| Monday 25 November 2024 | |
| Events for day: Wednesday 16 October 2024 |
| 14:00 - 15:00 Combinatorics and Computing Weekly Seminar Optimal Convergence Rates in Trace Distance and Relative Entropy for the Quantum Central Limit Theorem School MATHEMATICS As a landmark in probability theory, the Central Limit Theorem (CLT) asserts that the normalized sum of independent and identically distributed random variables with zero mean converges to a Gaussian random variable. Depending on the structure of the underlying distribution, this convergence can be formulated with respect to different topologies or metrics. To name two famous such CLTs, the Lindberg--Levy CLT states convergence in distribution assuming the finiteness of the second moment, and the Berry--Esseen CLT asserts the uniform convergence of cumulative distribution functions at the rate of $O(1/sqrt n)$ assuming the finiteness of the t ... 15:30 - 17:00 Geometry and Topology Weekly Seminar Interior Regularity of Monge-Ampere Equations School MATHEMATICS The second order elliptic partial differential equations have been studied for more than a century. The most important and basic example of such equations is the Laplace equation. It is a linear equation related to many topics in mathematics and Physics. The main property of such an equation is that solutions of Laplace equations are regular. Another important example of elliptic equations is the Monge-Ampere equation which is fully nonlinear. In contrast to the Laplace equation, the solutions of the Monge-Ampere equation may fail to be smooth. In this talk, we go over basic properties of Monge-Ampere equations. At last we will go over the c ... 17:30 - 19:00 Algebraic Geometry Biweekly Webinar Computational Tropical Geometry and its Applications School MATHEMATICS Tropical geometry is a combinatorial counterpart of algebraic geometry, transforming polynomials into piecewise linear functions and their solutions (varieties) into polyhedral fans. This transformation is intricately linked to the concept of Grobner bases, which provide a powerful tool in computational algebra. Specifically, all possible Grobner bases of an ideal are encoded within a polyhedral fan, with the tropical variety appearing as a subfan. Despite its significance, the computational complexity of tropical varieties often limits computations to small-scale instances. In this talk, we introduce a geometric approach that enables the eff ... |