| Thursday 25 April 2024 | |
| Events for day: Wednesday 05 April 2023 |
| 14:00 - 15:00 Combinatorics and Computing Weekly Seminar Learning of Simplices in R^ k from Noisy Data School MATHEMATICS I will talk about sample complexity bounds for learning a simplex from noisy samples. In particular, assume n i.i.d. samples drawn from a uniform distribution over an unknown simplex in R^k are given, where samples are corrupted by a multi-variate additive Gaussian noise of an arbitrary magnitude. Then, we prove the existence of an algorithm that with high probability outputs a simplex with an ℓ2 distance of at most ε from the true simplex (for any ε > 0). Also, we show that in order to achieve this bound, it is sufficient to have n ≥ k 2/ε2 e Θ(k/SNR2 ) samples, where SNR stands for the signal- ... 17:30 - 19:00 Number Theory Webinar Moments of L-functions and Mean Values of Long Dirichlet Polynomials School MATHEMATICS Establishing asymptotic formulae for moments of L-functions is a central theme in analytic number theory. This topic is related to various non-vanishing conjectures and and the generalized Lindel�f Hypothesis. A major breakthrough in analytic number theory occurred in 1998 when Keating and Snaith established a conjectural formula for moments of the Riemann zeta function using ideas from random matrix theory. The methods of Keating and Snaith led to similar conjectures for moments of many families of L-functions. These conjectures have become a driving force in this field which has witnessed substantial progress in the last two decades. ... |