IMPA Seminars

Monodromy action on non-singular level sets

Variedades de Calabi–YauSpeaker: Daniel Felipe López Garcia - IMPA

Tue 21 May 2019, 15:30 - Room 224

Abstract: For a holomorphic function $f:Y\rightarrow \mathbb{P}^1$, where $Y$ is a compact projective manifold, we consider the level set $Y_b=f^{-1}(b)$ of a regular value $b$. Let $C$ be the critical points of $f$. On the manifold $Y_b$ there is an action of the free group $\pi_1(\mathbb{P}^1\setminus{C})$ which descends to singular homology, which is called the monodromy action. In this talk, we will look at Dynkins diagrams associated to the intersection matrices in two variables, and by the Picard-Lefchestz formula we will compute the monodromy action for some examples.

Dynamic quantile models of rational behaviour

Interdisciplinary ColloquiumSpeaker: Luciano Irineu de Castro Filho - IMPA

Wed 22 May 2019, 16:00 - Auditorium 1

Abstract: I will describe a dynamic model of rational behavior under uncertainty, in which the agent maximizes the stream of the future τ-quantile utilities, for τ ∈ (0, 1). That is, the agent has a quantile utility preference instead of the standard expected utility. Quantile preferences have useful advantages, such as dynamic consistency, monotonicity, and allows the separation between risk aversion and elasticity of intertemporal substitution. Although quantiles do not share some of the helpful properties of expectations, such as linearity and the law of iterated expectations, we are able to establish all the standard results in dynamic models. Namely, we show that the quantile preferences are dynamically consistent, the corresponding dynamic problem yields a value function, via a fixed point argument, establish its concavity and differentiability and show that the principle of optimality holds. Additionally, we derive the corresponding Euler equation, which is well suited for using well- known quantile regression methods for estimating and testing the economic model.

Statistical Indicators of Asset Price Bubbles and the ‘Everything Bubble’

Mathematical Methods in FinanceSpeaker: Ana Cascon & William F. Shadwick - Omega Analysis

Mon 27 May 2019, 17:00 - Room 232

Abstract: Everyone knows that asset price bubbles exist. The history of financial markets is full of them, from the 17th Century Tulip Bubble to the 21st Century ‘Credit Bubble’

The critical issue for traders, long term investors and central banks is the extent to which bubbles can be recognised before they burst.

Our approach to this, initiated at the request of a G7 Central Bank, has identified statistical markers that have had high predictive power historically both in identifying bubbles and in quantifying the level to which they will subsequently correct.

It also identifies ‘anti-bubbles’ of panic selling and corresponding correction levels.

Ten years of unprecedented monetary intervention by the world’s Central Banks has produced bubbles in assets of all sorts. The extent of the coming corrections and the timing of the bubble deflation vary greatly across regions, countries and asset class sectors.

Some have already burst producing anti-bubbles of panic selling while others are still inflating. This produces a range of opportunities and challenges for market participants and policy makers.

Making Humans

Computer GraphicsSpeaker: Luiz Velho - IMPA

Wed 29 May 2019, 13:30 - Auditorium 3

Abstract: This talk is the sixth lecture of the VISGRAF Seminar Series "Next Media for Storytelling: Fundamentals and State-of-the-Art".

We will describe how to create digital models of virtual humans. The process starts with the definition of a complete representation of a humanoid character, including body shape, pose, and tissue dynamics. This leads to a mathematical and computational model that is simple, low-dimensional, easy to animate and fit to real data.