[PDF] Daniele Turchetti - Dalhousie University

Cours num ero 6 : Arithm etique et cryptographie

3 2 Quelques r esultats arithm etiques Rappelons d’abord le petit th eor eme de Fermat (voir par exemple Math ema-tiques d’Ecole ) : 3 1 Th eor eme Soient pun nombre premier et a2Z Alors pdivise ap a donc on a ap amodulo p Si de plus aest premier avec p, on a ap 1 1 (mod p) On a un corollaire de ce th eor eme : 6

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arithm”tiques, sur les suites g”om”triques et sur les suites r”currentes -Th”or‘mes sur la convergence des suites monotones born”es (admis) -Limite d’une suite du type Un+1 = f(Un) • Des rappels sur les suites seront faits sur des exemples • Suites r”currentes: un+1= f(un), oš f est continue On repr”sentera ces suites

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Ce sont les v?rit?s institu?es de l'arithm?tiques qui constituent le point de d?part du raisonnement du professeur, v?ritable dis cours qui se d?roule sans tenir compte de son allocutaire, ici l'?l?ve: "il en est ainsi, Medemoiselle ?a ne s'explique pas ?a se comprend par un raisonnement math?matique int?rieur On

Daniele Turchetti - Dalhousie University

07/2017 Journ ees arithm etiques XXX, Caen 01/2015 MAA-AMS Joint Mathematical Meeting, San Antonio 06/2014 G eom etrie Alg ebrique en Libert e XXII, SISSA, Trieste 07/2013 Journ ees arithm etiques XXVIII, Grenoble

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Daniele Turchetti

Address: Dept. of Mathematics & Statistics

Dalhousie University

B3H 4R2, Halifax, NSOce: 252 Chase Building

Email:daniele.turchetti@dal.ca

Website:www.mathstat.dal.ca/~dturchetti/Research Interests Algebraic geometry, analytic geometry, number theory, representation theory Berkovich spaces, analytic curves, moduli spaces and modular forms, tropical geometry, ramication theory of Galois covers, combinatorial commutative algebra, and group representations.

Education

10/2011 - 11/2014PhD in Mathematics,Universite de Versailles Saint-Quentin-en-Yvelines

Thesis titleContributions to arithmetic geometry in mixed characteristic.

09/2010 - 07/2011MSc in Algebra and Arithmetics,Universite de Paris 11(Orsay)

10/2005 - 08/2010BSc, MA in Mathematics,Universita di Padova

Professional experience

08/2018 - presentAARMS post-doctoral fellow,Dalhousie University

08/2018 - presentOutreach coordinator,Atlantic Association for Research in the Mathematical

Sciences(AARMS)

09/2016 - 07/2018Post-doctoral fellow,Universite de Caen - Normandie

09/2015 - 08/2016Post-doctoral fellow,Max Planck Institute for Mathematics - Bonn

02/2015 - 08/2015Post-doctoral fellow,University of Leiden

10/2011 - 09/2014Instructor and Teaching Assistant,Universite de Versailles

Recent grants and awards

04/2019\Research in Paris" allowance fromInstitut Henri Poincare(2,500 EUR)

01/2019NSERC PromoScience grant (90,000$ for outreach with AARMS)

05/2018Recipient of theFondation des Treilles Young Researcher Prize(6,500 EUR)

11/2017Conference organization grants byFoundation Compositio Mathematica;

Journal de Theorie des Nombres de Bordeaux; ANRGLOBES; GDRGAGC (5,000 EUR)

Daniele Turchetti Curriculum Vitae

Publications

[1] ( withL. F antini)T riangulationsof n on-archimedeanc urves,se mi-stablere duction,an dr ami- cation. To appear inAnnales de l'Institut Fourier. [2] ( withJ .P oineau)Be rkovichc urvesand S chottkyu niformization.T oapp eari n\Arithmetican d geometry over local elds",Lecture Notes in Mathematics, Springer (2021). [3] ( withL. F antini)Gal oisde scentof se mi-anoidsp aces.Mathematische Zeitschrift(2018), vol.

290: 1085-1114.

[4] ( withG .C hinello)W eilr epresentationan dmet aplecticgr oupso veran i ntegraldom ain.Com- munications in Algebra43 (2015), no. 6: 2388-2419.

Preprints

1 [Pp1] Eq uidistantl iftingsof Gal oisc oversof el ementaryab eliangr oups(2020) . [Pp2] ( withJ .P oineau)S chottkysp acesan du niversalMu mfordc urveso verZ(2020). [Pp3]

Hur witzgr aphsand Be rkovichcu rves( 2019).

Outreach texts

[i] D ansl escou lissesd uMoMath.Images des Mathematiques, CNRS, 2019. [ii] B uissonset b alais:l afor mede se spacesanal ytiquesn on-Archimediens .Images des Mathema- tiques, CNRS, 2013.

Teaching

2018-19, 2019-20 (Dalhousie University)

Instructor forMatrix Theory and Linear Algebra II, for second year students in the Faculty of Science. Topics included: abstract vector spaces, inner product and Hermitian spaces, and applications such as Fourier series, least squares approximation, and linear codes. Online content developer. In 2020 theMatrix Theory and Linear Algebracourse was oered online and I have developed remotely accessible resources and content that will be used by future teachers.

2016-17 (Universite de Caen)

Teaching Assistant forMathematiques, mathematics course for rst year students in Economics, Administration and Social Science. Topics include polynomial equations, linear algebra and graph theory with a focus on applications to economics.1

All the preprints are available online at

w ww.mathstat.dal.ca/~dturchetti/

Daniele Turchetti Curriculum Vitae

2014-15 (Leiden University College)

Instructor forStatistics, statistics course for rst year students majoring in Economics and Political Science. I was responsible both for teaching and running lab sessions, teaching the students to use the programR.

2011-12, 2012-13, and 2013-14 (Universite de Versailles)

For each of the three years of my Ph.D. program I have served as: Teaching Assistant forMathematiques Generales 3, course in calculus (including linear and ordinary dierential equations) and linear algebra for second year math students. Instructor forCours preparatoire au concours ENSI, to prepare students for the competitive selection process to get admission to the FrenchEcoles d'Ingegneurs.

Public Outreach Involvement

07/2022Co-organizer of theBRIDGES Math and Art in Halifaxconference

08/2018 - 12/2020Outreach coordinator ofAARMS

10/2018 - 12/2019Co-host ofMath challenge clubat Dalhousie University

11/2019Co-organizer ofDiscovery days: Rubik's cube and other puzzlesat the Dis-

covery Centre, Halifax, NS

06/2019Co-organizer of theDiscovery days: Tau Daymath festival at the Discovery

Centre, Halifax, NS

05/2019Outreach invited speaker at theAlgant Alumni Network Symposium 2019

05/2019Co-organizer ofAll SySTEMs go! 2019, Halifax, NS

2013 - 2019Contributor and referee for the CNRS sponsored websiteImages des maths

2017 - 2018Associated member of the equipeDiusion de la culture mathematiqueat

the University of Caen

11/2017Curator of the exhibitionIMAGINARY - Open Mathematicsin Caen

2013 - 2016Workshop presenter for theF^ete de la Scienceat Sorbonne Universite &

University of Caen

06/2013Workshop presenter for the scientic festival of the associationParis Mon-

tagneat theEcole Normale Superieure de Paris

Daniele Turchetti Curriculum Vitae

Service activities

2017 - OngoingReferee for peer-reviewed international mathematical journals

01/2020Co-organizer ofCombinatorial Algebra meets Algebraic Combinatorics 2020

(international research conference), Dalhousie University

10/2019Assistant organizer ofScience Atlantic - Mathematics, Statistics and Com-

puter Science 2019(research undergraduate event), Dalhousie University

11/2017Co-organizer of the conferenceAlgebraic Geometry with\Fancy"Coecients,

Universite de Caen

( internationalr esearchcon ference)

2012 - 2014Graduate student representative at the graduate schoolSciences et Tech-

nologies de Versailles

2012 - 2014Organizer of theYoung Researchers Seminarat Versailles

2012 - 2014Co-organizer of the workshopLes Incontournables, on the fundamental pa-

pers of algebraic geometry, Institut de Mathematiques de Jussieu

Selected Talks

Invited research talks

09/2021ConferenceNon-Archimedean and tropical geometry, Frankfurt

06/2021ConferenceFoCM 2020 - Computational Number Theory, Vancouver

07/2020(Quarantined) Number Theory and Algebraic Geometry Seminar, Vancouver

05/2019ConferenceAlgant Alumni Network Symposium, Benasque

04/2019Seminario di Geometria Algebrica e Teoria dei Numeri, Universita di Padova

03/2019Quebec-Vermont Number Theory seminar, McGill University, Montreal

12/2018Abstract Algebra guest lecture, Yeshiva University, New York

06/2018Seminaire de Theorie des Nombres, Universite de Bordeaux

03/2018Seminaire de Geometrie Algebrique, Universite de Montpellier

03/2018Seminaire d'Arithmetique et Geometrie Algebrique, Universite de Strasbourg

02/2018Galois seminar, University of Pennsylvania, Philadelphia

01/2018Seminaire d'Arithmetique, Universite de Rennes 1

07/2017ConferenceBerkovich spaces, Tropical Geometry and Model Theory, Bogota

06/2017Journee de la Federation Normandie Mathematiques, Rouen

05/2017MAGIC Seminar, Imperial College, LondonSymmetrie, Geometrie und Arithmetik seminar, Universitat Heidelberg

03/2016Seminaire geometrie et singularites, Universite de Rennes 1Ergodic Theory seminar, Ecole PolytechniqueSeminaire de theorie des nombres, Universite de Bordeaux 1

Daniele Turchetti Curriculum Vitae

06/2015Seminaire de Theorie des Nombres, Universite de Montpellier

05/2015Seminaire de Theorie des Nombres, Universite de Limoges

11/2014Galois seminar, University of Pennsylvania, Philadelphia

05/2014Algebra und Geometrie Oberseminar, Goethe University, Frankfurt

04/2014Seminaire de geometrie tropicale, Institut de Mathematiques de Jussieu,

Paris

03/2014Collaborative Number Theory Seminar, CUNY, New York

02/2014Algebraic geometry seminar, NYU, New York

Contributed conference talks

06/2020Algebraic and Tropical Online Meetings

01/2019Combinatorial Algebra meets Algebraic Combinatorics 2019, University of

Ottawa

06/2018Geometrie Algebrique en Liberte XXVI, Strasbourg

09/2017Jeunes en Arithmetique et Varietes Algebriques, Tatihou

07/2017Journees arithmetiques XXX, Caen

01/2015MAA-AMS Joint Mathematical Meeting, San Antonio

06/2014Geometrie Algebrique en Liberte XXII, SISSA, Trieste

07/2013Journees arithmetiques XXVIII, Grenoble

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