| Sunday 1 June 2025 | |
| Events for day: Wednesday 28 May 2025 |
| 14:00 - 15:00 Combinatorics and Computing Weekly Seminar Improved Asymptotic Expansion Lower Bounds for Random d-Regular Graphs (d ≥ 4) School MATHEMATICS In this talk we introduce the asymptotic almost sure expansion lower bounds of random d-regular graphs in the uniform model and provide improvements for d ≥ 4 through solving a parametrized relaxation of the expansion lower bound problem. As a concrete consequence of our main result, we prove that for large degrees d ≥ 6 � 10^4 the optimal a.a.s. expansion lower bound of d-regular graphs is greater than d/2 - 0.7942^{-} √d which is an improvement over the long-standing a.a.s. lower bound d/2 - 0.8326^{-} √d provided by B. Bollob�as (1988). Also, for small degrees, we apply our ... 17:30 - 19:00 Algebraic Geometry Biweekly Webinar Hadamard Products of Symbolic Powers and Hadamard Fat Grids School MATHEMATICS In this talk we study some properties of the Hadamard products of symbolic powers, in particular, if for points $P, Qin {mathbb{P}}^2$, we get $I(P)^m*I(Q)^n= I(P*Q)^{m+n−1}$. We obtain different results according to the number of zero coordinates in $P$ and $Q$. Successively, we define the so called Hadamard fat grids, which are the result of the Hadamard product of two sets of collinear points with given multiplicites. The most important invariants of Hadamard fat grids, as minimal resolution, Waldschmidt constant and resurgence, are then computed using also tools and known results in ${mathbb{P}}^1 imes{mathbb{P}}^1$. (This is a joi ... |