UPDATE: SISSA/IGAP Lecture on "Standard and less standard asymptotic methods" / Don Zagier

[ICTP Math Section]

_IMPORTANT:_ This is to inform you all that starting from today 
_Thursday 10 March_, Don Zagier's Course will be as follows:

- Thu 10-Mar 16.00 - 17-30

- Mon 14-Mar 14.00 - 15.30
- Wed 16-Mar 14.00 - 15.30

- Mon 21-Mar 14.00 - 15.30
- Wed 23-Mar 14.00 - 15.30

_*PLEASE NOTE ALSO:*_ The program of the course will be updated on the 
Poster accordingly.

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SISSA/IGAP Lecture on "Standard and less standard asymptotic methods"


Starts 15 Feb 2022 16:00
Ends 23 Mar 2022 15:30
Central European Time


Online:
Please register in advance for this meeting:
https://unesco-org.zoom.us/meeting/register/tJUvcO2qqDgtGtMYJCHfEtIForecwtoJIK4r

and then you will receive a confirmation email containing information 
about joining the meeting.

Presence: ICTP Leonardo Da Vinci Building - Budinich Lecture Hall (only if
provided with a green pass)

Lecturer: Don Zagier (MPIM/ICTP)

Course Type: SISSA PhD Course
Academic Year: 2021-2022
Period: 15 February to 23 March 2022
Research Group: SISSA-Geometry and Mathematical Physics
Duration: 20 h

Description:

In every branch of mathematics, one is sometimes confronted with the
problem of evaluating an infinite sum numerically and trying to guess its
exact value, or of recognizing the precise asymptotic law of formation of
a sequence of numbers {A_n} of which one knows, for instance, the first
couple of hundred values. The course will tell a number of ways to study
both problems, some relatively standard (like the Euler-Maclaurin formula
and its variants) and some much less so, with lots of examples. Here
are three typical examples: 1. The slowly convergent sum sum_{j=0}^\infty
(\binom{j+4/3}{j})^{-4/3} arose in the work of a colleague. Evaluate it
to 250 decimal digits. 2. Expand the infinite sum \sum_{n=0}^\infty
(1-q)(1-q^2)...(1-q^n) as \sum A_n (1-q)^n, with first coefficients 1, 1,
2, 5, 15, 53, ... Show numerically that A_n is asymptotic to n! * a *
n^b * c for some real constants a, b and c, evaluate all three to high
precision, and recognize their exact values. 3. The infinite series H(x)
= \sum_{k=1}^\infty sin(x/k)/k converges for every complex number x. 
Compute this series to high accuracy when x is a large real number, so
that the series is highly oscillatory.

The courses are scheduled as follows:

8 Thu 10-Mar 16.00 - 17-30

9 Mon 14-Mar 14.00 - 15.30
10 Wed 16-Mar 14.00 - 15.30

11 Mon 21-Mar 14.00 - 15.30
12 Wed 23-Mar 14.00 - 15.30


These will be hybrid courses. All are very welcome to join either online
or in person (if provided with a green pass). Venue: Budinich Lecture Hall
(ICTP Leonardo Da Vinci Building), for those wishing to attend in person.

http://indico.ictp.it/event/9872/