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<center>
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<div style="padding:1.1em 0.5em; font-size:150%; color: black;"> '''3nd edition of the Mini-school on mathematics in electronic structure theory of GDR NBODY 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])
 
</div>
 
</div>
 
</center>
 
</center>
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* '''Date:'''  19-21 June 2019
 
* '''Date:'''  19-21 June 2019
  
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* '''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  
+
* '''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]
 
* '''Lecturers: ''' [https://web.physics.wustl.edu/cmb/ Carl Bender] and [http://antoine.levitt.fr/ Antoine Levitt]
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* 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.
 
* 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==
 
==Program==
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- Contour integrals, functional calculus. Application to finite temperature perturbation theory<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>
 
- 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<br>
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- Paley Wiener theory. Application to Fourier and Chebyshev approximation, and decay of the density matrix
 +
 
 +
<font color="red">
 +
'''Download [http://antoine.levitt.fr/complex_analysis.pdf lecture notes]'''
 +
</font>
  
  
 
* 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
 
* 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): to be announced
+
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]'''
 +
</font>
 +
 
 +
<center>
 +
[[Fichier:Levitt 2019.jpg|500px]] [[Fichier:Bender 2019.jpg|500px]]
 +
</center>
  
 
== Schedule ==
 
== Schedule ==
  
 
{| border="5" |
 
{| border="5" |
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! <font color="blue">Wednesday 19 June Morning</font>  
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! <center><font color="blue">Wednesday 19 June Morning</font> <br>
−
Tower 15-16, room 309
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Tower 15-16, room 309</center>
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! <font color="blue">Thursday 20 June Morning</font>  
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! <center><font color="blue">Thursday 20 June Morning</font> <br>
−
Tower 15-16, room 309
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Tower 15-16, room 309</center>
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! <font color="blue">Friday 20 June Morning</font>
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! <center><font color="blue">Friday 21 June Morning</font><br>
−
Tower 15-16, room 309  
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Tower 15-16, room 309 </center>
 
|- align="left"
 
|- align="left"
 
!'''<font color="red">8:45-9:00 Arrivals/Welcome</font>'''!! !!
 
!'''<font color="red">8:45-9:00 Arrivals/Welcome</font>'''!! !!
 
|- align="left"
 
|- align="left"
−
! '''9:00-10:30''' Lecture 1
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! '''9:00-10:30''' Carl Bender 1
−
!'''9:00-10:30''' Lecture 5
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!'''9:00-10:30''' Carl Bender 3
−
!'''9:00-10:30''' Lecture 9
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!'''9:00-10:30''' Carl Bender 5
 
|-align="left"
 
|-align="left"
 
!<font color="green">10:30-10:45 Coffee break</font>  
 
!<font color="green">10:30-10:45 Coffee break</font>  
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!<font color="green">10:30-10:45 Coffee break</font>
 
!<font color="green">10:30-10:45 Coffee break</font>
 
|-align="left"
 
|-align="left"
−
!'''10:45-12:15''' Lecture 2
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!'''10:45-12:15''' Carl Bender 2
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!'''10:45-12:15''' Lecture 6
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!'''10:45-12:15''' Carl Bender 4
−
!'''10:45-12:15''' Lecture 10
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!'''10:45-12:15''' Carl Bender 6
 
|-align="left"
 
|-align="left"
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!  <font color="green">12:15-14:00 Lunch</font>
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!  <font color="green">12:15-14:00 Lunch at L'Ardoise (Tower 25)</font>
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!  <font color="green">12:15-14:00 Lunch</font>
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!  <font color="green">12:15-14:00 Lunch at L'Ardoise (Tower 25)</font>
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!  <font color="green">12:15-14:00 Lunch</font>
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!  <font color="green">12:15-14:00 Lunch at L'Ardoise (Tower 25)</font>
 
|-align="left"
 
|-align="left"
−
! <font color="blue">Wednesday 19 June Afternoon</font>  
+
! <center><font color="blue">Wednesday 19 June Afternoon</font> <br>
−
Tower 15-16, room 309
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Tower 15-16, room 309</center>
−
! <font color="blue">Thursday 20 June Afternoon</font>  
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! <center><font color="blue">Thursday 20 June Afternoon</font> <br>
−
Tower 15-16, room 309
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Tower 15-16, room 309</center>
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! <font color="blue">Friday 20 June Afternoon</font>
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! <center><font color="blue">Friday 21 June Afternoon</font><br>
−
<font color="red">Tower 15-25, room 102</font>
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<font color="red">Tower 15-25, room 102</font></center>
 
|-align="left"
 
|-align="left"
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!'''14:00-15:30''' Lecture 3
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!'''14:00-15:30''' Antoine Levitt 1
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!'''14:00-15:30''' Lecture 7
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!'''14:00-15:30''' Antoine Levitt 3
−
!'''14:00-15:30''' Lecture 11
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!'''14:00-15:30''' Antoine Levitt 5
 
|-align="left"
 
|-align="left"
 
!  <font color="green">15:30-15:45 Coffee break</font>  
 
!  <font color="green">15:30-15:45 Coffee break</font>  
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!  <font color="green">15:30-15:45 Coffee break</font>  
 
!  <font color="green">15:30-15:45 Coffee break</font>  
 
|-align="left"
 
|-align="left"
−
!'''15:45-17:15''' Lecture 4
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!'''15:45-17:15''' Antoine Levitt 2
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!'''15:45-17:15''' Lecture 8
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!'''15:45-17:15''' Antoine Levitt 4
−
!'''15:45-17:15''' Lecture 12
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!'''15:45-17:15''' Antoine Levitt 6
 
|}
 
|}
  
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=== Registration ===
 
=== Registration ===
  
−
If you are interested and willing to participate, please register by sending an email at
+
'''Registration is closed.'''
−
 
 
−
[mailto:minischool@lct.jussieu.fr minischool@lct.jussieu.fr]
 
−
 
 
−
and indicate:<br>
 
−
- your name and affiliation;<br>
 
−
- whether you want to participate to the group lunches the 3 days;<br>
 
−
- whether you are a CNRS staff (permanent or non permanent).<br>
 
  
 
To facilitate the participation of young researchers, no registration fees will be asked.
 
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.
−
'''Warning: the maximum number of participants will be around 50.'''
 
  
 
=== Location of the mini-school ===  
 
=== Location of the mini-school ===  
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Subway (Metro) lines 7 or 10: get off at "Jussieu" station.  
 
Subway (Metro) lines 7 or 10: get off at "Jussieu" station.  
  
−
From the main entrance of the campus, go to ...
+
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 ===  
 
=== 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]]).
+
Each day, lunch will be offered to the first 50 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 ===  
 
=== Arriving by Plane ===  

Dernière version du 21 juin 2019 à 18:56

3rd edition of the Mini-school on mathematics for theoretical chemistry and physics

(supported by GDR NBODY and IP2CT)

Maths1.jpg

In the same spirit than the 1st edition of the mini-school and 2nd edition of the mini-school


  • 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. Warning: on the last afternoon, we will change room: Tower 15-25, room 102


Presentation[modifier]

  • 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[modifier]

Two courses will be proposed:

  • 1) Complex analysis (9 hours) by Antoine Levitt, INRIA and Ecole des Ponts, Paris, France.

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

Download lecture notes


  • 2) Perturbation theory, summation theory, and PT-symmetric quantum theory (9 hours) by Carl Bender, Washington University in St. Louis, USA

Indicative program (subject to changes and extension):
- Introduction to perturbation theory and methods
- Asymptotic series
- WKB analysis and eigenvalue problems
- Summation theory
- PT-symmetric quantum theory
- Classical PT symmetry

Download slides lecture 1 lecture 2 lecture 3

Levitt 2019.jpg Bender 2019.jpg

Schedule[modifier]

Wednesday 19 June Morning
Tower 15-16, room 309
Thursday 20 June Morning
Tower 15-16, room 309
Friday 21 June Morning
Tower 15-16, room 309
8:45-9:00 Arrivals/Welcome
9:00-10:30 Carl Bender 1 9:00-10:30 Carl Bender 3 9:00-10:30 Carl Bender 5
10:30-10:45 Coffee break 10:30-10:45 Coffee break 10:30-10:45 Coffee break
10:45-12:15 Carl Bender 2 10:45-12:15 Carl Bender 4 10:45-12:15 Carl Bender 6
12:15-14:00 Lunch at L'Ardoise (Tower 25) 12:15-14:00 Lunch at L'Ardoise (Tower 25) 12:15-14:00 Lunch at L'Ardoise (Tower 25)
Wednesday 19 June Afternoon
Tower 15-16, room 309
Thursday 20 June Afternoon
Tower 15-16, room 309
Friday 21 June Afternoon
Tower 15-25, room 102
14:00-15:30 Antoine Levitt 1 14:00-15:30 Antoine Levitt 3 14:00-15:30 Antoine Levitt 5
15:30-15:45 Coffee break 15:30-15:45 Coffee break 15:30-15:45 Coffee break
15:45-17:15 Antoine Levitt 2 15:45-17:15 Antoine Levitt 4 15:45-17:15 Antoine Levitt 6

Practical details[modifier]

Registration[modifier]

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[modifier]

The mini-school will take place on the Pierre et Marie Curie (or Jussieu) campus of 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.
Warning: on the last afternoon, we will change room: Tower 15-25, room 102

Lunches[modifier]

Each day, lunch will be offered to the first 50 registered participants to the mini-school (see the list of registered participants on the page List of registered participants).

Arriving by Plane[modifier]

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 Paris airports website.

From Paris-Charles de Gaulle (CDG) airport[modifier]

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[modifier]

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[modifier]

All the railway stations are in downtown Paris and are connected to the subway network. For train reservation, check the SNCF web site.

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

Arriving by Subway or Bus[modifier]

For more information on the RER, Subway and Bus systems, check the RATP web site, and in particular the Subway and RER map.

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