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**From**: Károlyi György <karolyi AT reak.bme.hu>**To**: undisclosed-recipients: ;**Subject**: [Fizinfo] Alkalmazott Matematikai Nap a BME-n**Date**: Thu, 10 Oct 2019 12:25:11 +0200

Meghívó

Alkalmazott Matematikai Nap

a BME Matematika Intézet

és

a BME Morfodinamikai Kutatócsoport

szervezésében

Mottó: Ha egy matematikai diszciplína messzire távolodik tapasztalati

forrásától, az súlyos veszélyt rejt magában. A forrásától eltávolodott

folyó jelentéktelen ágak sokaságává különül el és a diszciplína

részletek és bonyodalmak szervezetlen tömegévé válik.

/Neumann János/

The Geometry of Turbulence

Turbulence is one of the oldest unsolved mysteries of modern science. In these

two talks we give a glimpse of how, inspired by centuries-old ideas, current

theoretical research is coming closer to understanding the most basic

questions.

Időpont: 2019. október 16. 16:30

Helyszín: Budapesti Műszaki és Gazdaságtudományi Egyetem

K épület I. emelet 150. terem

Honlap: http://math.bme.hu/alkmatnap

Program:

16:30

Székelyhidi László

Universität Leipzig

Rigid surfaces from Euclid to Nash and how to bend them.

Összefoglaló:

A compact surface is called rigid if the only length-preserving

transformations of it are congruencies of the ambient space - in simple

terms rigid surfaces are unbendable. Rigidity is a topic which is already

found in Euclid's Elements. Leonhard Euler conjectured in 1766 that every

smooth compact surface is rigid. The young Augustin Cauchy found a proof

in 1813 for convex polyhedra, but it took another 100 years until a proof

for smooth convex surfaces appeared. Whilst it seems clear that convexity,

and more generally curvature plays an important role for rigidity, it came

as a shock to the world of geometry when John Nash showed in 1954 that every

surface can be bent in an essentially arbitrary, albeit non-convex manner.

The proof of Nash involves a highly intricate fractal-like construction,

that has in recent years found applications in many different branches of

applied mathematics, such as the theory of solid-solid phase transitions

and hydrodynamical turbulence. The talk will provide an overview of this

fascinating subject and present the most recent developments.

17:30

Uriel Frisch

CNRS Paris

Leonardo da Vinci, Tódor Kármán and many more: the decay of turbulence

Leonardo had a strong interest in mathematics (at the time, mostly geometry

and simple algebraic equations). In the early part of his life, spent in

Florence, Leonardo became interested in chaotic hydrodynamics (called by

him, for the first time "turbulence"), a topic which will persist throughout

his life. Examining the "turbulences" (eddies) in the river Arno he found in

the late 1470 that the amplitude of the turbulence was decreasing very

slowly in time, until it would come to rest (within the surrounding river).

This topic would remain dormant for close to 5 centuries, until in 1938

Tódór (Theodore) Kármán, triggered by Geoffrey Taylor, established that

the amplitude of the turbulence should decrease very slowly, indeed like

an inverse power of the time elapsed. Three years later, Andrei Kolmogorov

found an algebraic mistake in Kármán's calculation; Kolmogorov himself found

another inverse power (5/7) of the time elapsed. This, likewise was wrong.

In the talk we will present developments in a historical context and connect

to recent progress on this topic. Very recently, we found that the law of

decay of the amplitude need not be exactly an inverse of the time elapsed.

Furthermore, more exotic laws of decay were obtained for "weak"

(distributional) solutions using a Nash-like construction.

Minden érdeklődőt szeretettel várnak a szervezők,

Domokos Gábor, G. Horváth Ákos, Károlyi György

**[Fizinfo] Alkalmazott Matematikai Nap a BME-n**,*Károlyi György, 10/10/2019*

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