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UID:5ea0c8037105255a5747c8ae7835249a
CATEGORIES:Hyperbolic & Dispersive PDE Seminar
CREATED:20240417T125828
SUMMARY: Daniel Eceizabarrena -- Multifractality in the evolution of vortex filaments
LOCATION:Hill 705
DESCRIPTION:Vortex filaments that evolve according the binormal flow are expected to ex
 hibit turbulent properties. Aiming to quantify this, I will discuss the mul
 tifractal properties of the family of functions\n\n\nthat approximate the t
 rajectories of regular polygonal vortex filaments. These functions are a ge
 neralization of the classical Riemann's non-differentiable function, which 
 we recover when x0 = 0. I will highlight how the analysis seems to critical
 ly depend on x0, and I will discuss the important role played by Gauss sums
 , a restricted version of Diophantine approximation, the Duffin-Schaeffer t
 heorem, and the mass transference principle.\nThis talk is based on the art
 icle https://arxiv.org/abs/2309.08114 in collaboration with Valeria Banica 
 (Sorbonne Universite), Andrea Nahmod (University of Massachusetts) and Luis
  Vega (BCAM, UPV/EHU).\n
X-ALT-DESC;FMTTYPE=text/html:<p>Vortex filaments that evolve according the binormal flow are expected to
  exhibit turbulent properties. Aiming to quantify this, I will discuss the 
 multifractal properties of the family of functions<code><br></code></p><p><
 img src="https://www.math.rutgers.edu/images/Riemann.png" width="311" heigh
 t="60" alt="Riemann" style="display: block; margin-left: auto; margin-right
 : auto;"></p><p>that approximate the trajectories of regular polygonal vort
 ex filaments. These functions are a generalization of the classical Riemann
 's non-differentiable function, which we recover when<em>&nbsp;x<sub>0</sub
 >&nbsp;= 0.</em> I will highlight how the analysis seems to critically depe
 nd on <em>x<sub>0</sub></em>, and I will discuss the important role played 
 by Gauss sums, a restricted version of Diophantine approximation, the Duffi
 n-Schaeffer theorem, and the mass transference principle.</p><p>This talk i
 s based on the article <a href="https://arxiv.org/abs/2309.08114">https://a
 rxiv.org/abs/2309.08114</a> in collaboration with Valeria Banica (Sorbonne 
 Universite), Andrea Nahmod (University of Massachusetts) and Luis Vega (BCA
 M, UPV/EHU).</p>
CONTACT: Daniel Eceizabarrena (University of Massachusetts Amherst)
DTSTAMP:20260828T011737
DTSTART;TZID=America/New_York:20240509T155000
DTEND;TZID=America/New_York:20240509T165000
SEQUENCE:0
TRANSP:OPAQUE
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