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• Metastable regimes of diffusion processes

  Speaker: Mauro Mariani (National Research University Higher School of Economics, Moscow) - https://www.hse.ru/en/org/persons/209427823
  

  When: Wed, September 12, 2018 - 2:00pm
  Where: Kirwan Hall 1313
  

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  Abstract: I will discuss a classical example featuring a metastable
  behavior: finite-dimensional diffusion processes in the vanishing
  noise limit. Exponential estimates have been introduced fifty years
  ago by Freidlin and Wentzell. Recent developments in potential theory
  and variational convergence allowed a refinement of those results. I
  will focus on the non-reversible case, with motivations coming from
  MCMC and open problems in the context of wKAM theory. The talk is
  based on recent papers with G.DiGesu (TU Wien), C.Landim (IMPA) and
  I.Seo (UC Berkeley/Seoul NU).
  
• Exit problems and rare transitions in noisy heteroclinic networks.

  Speaker: Yuri Bakhtin (NYU) - https://cims.nyu.edu/~bakhtin/
  

  When: Wed, November 7, 2018 - 2:00pm
  Where: 1313.0
  

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  Abstract: I will talk about extending my earlier work on the vanishing noise limit of diffusions in noisy heteroclinic networks to longer time scales. In this field, the results are based on sequential analysis of exit locations and exit times for neighborhoods of unstable equilibria. The new results on exit times and the emergent hierarchical structure are joint with Zsolt Pajor-Gyulai.