided that k is large enough. In the deterministic setting, the number of measurements k has to be at least twice the dimension of the state space X. This was proved in several categories and can be seen as dynamical versions of the classical (non-dynamical) embedding theorems. We provide a probabilistic counterpart of this theory, in which one is interested in reconstructing almost every state x, subject to a given probability measure. We prove that in this setting it suffices to take k greater than the Hausdorff dimension of the considered measure, hence reducing the number of measurements at least twice. Using this, we prove a related conjecture of Shroer, Sauer, Ott and Yorke in the ergodic case. We also construct an example showing that the conjecture does not hold in its original formulation. This is based on joint works with Krzysztof Barański and Yonatan Gutman.