Modification de MINI-SCHOOL 2022

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<div style="padding:1.1em 0.5em; font-size:150%; color: black;"> '''4th edition of the Mini-school on mathematics for theoretical chemistry and physics'''
(organized by [[Accueil|GDR NBODY]] with support from [https://www.inc.cnrs.fr CNRS INC], [https://www.lct.jussieu.fr/ LCT], [https://www.ljll.math.upmc.fr/ LJLL], and [https://erc-emc2.eu/ ERC EMC2])
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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],  [http://gdrcorelec.ups-tlse.fr/index.php?title=MINI-SCHOOL_2018 2nd edition], and the [https://wiki.lct.jussieu.fr/gdrnbody/index.php/MINI-SCHOOL_2019 3rd edition].
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* '''Date:'''  30 May - 1 June 2022

* '''Location:''' Sorbonne Université, Pierre et Marie Curie (or Jussieu) campus, 4 place Jussieu, 75005, Paris. 
Room to be confirmed.

* '''Lecturers: ''' [https://www.ceremade.dauphine.fr/~lewin/ Mathieu Lewin] and [https://www.lct.jussieu.fr/?page_id=368 Emmanuel Giner]

* '''Organizers:''' [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 2022 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 some mathematical aspects of the field. 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) '''Finite group theory''' (9 hours) by '''[https://www.lct.jussieu.fr/?page_id=368 Emmanuel Giner]''', Laboratoire de Chimie Théorique, CNRS and Sorbonne Université, Paris.

''Indicative program (subject to changes and extension):''<br>
- Definition of symmetries in quantum mechanics<br>
- Definition of groups and related concepts (group axioms, classes)<br>
- Basics of linear representation of groups (representation, irreducible representations, characters)<br>
- Useful theorems of linear representation of groups and their application in quantum mechanics (Schur's lemma and the Hamiltonian, orthogonality theorems, projection operators)<br>
- Product representations (representation on tensor-product vector spaces, Clebsch-Gordon coefficients, irreducible tensor operators)<br>
- Examples for electronic-structure theory 

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'''Download [[Media:Lecture notes giner.pdf|lecture notes]]'''
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* 2) '''The mathematical description of solids''' (9 hours) by '''[https://www.ceremade.dauphine.fr/~lewin/ Mathieu Lewin]''', CEREMADE, CNRS and Université Paris Dauphine, Paris
       
''Indicative program (subject to changes and extension):''<br>
I. Quick introduction to spectral theory<br>
- A bit of history about the concept of self-adjoint operators<br>
- Continuous spectrum and generalized eigenfunctions, example of plane waves<br>

II. One-electron systems in a periodic background<br>
- Bloch-Floquet theory<br>
- Regularity of Bloch surfaces, absolute continuity of the spectrum<br>
- Symmetry groups and the universality of Dirac cones in 2D, graphene<br>
- Spectral projections, infinite Hartree-Fock states<br>
- SCF models, Kohn-Sham<br>

III. Interacting systems<br>
- Thermodynamic limit for Coulomb systems<br>
- Uniform Electron Gas: the known and the unknown<br>


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[[Image:emmanuel_giner_2022.jpg|300px]] [[Image:mathieu_lewin_2022.jpg|300px]] [[Image:participants_minischool_2022.jpg|300px]] 
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== Schedule ==

{| border="5" |
! <center><font color="blue">Monday 30 May Morning</font> <br>
Tower 15-16, room 309</center>
! <center><font color="blue">Tuesday 31 May Morning</font> <br>
Tower 15-16, room 309</center>
! <center><font color="blue">Wednesday 1 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''' Giner 1
!'''9:00-10:30''' Lewin 3
!'''9:00-10:30''' Giner 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''' Giner 2
!'''10:45-12:15''' Lewin 4
!'''10:45-12:15''' Giner 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">Monday 30 May Afternoon</font> <br>
Tower 15-16, room 309</center>
! <center><font color="blue">Tuesday 31 May Afternoon</font> <br>
Tower 15-16, room 309</center>
! <center><font color="blue">Wednesday 1 June Afternoon</font><br>
Tower 15-16, room 309</center>
|-align="left"
!'''14:00-15:30''' Lewin 1
!'''14:00-15:30''' Giner 3
!'''14:00-15:30''' Lewin 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''' Lewin 2 
!'''15:45-17:15''' Giner 4
!'''15:45-17:15''' Lewin 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> 

=== Lunches === 

Each day, lunch at Restaurant L'Ardoise (Jussieu campus, entrance near Tower 25) will be offered to a maximum 50 registered participants to the mini-school (see the list of registered participants on the page [[MINI-SCHOOL 2022 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].

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