Pierre CHAROLLOIS


Equipe de théorie des nombres, Institut de mathématiques de Jussieu, Université Paris 6.



born April 21st @ Roanne (LO), France 

A detailed CV can be found here : (CV.pdf), 


Postal address : 

Equipe de théorie des nombres 

Case 247 - 4, place Jussieu - 

75252 Paris Cedex 

France 


You can find me at  

Office 417 tour 15-25 

Université Paris 6

4 Place Jussieu

75005 Paris 


Map to come for a visit at Jussieu OR .

phone number : 33 (1) 44 27 54 41 / Fax +33 (1) 44 27 73 21 



- Current position (2006-...) : maître de conférences à l'Université Paris 6, Institut de Mathématiques de Jussieu.

- Formerly : (2005-2006) : CRM post-doc at McGill Univ. and Univ. de Montréal, on the invitation of Prof. Henri Darmon.

- visiting Harvard Math.  for the Fall semester 2007. - visiting UC Santa Cruz  during sept.-oct. 2008. courtesy of S. Dasgupta.
- visiting UC Santa Cruz  during mar.-apr. 2010. Courtesy of S. Dasgupta.

- visiting McGill Univ.  march. 2011. Courtesy of H. Darmon.
- visiting Tokyo Univ.  oct-nov. 2013. Courtesy of T. Oda.


- co-organizer with  Carine Apparicio of the "prime twins project" (start. June 22nd 2011, Paris) "Twins", co-starring Jules and Arthur.

- co-organizer with  Matthew Greenberg and Samit Dasgupta of the BIRS workshop (nov. 2011, Banff) "Cycles on modular varieties".

- co-organizer of the "London-Paris Number theory seminar".

- solo organizer of the Workshop "Regulators and modularity" in Jussieu, Nov 30-Dec 1st 2015.

- co-organizer with F. Deglise, G. Freixas, X. Ma and V. Maillot of the Conference "Regulators IV" in Paris, IMJ-PRG May 23-28 2016.

- formerly co-organizer with  Huayi Chen du "séminaire de théorie des nombres de Chevaleret".




Enseignements

- Préparation à l'agrégation externe de mathématiques. En particulier, préparation de l'épreuve écrite d'algèbre. Entraînement 2017

- 2016-2017. M1 Calcul Algébrique : 2nd semestre, 6ECTS. (polynômes en plusieurs variables, actions de groupes, méthodes effectives).

- Licence première année : 1M002 (suites et intégrales, algèbre linéaire)



Papers and preprints

- " Sommes de Dedekind associées à un corps de nombres totalement réel." Published in J. Reine Angew. Math. vol. 610 (2007), 125-147.

We introduce and study the main properties of certain Dedekind sums attached to a totally real number field. These are not rational numbers but rather real-analytic functions. They arise in the transformation formula of an ad-hoc analog of the logarithm of the Dedekind eta function for the Hilbert modular group.


- arXiv numbermath.NT/0405262 (original and expanded version of the above): (sommes_arxiv)


- (with Henri Darmon) : "Arguments des unités de Stark et périodes de séries d'Eisenstein." Published in Algebra & Number Theory Vol 2.6 (2008), p. 655-688

We describe a conjectural construction (in the spirit of Hilbert’s 12th problem) of units in abelian extensions of certain base fields which are neither totally real nor CM. These base fields are quadratic extensions with exactly one complex place of a totally real number field F, and are referred to as Almost Totally Real (ATR) extensions. Our construction involves certain null-homologous topological cycles on the Hilbert modular variety attached to F. The special units are the images of these cycles under a map defined by integration of weight two Eisenstein series on GL2(F). This map is formally analogous to the higher Abel–Jacobi maps that arise in the theory of algebraic cycles.
We show that our conjecture is compatible with Stark’s conjecture for ATR extensions ; it is, however, a genuine strengthening of Stark’s conjecture in this context since it gives an analytic formula for the arguments of the Stark units and not just their absolute values. The last section provides numerical evidences for our conjecture.


- (d'après Halberstadt-Kraus) : " Generalized Fermat equations." Published in "Arithmetic Geometry", Clay Mathematics Proceedings, 8. American Mathematical Society, Providence, RI, 2009.


- (with Samit Dasgupta) : " Integral Eisenstein cocycles on GLn, I : Sczech's cocycle and p-adic L-functions of totally real fields." Published in Cambridge J. of Mathematics, Vol 2.1 (2014), 49-90.

We define an integral version of Sczech's Eisenstein cocycle on GLn by smoothing at a prime ell. As a result we obtain a new proof of the integrality of the values at nonpositive integers of the smoothed partial zeta functions associated to ray class extensions of totally real fields. We also obtain a new construction of the p-adic L-functions associated to these extensions. Our cohomological construction allows for a study of the leading term of these p-adic L-functions at s=0.
We apply Spiess's formalism to prove that the order of vanishing at s=0 is at least equal to the expected one, as conjectured by Gross. This result was already known from Wiles' proof of the Iwasawa Main Conjecture.


- (with Samit Dasgupta, Matthew Greenberg) : " Integral Eisenstein cocycles on GLn, II : Shintani's method." Published in Commentarii Math. Helv. , Vol. 90.2 (2015), 435-477.

We define a cocycle on Gln using Shintani's method. This cocycle is closely related to cocycles defined earlier by Solomon and Hill, but differs in that the cocycle property is achieved through the introduction of an auxiliary perturbation vector Q. As a corollary of our result we obtain a new proof of a theorem of Diaz y Diaz and Friedman on signed fundamental domains, and give a cohomological reformulation of Shintani's proof of the Klingen--Siegel rationality theorem on partial zeta functions of totally real fields.
Next we prove that the cohomology class represented by our Shintani cocycle is essentially equal to that represented by the Eisenstein cocycle defined by Sczech. This generalizes a result of Sczech and Solomon in the case n=2. It implies that the formulae for values of partial zeta functions arising from Shintani's method and from Sczech's method are identical.
Finally we introduce an integral version of our Shintani cocycle by smoothing at an auxiliary prime ell. Applying the formalism of the first paper in this series, we prove that certain specializations of the smoothed class yield the p-adic L-functions of totally real fields. Combining our cohomological construction with a theorem of Spiess, we show that the order of vanishing of these p-adic L-functions is at least as large as the expected one.


- (with Matthew Greenberg) : "Rationality of secant zeta values." Published in Annales math. du Québec, Vol. 38.1 (2014), 1-6.

Lalin, Rodrigue and Rogers recently introduced the secant zeta function, as an analog of the Lerch-Berndt-Arakawa cotan zeta function. These are both Dirichlet series attached to a real quadratic irrational number α. These authors conjectured that, like the cotan funtion, the values at a specific range of negative integers of the secant Dirichlet series are algebraic numbers that belong to the field generated by α.
In this short note we provide two different proofs of their conjecture.


- (with Robert Sczech) : " Elliptic functions according to Eisenstein and Kronecker : An Update. Newly Found Notes of Lectures by Kronecker on the work of Eisenstein." Published in the EMS Newsletter 101 (Sept. 2016), 8-14.

This article introduces a set of recently discovered lecture notes from the last course of Leopold Kronecker, delivered a few weeks before his death in December 1891. The notes, written by F. von Dalwigk, elaborate on the late recognition by Kronecker of the importance of the ``Eisenstein summation process'', invented by the ``companion of his youth'', in order to deal with conditionally convergent series known today as Eisenstein series. We take this opportunity to give a brief update of the well known book by André Weil (1976) that brought these results of Eisenstein and Kronecker back to light. We believe that Eisenstein's approach to the theory of elliptic functions was in fact a very important part of Kronecker's planned proof of his visionary ``Jugendtraum''.





Documents related to Kronecker last lectures on Elliptic Functions





Conferences, seminar

Conferences talks

- Conférence Gauss-Dirichlet, Göttingen (20-24/06/2005) 

- Workshop informel sur les conjectures de Stark à Montréal (01-03/11/2005) (co-organisateur) 

- Summer school Arithmetic geometry à Göttingen organisée par le Clay Institute (17/7-11/8/2006) 

- BIRS workshop on Modular forms: arithmetic and computation. (Banff) (5/6/2007) 

- Meeting Canada-France, session théorie des nombres (Montreal) (5/6/2008) 

- BIRS workshop "Dedekind sums" (Banff)  (10/2009)

- Journée "Dr Honoris Causa" de Martin J. Taylor (Bordeaux)  (26/10/2009)

- Conference "Arithmetic cycles and special values of L-functions", (CRM Barcelona) (12/2009)

- Conference "Algorithmic of L-functions", (Univ. Lyon 1) (20/6/2011)

- Workshop "Rational points on curves", (Univ. Oxford) (29/9/2012)

- Workshop "Effective methods for Darmon points", (Benasque) (30/8/2013)

- Workshop "Explicit formulae and Arakelov geometry", (IMJ) (19/9/2013)

- Workshop "Harmonic analysis on spherical homogeneous spaces", (Hakuba, Japon) (8/11/2013)

- Rencontre "Théorie des nombres et applications", (CIRM) (13/3/2014)

- Workshop "Arithmetic of Eisenstein series", (Darmstadt, Allemagne) (21/9/2014)


Seminar talks :

- Séminaire de théorie des nombres de Toulouse 2 Le Mirail (18/11/2004) 

- Séminaire d'algèbre et de théorie des nombres de l'EPFL (Lausanne) (25/01/2005) 

- Séminaire d'arithmétique de Saint-Etienne (01/02/2005) 

- Séminaire de théorie algébrique des nombres de Limoges (07/02/2005) 

- Séminaire de théorie des nombres de Québec-Vermont (Montréal) (31/03/2005) 

- Séminaire de théorie des nombres de Montpellier (04/04/2005) 

- Séminaire de théorie des nombres et combinatoire de Lyon (14/04/2005) 

- Séminaire de théorie des nombres de Caen (15/04/2005) 

- Galois seminar, University of Pennsylvania (Philadelphie) (17/02/2006) 

- Séminaire ''autour de la géométrie d'Arakelov'' de Jussieu (24/4/2006) 

- Colloquium Rutgers-Newark university (4/12/2006) 

- Séminaire de théorie des nombres de Chevaleret(05/02/2007) 

- Séminaire de théorie des nombres de Bordeaux (06/04/2007) 

- Number Theory Seminar de Harvard (7/11/2007) 

- Algebra seminar, Boston university (4/12/2007)

- Colloquium Rutgers-Newark university (10/12/2007)

- Séminaire d'arithmétique à Lyon (7/4/2008)

- Seminar UC Santa Cruz (oct. 2009)

- Seminar UC Santa Cruz (mar. 2010)

- QVNTS Montreal, mar. 2011

- Univ. Laval à Québec, mar. 2011

- Séminaire Algo INRIA Rocquencourt (mai 2012)

- Séminaire de théorie des nombres de Chevaleret (08/10/2012) 

- Séminaire de théorie des nombres de Bordeaux (1/03/2013) 

- Séminaire de théorie des nombres de Lyon (6/05/2013) 

- Number Theory Seminar, Univ. of Tokyo (30/10/2013) 

- Univ. Laval à Québec, (27/2/2015)

- EPFL Lausanne (7/5/2015)

- Univ. Lille 1 (28/6/2016)




Master students :

- Ronan Terpereau (2007)

- Pierre Le Boudec (2008)

- Samuel Le Fourn (2009)

- Nicolas Provost (2009)

- Claire Glanois (2010)

- Laura Rastelli (2011)

- Raphael Achet (2011)

- Macarena Peche Irissarry (2012)

- Giacomo Cherubini (2012)

- Cyril Benezet (2013)

- Victor Cauchois (2013)

- Wouter van de Vijver (2015)

- Pranav Nuti (2016)



Links :

-Philippe Cassou-Noguès 

-Ted Chinburg 

-Henri Darmon 

-Samit Dasgupta 

-Jean Gillibert 

-Matthew Greenberg 

-Yingkun Li 

-Guillaume Ricotta 

-Martin Taylor 



Thesis : "Sommes de Dedekind et périodes de formes modulaires de Hilbert",


Supervised by Philippe Cassou-Noguès et Martin Taylor.


French Keywords :

Valeurs spéciales de fonctions L, conjectures de Stark, 12ème problème de Hilbert, périodes de séries d'Eisenstein,
groupe modulaire de Hilbert, fonction Phi de Rademacher, sommes de Dedekind, invariants de Hirzebruch-Atiyah-Singer-Shimizu. 

Soutenue le 13 décembre 2004 à l'Université Bordeaux 1 après avis favorable des rapporteurs : 


M. BRUGGEMAN Roelof (Université d'Utrecht)
M. DARMON Henri (Université Mc Gill, Montréal)


devant un jury composé de


M. MEREL Loïc, Professeur, et Président
M. CASSOU-NOGUES Philippe, Professeur
M. KOWALSKI Emmanuel, Professeur
M. BAVARD Christophe, Professeur
M. PERRET Marc, Professeur
M. TAYLOR Martin, Professeur


The complete text of my thesis is available as a pdf file at (thèse.pdf), or as a .ps file at (thèse.ps). 

A summary is also avalaible here (résumé.pdf),



To contact me : full lastname at math DOT jussieu DOT fr 


Page modified on 1/9/2016