# Seminários

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## PRÓXIMOS

Homogenization of Stochastic Conservation Laws

Expositor: Hermano Frid - IMPA
Qui 17 jun 2021, 13:30 - Palestra Virtual / Online LectureSeminário de Análise e Equações Diferenciais Parciais

Resumo: We consider the generalized almost periodic homogenization problem for two different types of stochastic conservation laws with oscillatory coefficients and multiplicative noise. In both cases the stochastic perturbations are such that the equation admits special stochastic solutions which play the role of the steady-state solutions in the deterministic case. Specially in the second type, these stochastic solutions are crucial elements in the homogenization analysis. Our homogenization method is based on the notion of stochastic two-scale Young measure, whose existence is established here.

This is a joint work with Kenneth Karlsen and Daniel Marroquin.

## HOJE

Abelian integrals for trivial global monodromy polynomials

Expositor: Salomón Rebollo Perdomo - Universidad del Bío-Bío, Chile
Sex 18 jun 2021, 10:30 - Palestra Virtual / Online LectureGeometry, Arithmetic and Differential Equations of Periods (GADEPs)

Resumo: Let $H(x,y)$ be a primitive polynomial having trivial global monodromy group of degree $m + 1$ and let $\omega$ be a polynomial 1-form of degree $n$. We will give a polynomial upper bound $Z_{TM}(m, n)$ for the maximum number of zeros of the Abelian integral defined by $H(x,y)$ and $\omega$.

A Mathematical Model Predicting the Course of Covid-19 and other epidemic and endemic disease.

Expositor: Ana Cascon and William F. Shadwick - Omega Analysis and IMPA
Qua 23 jun 2021, 14:00 - Palestra Virtual / Online LectureSeminário de Matemática Aplicada e Computacional

Resumo: We show that the Gompertz Function provides a generically excellent fit to viral and bacterial epidemics and endemic data. Gompertz Functions are based on the Gumbel probability distribution—one of the exceptional distributions for the geometry induced by the ‘location-scale’ group. This is the key to its role as an Extreme Value Theory attractor and the latter helps to explain the inevitability of its presence in epidemic data. There is a ‘good’ Gompertz Function fit for each time t, starting very early in any outbreak. Successive fits provide excellent forecasts for extended periods. Examples include the Danish Cholera epidemic of 1853, the ‘Spanish Flu’ pandemic of 1918-19 and many others prior to 2020, as well as Covid-19 outbreaks worldwide From the initial Covid-19 outbreaks in 2020 to the present this model has accurately predicted the course of the epidemic and subsequent waves. Critically, these predictions are accurate enough to use in forecasting health care resource requirements, initially for short periods and then for multiple weeks into the future. This is an important resource for responding to cyclical outbreaks such as we now see for the current respiratory virus season in Brazil. The cycles are characterised by an alternation between Gompertz Function growth and linear growth. The disease course is is easily predicted in both cases. This reduces the forecasting problem to dealing with the transition from linear to Gompertz Function growth and the early phase of the latter where the Gompertz Function Model’s predictive power is lowest. We indicate briefly how Extreme Value Theory can be used to address this problem. The Gompertz Function Model provides natural epidemic time scales and has important implications for disease transmissibility and for herd immunity.