Modification de MINI-SCHOOL 2019

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<div style="padding:1.1em 0.5em; font-size:150%; color: black;"> '''3rd edition of the Mini-school on mathematics for theoretical chemistry and physics'''
(supported by [[Accueil|GDR NBODY]] and [http://www.ip2ct.upmc.fr/ IP2CT])
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[[Image:Maths1.jpg|500px]]
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In the same spirit than the [http://gdrcorelec.ups-tlse.fr/index.php?title=MINI-SCHOOL_2017 1st edition of the mini-school] and [http://gdrcorelec.ups-tlse.fr/index.php?title=MINI-SCHOOL_2018 2nd edition of the mini-school]
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* '''Date:'''  19-21 June 2019

* '''Location:''' Sorbonne Université, Pierre et Marie Curie (or Jussieu) campus, 4 place Jussieu, 75005, Paris. Laboratoire Jacques-Louis Lions, tower/corridor 15-16, 3rd floor, room 309. <font color="red">'''Warning: on the last afternoon, we will change room: Tower 15-25, room 102'''</font>

* '''Lecturers: ''' [https://web.physics.wustl.edu/cmb/ Carl Bender] and [http://antoine.levitt.fr/ Antoine Levitt]

* '''Organizers:''' [http://qmcchem.ups-tlse.fr/index.php?title=Michel_Caffarel Michel Caffarel], [http://cermics.enpc.fr/~cances/ Eric Cancès], [http://quantique.u-strasbg.fr/doku.php?id=en:pageperso:ef:welcome Emmanuel Fromager], Emmanuel Giner, [http://www.irsamc.ups-tlse.fr/loos/index.html Pierre-François Loos], [http://www.lct.jussieu.fr/pagesperso/toulouse/ Julien Toulouse]. [mailto:minischool@lct.jussieu.fr  email contact]

* '''[[MINI-SCHOOL 2019 List of registered participants|List of registered participants]]'''


==Presentation==  

* The lectures delivered are intended to be of interest to any person working in the field of theoretical chemistry and physics and willing to discover or deepen the mathematical aspects of the theoretical methods. Master and PhD students, post-docs and any academic are welcome!

* To provide a detailed presentation of subjects, we have chosen to give a good amount of time to each lecturer. The mini-school will thus involve only two lecturers over a three-day period.


==Program==

Two courses will be proposed:

* 1) '''Complex analysis''' (9 hours) by '''[http://antoine.levitt.fr/ Antoine Levitt]''', INRIA and Ecole des Ponts, Paris, France.

Indicative program (subject to changes and extension):<br>
- Complex numbers<br>
- Holomorphic functions, elliptic functions. Applications to electrostatics and fluid mechanics <br>
- Power series, analytic continuation, poles and branches<br>
- Contour integrals, functional calculus. Application to finite temperature perturbation theory<br>
- Fourier and Laplace transforms of causal functions, the "i0+ trick", Kramers Kronig relations <br>
- Paley Wiener theory. Application to Fourier and Chebyshev approximation, and decay of the density matrix

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'''Download [http://antoine.levitt.fr/complex_analysis.pdf lecture notes]'''
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* 2) '''Perturbation theory, summation theory, and PT-symmetric quantum theory''' (9 hours) by '''[https://web.physics.wustl.edu/cmb/ Carl Bender]''', Washington University in St. Louis, USA
       
Indicative program (subject to changes and extension):<br>
- Introduction to perturbation theory and methods<br>
- Asymptotic series<br>
- WKB analysis and eigenvalue problems<br>
- Summation theory<br>
- PT-symmetric quantum theory<br>
- Classical PT symmetry

<font color="red">'''Download slides [http://www.lct.jussieu.fr/pagesperso/toulouse/bender_lecture1.pdf lecture 1] [http://www.lct.jussieu.fr/pagesperso/toulouse/bender_lecture2.pdf lecture 2] [http://www.lct.jussieu.fr/pagesperso/toulouse/bender_lecture3.pdf lecture 3]'''
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[[Fichier:Levitt 2019.jpg|500px]] [[Fichier:Bender 2019.jpg|500px]]
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== Schedule ==

{| border="5" |
! <center><font color="blue">Wednesday 19 June Morning</font> <br>
Tower 15-16, room 309</center>
! <center><font color="blue">Thursday 20 June Morning</font> <br>
Tower 15-16, room 309</center>
! <center><font color="blue">Friday 21 June Morning</font><br>
Tower 15-16, room 309 </center>
|- align="left"
!'''<font color="red">8:45-9:00 Arrivals/Welcome</font>'''!! !!
|- align="left"
! '''9:00-10:30''' Carl Bender 1
!'''9:00-10:30''' Carl Bender 3
!'''9:00-10:30''' Carl Bender 5
|-align="left"
!<font color="green">10:30-10:45 Coffee break</font> 
!<font color="green">10:30-10:45 Coffee break</font>
!<font color="green">10:30-10:45 Coffee break</font>
|-align="left"
!'''10:45-12:15''' Carl Bender 2
!'''10:45-12:15''' Carl Bender 4
!'''10:45-12:15''' Carl Bender 6
|-align="left"
!  <font color="green">12:15-14:00 Lunch at L'Ardoise (Tower 25)</font>
!  <font color="green">12:15-14:00 Lunch at L'Ardoise (Tower 25)</font>
!  <font color="green">12:15-14:00 Lunch at L'Ardoise (Tower 25)</font>
|-align="left"
! <center><font color="blue">Wednesday 19 June Afternoon</font> <br>
Tower 15-16, room 309</center>
! <center><font color="blue">Thursday 20 June Afternoon</font> <br>
Tower 15-16, room 309</center>
! <center><font color="blue">Friday 21 June Afternoon</font><br>
<font color="red">Tower 15-25, room 102</font></center>
|-align="left"
!'''14:00-15:30''' Antoine Levitt 1
!'''14:00-15:30''' Antoine Levitt 3
!'''14:00-15:30''' Antoine Levitt 5
|-align="left"
!  <font color="green">15:30-15:45 Coffee break</font> 
!  <font color="green">15:30-15:45 Coffee break</font> 
!  <font color="green">15:30-15:45 Coffee break</font> 
|-align="left"
!'''15:45-17:15''' Antoine Levitt 2
!'''15:45-17:15''' Antoine Levitt 4
!'''15:45-17:15''' Antoine Levitt 6
|}

== Practical details ==

=== Registration ===

'''Registration is closed.'''

To facilitate the participation of young researchers, no registration fees will be asked.
However, accommodation will not be provided but must be arranged independently by the participants.

=== Location of the mini-school === 

The mini-school will take place on the Pierre et Marie Curie (or Jussieu) campus of [http://www.sorbonne-universite.fr/ Sorbonne Université], 4 place Jussieu, 75005 Paris.

Subway (Metro) lines 7 or 10: get off at "Jussieu" station. 

From the main entrance of the campus, go to '''Tower 16'''. Take the stairs or the elevator to the '''third level'''. Find '''corridor 15-16''', and then the '''room 309'''. This is the seminar room of Laboratoire Jacques-Louis Lions.<br> 
<font color="red">'''Warning: on the last afternoon, we will change room: Tower 15-25, room 102'''</font>

=== Lunches === 
Each day, lunch will be offered to all registered participants to the mini-school (see the list of registered participants on the page [[MINI-SCHOOL 2019 List of registered participants|List of registered participants]]).

=== Arriving by Plane === 

Both Paris-Charles de Gaulle (CDG) and Paris-Orly international airports are connected to the center of Paris by RER (fast regional railway) or coaches. The RER is connected to the subway (Metro) network. It costs about 10 euros to go from either airport to the center of Paris and it takes about one hour. 

For more information, check the [http://www.aeroportsdeparis.fr/Adp/en-GB/Passagers/ Paris airports website].

=====From Paris-Charles de Gaulle (CDG) airport=====
From the airport take RER line B. Stop at "St-Michel-Notre-Dame" station. Take subway line 10 direction "Austerlitz" and stop at "Jussieu" station.

=====From Paris-Orly airport=====
From the airport take the monorail "OrlyVal" to "Antony". Take RER line B. Stop at "St-Michel-Notre-Dame" station. Take subway line 10 direction "Austerlitz" and stop at "Jussieu" station.

===Arriving by Train===

All the railway stations are in downtown Paris and are connected to the subway network. For train reservation, check the [http://www.voyages-sncf.com SNCF web site].

From any train station follow the sign "M" to the subway.

===Arriving by Subway or Bus===
For more information on the RER, Subway and Bus systems, check the [http://www.ratp.fr/ RATP web site], and in particular the [http://www.ratp.fr/plan-interactif/ Subway and RER map].