Telegram Group & Telegram Channel
https://www.math.columbia.edu/~okounkov/AMScolloq.pdf

хочется напонить еще текст «Limit shapes, real and imaginary» Андрея Окунькова

«We are surrounded by random surfaces. In fact, every shape around us is random on a sufficiently small scale. The definite shapes that we perceive are manifestations of the law of large numbers that makes averages much larger than the fluctuations around them. Same law is at work e.g. with a balloon floating through the air. Our eyes trace out a smooth trajectory while air molecules hit the balloon randomly from all directions.

Can mathematical physics link the microscopic dynamics to the resulting macroscopic shape, say, for objects of inorganic natural origin? The endless variety of snowflake shapes produced by commonplace water under ordinary conditions illustrates how challenging this question is.

Yet, at or near equilibrium a successful theory explaining the macroscopic shape from the microscopic laws may be developed. It requires deep and powerful mathematics that we can only begin to explore it the course of 3 lectures. In turn, it impacts areas of mathematics that may seem very distant from equilibrium crystals or liquid droplets.

Mathematics and physics are full of random geometric objects, especially when surveyed with a trained eye. In dealing with them, the experience and intuition acquired in the study of equilibrium crystals can be very valuable.

***

The main goal of this lecture is to provide an accessible introduction to an area of mathematical physics that I, personally, find captivating. (…)»



group-telegram.com/cme_channel/3839
Create:
Last Update:

https://www.math.columbia.edu/~okounkov/AMScolloq.pdf

хочется напонить еще текст «Limit shapes, real and imaginary» Андрея Окунькова

«We are surrounded by random surfaces. In fact, every shape around us is random on a sufficiently small scale. The definite shapes that we perceive are manifestations of the law of large numbers that makes averages much larger than the fluctuations around them. Same law is at work e.g. with a balloon floating through the air. Our eyes trace out a smooth trajectory while air molecules hit the balloon randomly from all directions.

Can mathematical physics link the microscopic dynamics to the resulting macroscopic shape, say, for objects of inorganic natural origin? The endless variety of snowflake shapes produced by commonplace water under ordinary conditions illustrates how challenging this question is.

Yet, at or near equilibrium a successful theory explaining the macroscopic shape from the microscopic laws may be developed. It requires deep and powerful mathematics that we can only begin to explore it the course of 3 lectures. In turn, it impacts areas of mathematics that may seem very distant from equilibrium crystals or liquid droplets.

Mathematics and physics are full of random geometric objects, especially when surveyed with a trained eye. In dealing with them, the experience and intuition acquired in the study of equilibrium crystals can be very valuable.

***

The main goal of this lecture is to provide an accessible introduction to an area of mathematical physics that I, personally, find captivating. (…)»

BY Непрерывное математическое образование


Warning: Undefined variable $i in /var/www/group-telegram/post.php on line 260

Share with your friend now:
group-telegram.com/cme_channel/3839

View MORE
Open in Telegram


Telegram | DID YOU KNOW?

Date: |

"There are several million Russians who can lift their head up from propaganda and try to look for other sources, and I'd say that most look for it on Telegram," he said. The news also helped traders look past another report showing decades-high inflation and shake off some of the volatility from recent sessions. The Bureau of Labor Statistics' February Consumer Price Index (CPI) this week showed another surge in prices even before Russia escalated its attacks in Ukraine. The headline CPI — soaring 7.9% over last year — underscored the sticky inflationary pressures reverberating across the U.S. economy, with everything from groceries to rents and airline fares getting more expensive for everyday consumers. The fake Zelenskiy account reached 20,000 followers on Telegram before it was shut down, a remedial action that experts say is all too rare. Unlike Silicon Valley giants such as Facebook and Twitter, which run very public anti-disinformation programs, Brooking said: "Telegram is famously lax or absent in its content moderation policy." Since its launch in 2013, Telegram has grown from a simple messaging app to a broadcast network. Its user base isn’t as vast as WhatsApp’s, and its broadcast platform is a fraction the size of Twitter, but it’s nonetheless showing its use. While Telegram has been embroiled in controversy for much of its life, it has become a vital source of communication during the invasion of Ukraine. But, if all of this is new to you, let us explain, dear friends, what on Earth a Telegram is meant to be, and why you should, or should not, need to care.
from us


Telegram Непрерывное математическое образование
FROM American