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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:<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="images/Riemann.png" width="311" height="60" alt="Riemann" style="d
 isplay: block; margin-left: auto; margin-right: auto;"></p><p>that approxim
 ate the trajectories of regular polygonal vortex filaments. These functions
  are a generalization of the classical Riemann's non-differentiable functio
 n, which we recover when<em>&nbsp;x<sub>0</sub>&nbsp;= 0.</em> I will highl
 ight how the analysis seems to critically depend on <em>x<sub>0</sub></em>,
  and I will discuss the important role played by Gauss sums, a restricted v
 ersion of Diophantine approximation, the Duffin-Schaeffer theorem, and the 
 mass transference principle.</p><p>This talk is based on the article <a hre
 f="https://arxiv.org/abs/2309.08114">https://arxiv.org/abs/2309.08114</a> i
 n collaboration with Valeria Banica (Sorbonne Universite), Andrea Nahmod (U
 niversity of Massachusetts) and Luis Vega (BCAM, UPV/EHU).</p>
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:20260827T173349
DTSTART;TZID=America/New_York:20240509T155000
DTEND;TZID=America/New_York:20240509T165000
SEQUENCE:0
TRANSP:OPAQUE
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