Direttore Vicario: Prof. Gabriele Grillo
Responsabile Gestionale: Dr.ssa Franca Di Censo


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Prossimi Seminari

  • A mathematical-physics approach to machine learning
    Pierluigi Contucci, Dipartimento di Matematica Università di Bologna
    giovedì 30 gennaio 2020 alle ore 14:00, Aula Saleri VI piano

Seminari Passati

  • Symmetry results for critical $p$-Laplace equations
    Giulio Ciraolo, Università degli Studi di Milano
    mercoledì 23 ottobre 2019 alle ore 15:15, Aula seminari 3° piano
    It is known that positive solutions to $\Delta_p u + u^{p^*-1}=0$ in $\mathbb{R}^n$, with $n \geq 3$ and $1
    We provide a new approach to this problem which allows us to give a complete classification of the solutions in an anisotropic setting as well as to a suitable generalization of the problem in convex cones.

    This is a joint work with A. Figalli and A. Roncoroni.
  • Pricing and hedging in rough Heston models
    Omar El Euch, Spire Europe Limited
    martedì 22 ottobre 2019 alle ore 14:15, Aula seminari del terzo piano
    It has been recently shown that rough volatility models, where the volatility is driven
    by a fractional Brownian motion with small Hurst parameter, provide very relevant dynamics in order to reproduce the behavior of both historical and implied volatilities. However, due to the non-Markovian nature of the fractional Brownian motion, they raise new issues when it comes to derivatives pricing and hedging. Using an original link between nearly unstable Hawkes processes and fractional volatility models, we compute the characteristic function of the log-price in rough Heston models and obtain explicit hedging strategies. The replicating portfolios contain the underlying asset and the forward variance curve, and lead to perfect hedging (at least theoretically). From a probabilistic point of view, our study enables us to disentangle the infinite-dimensional Markovian structure associated to rough volatility models.
  • L'interazione fra neuroscienze e matematica: analisi della connettività cerebrale utilizzando i grafi
    Paolo Finotelli,  Politecnico di Milano
    mercoledì 16 ottobre 2019 alle ore 15:30, Sala Consiglio - piano 7° - edificio 14 - via Ponzio 31/p
    L'intento di questo seminario è mostrare come l'interazione fra le neuroscienze e la matematica sia in continua crescita e sia destinata a costituire la base della medicina moderna. In particolare, verranno introdotti i fondamenti della connettività cerebrale e della teoria delle reti complesse, di cui la teoria dei grafi costituisce l’impalcatura matematica. Come caso particolare verrà presentato un recente modello per la determinazione della connettività cerebrale basato sulla teoria dei grafi.
  • Control problems in Wasserstein space
    Antonio Marigonda, University of Verona
    lunedì 14 ottobre 2019 alle ore 15:15, Aula seminari 6° piano
    In this talk we present recent results about the existence and uniqueness of the viscosity solution for a certain classes on Hamilton-Jacobi Equations in the Wasserstein space of probability measure, arising in problem of mean field control of multi-agent systems. We consider a multi-agent system subject to a centralized controller
    aiming to minimize a cost function. The microscopic dynamics of each agent is given by a differential inclusion. We model the distribution of agents by a probability measure, and formulate the minimization problem
    as a Mayer problem for a dynamics in the Wasserstein space represented by a controlled continuity equation describing the macroscopical evolution of the system. We prove that the value function V of the
    problem solves a Hamilton-Jacobi equation in the Wasserstein space in a suitable viscosity sense, and prove a comparison principle for such an equation, thus characterizing V as the unique viscosity solution of the
    Hamilton-Jacobi equation associated to the problem.
  • How Mathematics helps structuring climate discussions
    Rupert Klein, FU Berlin & ECMWF Fellow
    giovedì 3 ottobre 2019 alle ore 14:00, Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
    Mathematics in climate research is often thought to be mainly a provider of techniques for solving the continuum mechanical equations for the flows of the atmosphere and oceans, for the motion and evolution of Earth's ice masses, and the like. Three examples will elucidate that there is a much wider range of opportunities. Climate modellers often employ reduced forms of the continuum mechanical equations to efficiently address their research questions of interest. The first example discusses how mathematical analysis can provide systematic guidelines for the regime of applicability of such reduced model equations. Meteorologists define 'climate', in a narrow sense, as the statistical description in terms of the mean and variability of relevant quantities over a period of time (World Meteorological Society,; see the website for a broader sense definition). Now, climate researchers are most interested in changes of the climate over time, and yet there is no unique, well-defined notion of time dependent statistics. In fact, there are restrictive conditions which data from time series need to satisfy for classical statistical methods to be applicable. The second example describes recent developments of analysis techniques for time series with non-trivial temporal trends. Modern climate research has joined forces with economy and the social sciences to generate a scientific basis for informed political decisions in the face of global climate change. One major type of problems hampering progress of the related interdisciplinary research consists of often subtle language barriers. The third example describes how mathematical formalization of the notion of 'vulnerability' has helped structuring related interdisciplinary research efforts.

  • Mountain pass structure, non-degeneracy conditions and variational gluing
    Paul H. Rabinowitz, University of Wisconsin, Madison
    venerdì 20 settembre 2019 alle ore 14:00, Sala di Rappresentanza, Via C. Saldini 50
    The effect of non-degeneracy conditions on the applicability of variational gluing arguments for some variational problems possessing mountain pass structure will be discussed.

  • Decay and Sobolev regularity properties for solutions at infinity of (nonlinear) PDEs
    Stefano Pigola, Università dell’Insubria
    venerdì 20 settembre 2019 alle ore 11:15, Aula seminari 3° piano
    I will present some recent results on the global behaviour of nonnegative and bounded subsolutions of $\Delta_p u = f(u)$ over an exterior domain of a complete Riemannian manifold. I shall discuss geometric conditions under which such a subsolution decays to zero at infinity. The main tools are represented by (a nonlinear version of) the Feller property and some global comparison results. These, in turn, are related to a new characterization of the ($p$-)stochastic completeness of the manifold in terms of the Sobolev space $W^{1,p}$.
  • Algebraic Option Pricing
    Peter Carr, New York University
    venerdì 13 settembre 2019 alle ore 12:15, Sala Consiglio settimo piano
    Optionality arises whenever an investor can choose between owning either of two
    assets. We treat the value of optionality as a modified sum. We then explore
    options on options as sums of sums. This viewpoint allows us to derive a simple
    closed form formula for a Bermudan option.