Research at Uppsala University

• A Novel Approach to Boundary Value Problems for Parabolic Equations and Systems

  Research project from 2018-01-01 to 2021-12-31

  Parabolic equations and systems are indispensable models in mathematics, physics, chemistry, biology, finance and in most engineering disciplines. These models appear in contexts involving time dependent ...

• A high-fidelity model of acoustic-gravity waves from volcanic eruptions

  Research project from 2018-01-01 to 2021-12-31

  The present project focuses on high-fidelity mathematical and numerical models, in collaboration with Stanford University, to simulate infrasound from a wide range of volcanic activity. The first task ...

• Abelian integrals and Hilbert´s 16th problem

  Research project from 2019-01-01 to 2022-12-31

  The aim of this project is to significantly improve our knowledge about the solution to Hilbert´s 16th problem and its infinitesimal version, both of which ask for the maximal number of isolated periodic ...

• Ansökan från Amy Goldberg inom programmet Graduate Research Opportunity Worldwide

  Research project from 2014-01-01 to 2014-12-31

  Ansökan från Amy Goldberg inom programmet Graduate Research Opportunity Worldwide ...

• Dynamical and spectral problems on homogeneous spaces, with applications in number theory and mathematical physics

  Research project from 2012-01-01 to 2015-12-31

  The proposed research is a multifaceted investigation centering on problems in homogeneous dynamics and fundamental questions about lattices. We will focus in particular on problems which hold the promise ...

• Boundary behavior and potential theory for the degenerate parabolic p-Laplace equation

  Research project from 2015-01-01 to 2017-12-31

  In this project we are concerned with solutions to the so-called degenerate parabolic p-Laplace equation, a parabolic version of the classical p-Laplace equation.This project has two directions. The first ...

• Noise distribution in the environment

  Research project from 2019-01-01 to 2021-12-31

  1) Develop a high-fidelity 3D atmospheric wave propagation model to simulate sound propagation from a diverse set of sound-sources, such as wind-turbines, construction work, traffic roads, airplanes, railways ...

• Compositions of stochastic processes

  Research project from 2014-01-01 to 2017-12-31

  The goal of this research proposal is the study of the pathwise composition of various classes of stochastic processes, in particular, their asymptotics as the number of processes goes to infinity, their ...

• Degenerate parabolic equations and applications to AI

  Research project from 2020-01-01 to 2023-12-31

  In this project we are concerned with degenerate parabolic equations and their applications to AI.This project has two directions. The first direction concerns boundary comparison principles, specifically ...

• Dynamics and asymptotics on homogeneous spaces, and applications

  Research project from 2016-01-01 to 2019-12-31

  The research proposed here is a multifaceted investigation centeringon problems in dynamics on homogeneous spaces andfundamental questions about lattices. I will focus in particular onproblems which hold ...

• Equations of Kolmogorov type in Analysis, Finance and Physics

  Research project from 2014-01-01 to 2017-12-31

  Degenerate parabolic equations of Kolmogorov type occur in many areas of analysis, physics and applied mathematics. In their simplest form these equations were introduced and studied by Kolmogorov in ...

• Geometric Inverse Problems in PDE

  Research project from 2013-01-01 to 2016-12-31

  This project studies the mathematical models arising from a variety of imaging techniques. These problems are formulated mathematically as "inverse problems" where one deduces information about the differential ...

• Geometric foliations and conserved quantities in mathematical general relativity

  Research project from 2017-01-01 to 2020-12-31

  Conserved quantities are important in various areas of physics, as in many cases they provide an essential characterization of a physical system. However, to define the mass, center of mass, angular and ...

• Non-uniformly hyperbolic dynamical systems

  Research project from 2017-01-01 to 2019-12-31

  The first part of the project (with J. Graczyk, Orsay) concerns the abundance of maps satisfying an expontential growthcondition at the critical value.(Collet-Eckmann-condition) for parameters of the complex ...

• Nonlinear eigenvalue problems and regularity theory for nonlocal nonlinear equations

  Research project from 2018-01-01 to 2021-12-31

  One part of this project concerns nonlinear eigenvalue problems. These problems have a long history and arise in a variety of applications. We intend to develop methods based on inverse iteration and the ...

• Relative equilibria for the n-body problem: a millenium problem

  Research project from 2014-01-01 to 2017-12-31

  Ett klassiskt problem från celest mekanik är att beskriva hur N stycken kroppar (planeter, stjärnor eller satelliter) samverkar och rör sig under gravitationens påverkan. Tidigare försök (av Poincare och ...

• Stability regions in the planetary problem

  Research project from 2020-01-01 to 2023-12-31

  The main purpose of this project is to prove existence of quasi-periodic motion in the 3-body problem with realistic parameters of Sun, Jupiter and Saturn. The aim is to prove that KAM theory can be applied ...

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