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Prior to enrolment: have a PhD-project with a mathematician from University-Paris Dauphine who has an accreditation to supervise research (HDR).
Sources: details on different financing sources are given below.
Important: whatever your funding, you need to enrol in the Dauphine Doctoral school within the dates indicated below.

PROGRAM NAME	FINANCING INSTITUTION	MANAGING INSTITUTION	ELIGIBILITY	APPLICATION DATES
Doctoral school Note that there is an extra multidisciplinary funding	University Paris-Dauphine	Doctoral school	Scientific project	First round April 12 - May 22, 2023 (noon) Application form Second round July 17 - Sept. 15, 2023
PSL Mathematics graduate program	PSL université Paris	PSL université Paris	Scientific project	March 23 - April 26, 2023 Application form
Jean-Pierre Aguilar scholarships	Fondation CFM	Fondation CFM	Scientific project	Internal Deadline June 6, 2023 Online Deadline June 15, 2023
Cofund	Europe (2/3) - Doctoral school (1/3)	Fondation Sciences Mathematiques de Paris	Not more than 12 months in France from 13/02/2018 to 13/02/2021	CLOSED
Paris Region PhD	Ile de France Region	Fondation Sciences Mathematiques de Paris	Major fields of interest as defined here	CLOSED

"Obligation de formation": each year you should follow at least one of

In your first year, you should also follow a "Formation à l'éthique scientifique", organized by the College Doctoral of PSL.

This information needs to be filled in Adum

Update your profile on ADUM in June.
If you are a 1st year or 2nd year student: sit for a CST (comité de suivi de thèse) in June. Enrol in June for the next year.
If you are a 3rd year student: sit for a CST (comité de suivi de thèse) before September. Enrol in September for the next year.

You should pass a "Pré-soutenance". When: in the last year of your PhD (ideally 6 months before your defence). The rules and the application form can be found here.

It is important that you attend conferences. This must be prepared administratively for financial and insurance reasons.

Then ask the chair of the mathematics program for authorization, with your advisor CC'ed, with an estimate of the remaining cost. You will be told whether these travel expenses can be paid by the Doctoral School or the Ceremade.

Process a "demande d'ordre de mission". This takes some time + train or flight tickets can get expensive at the last minute, so you should plan this well in advance

Other sources of funding than Ceremade or École doctorale exist for longer travels, for instance:

Jean Walter Zellidja scholarships, provided by Académie Française, for visits of about one year in a foreign laboratory (application to be filled in at École doctorale usually before January).
Chateaubriand scholarships, provided by Ambassade de France in the USA (next opening October 2020).

When the thesis director agrees the thesis should be defended, it is advised to fill in a defense request at least 8 weeks before the defense.
See more details on the page of the doctoral school

General information about careers in Academics, especially in France, can be found here.

One-year positions called ATER can be found in French universities. Such a position may be convenient the year of your defense, but requires quite a lot of teaching.

Typical positions after a PhD are, in the academics, postdoctoral positions. Usually you will need the help of your advisor to get to be known and to find such a position.