AntoineMARNATForschungassistent

Technische Universität GrazAustria

H (0033) 6 82 76 65 95B marnat@math.tu-graz.at

Born 06/11/88 in Strasbourg (France)French National

"Das Wesen der Mathematik liegt gerade in ihrer Freiheit"- Georg Cantor

EmployementDecember

2018Research Assistant in Number Theory, Technische Universität Graz,Austria.

Sept. 2017 -Nov. 2018

Postdoctoral Research Associate, University of York, UK.

2016 -August 2107

Research Assistant in Number Theory, Technische Universität Graz,Austria.

Education2012–2015 PhD in Pure Mathematics, Université de Strasbourg, On the spectrum of

classical and twisted exponents of Diophantine approximation.Supervised by Yann Bugeaud and Nicolas Chevallier

2012 Master Degree in Pure Mathematics, Université Joseph Fourier (Grenoble,France), "Geometric Number Theory".Master thesis supervised by Yann Bugeaud, "Exposants des approximations diophanti-ennes en dimension 2"

2011 Agrégation de Mathématiques, ENS Cachan, Campus from Ker Lann(Rennes).

2008-2012 Normalien at ENS Cachan, Campus from Ker Lann (Rennes).Licences in both Mathematics and Computerscience, Master in Pure MathematicsInternships at Université de Strasbourg, (1 month, 1st year) with Christian Kassel andat Macquarie University in Sydney, Australia, (2 months, 2nd year) with ChristopheDoche

2006-2008 Classes préparatoires MPSI-MP*, Lycée Kleber, Strasbourg.Two-year intensive program in Advanced Mathematics and Physics in preparation forthe nationwide competitive examination to the French Grandes Écoles

2006 Abibac in Science, Lycée Jean Monnet, Strasbourg (France), Highest Honors.Both french and german High School Diploma

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Fields of ResearchGeometric Number Theory, homogeneous and inhomogeneous DiophantineApproximation.Parametric geometry of numbers introduced recently by W. M. Schmidt and L.Summerer.

PublicationsSee my ArXiv account

2019 Hausdorff and Packing dimension of Diophantine sets.2018 Diophantine transference inequalities: weighted, inhomogeneous and

intermediate exponents, with Sam Chow, Anish Ghosh, Lifan Guan andDavid Simmons, submitted.

2018 An optimal bound for the ratio between ordinary and uniformexponents of Diophantine approximation, with Nikolay Moshchevitin,submitted.

2017 Note on the spectrum of classical and uniform exponents of Diophan-tine approximation, Acta Arithmetica, to appear.

2017 On Diophantine transference principles, avec Anish Ghosh, Math-ematical Proceedings of the Cambridge Philosophical Society, 1-17.doi:10.1017/S0305004118000014.

2017 About Jarník-type relation in higher dimension, Annales de l’InstitutFourier, Annales de l’institut Fourier, 68 no. 1 (2018), pp. 131-150, doi:10.5802/aif.3154.

2016 There is no analogue to Jarník’s relation for twisted diophantine ap-proximation, Monatshefte für Mathematik, 2016, Volume 181, Issue 3, pp.675–688.

2015 Sur le spectre des exposants d’approximation diophantienne clas-siques et pondérés, PhD Thesis.

ExperienceProjectImportant member of the FWF - RSF project Geometry of Numbers andDiophantine approximation, collaboration between Austria and Russia.

ReviewReviewer for Mathematical Reviews.Referee for Monatshefte für Mathematik, The American Mathematical Monthly,Journal de Théorie des Nombres de Bordeaux, and Publicationes Mathematicae.

TeachingAutumn

2017Metric Spaces MAT00037H, University of York, UK.

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May 2017 Recent aspects of Geometry of Numbers, Minicourse for PhD Student,TU Graz.

March 2015 Tournoi Français de Jeunes Mathématiciennes et Mathématiciens(TFJM), Jury Member of a french young national tournament in mathematics.

2012-2015 Formal Calculus, First & Second year, Université de Strasbourg, France.>64 hours per year

2013-2015 Colles in Mathematics, Classes Préparatoires MPSI, Lycée Kleber (Stras-bourg, France, 2 hours weekly.Weekly oral interrogation for students preparing the nationwide competitive examinationto the French Grandes Écoles.

2012-2013 Cercle Mathématiques, 2 hours weekly, Université de Strasbourg, France.Extra courses for interested High School Students to prepare for example for Interna-tional Mathematical Olympiad

2011-2012 Colles in Computerscience, Classes Préparatoires MPSI, Lycée Champollion(Grenoble, France), 4 hours weekly.Formal Calculus lecture and tutorial for students preparing the nationwide competitiveexamination to the French Grandes Écoles.

2010-2011 Colles in Mathematics, Classes Préparatoires MPSI & ENSD2, LycéeChateaubriand & Lycée Vitor et Hélène Basch (Rennes, France), 3 hours weekly.Weekly oral interrogation for students preparing the nationwide competitive examinationto the French Grandes Écoles.

Conferences & Workshop25-29 Mars

2019Number Theory and Dynamics, Cambridge, UK.

1-5 Oct.2018

6e Colloque international sur la théorie de la répartition uniforme –UDT2018 , CIRM, Luminy, France.

10-14 Sept.2018

Approximation diophantienne et transcendance, CIRM, Luminy, France.

20-25 Mai2018

Géométrie diophantienne, CIRM, Luminy, France.

4-8December

2017

Workshop: Fractals and Dimensions, Institut Mittag Leffler, Stockholm,Sweden.

17-22 July2017

Combinatorics and Number theory, Vilnius, Lithuania.

9-14 July2017

Specialization Problems in Diophantine Geometry, Cetraro, Italy.

12-30 June2017

Géométrie d’Arakelov et application diophantiennes, Summer School,Institut Fourier, Grenoble, France.

13-17 March2017

Dynamical systems in number theory, SFB Workshop by V. Bergel-son, Universität Salzburg, Salzburg, Austria.

14-18 Nov.2016

Normal Numbers: Arithmetical, Computational and ProbabilisticAspects, Erwin Schrödinger Institut, Vienna, Austria.

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5 Nov. 2016 Symposium Edmund Hlawka, Österreichiche Akademie der Wissenschaft,Vienna, Austria.

9-14 Oct.2016

Arbeitsgemeinschaft: Diophantine Approximation, Fractal Geometryand Dynamics, Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach,Germany.

5-9 Sept.2016

ELAZ2016, Elementary and analytic number theory, Strobl am Wolf-gangsee, Austria.

20-24 June2016

Rencontres Lyon/Ottawa: Algèbre et Théorie des Nombres, Lyon,France.

12-17 June2016

LEUCA16, Michel Waldschmidt’s 70th Birthday , Patù, Italy.

10-16 April2016

Diophantische Approximationen, Mathematisches Forschungsinstitut Ober-wolfach, Oberwolfach, Germany.

15-19 Feb.2016

Computational Aspects of Diophantine Equations, University ofSalzburg, Salzburg, Austria.

19 Mai 2015 Numeration 2015, Université de Lorraine, Institut Élie Cartan, Nancy, France.15-19 Sept.

2014Approximation diophantienne et transcendance, Centre International deRencontres Mathématiques (CIRM), Marseille, France.

March 31 -April 4, 2014

Dynamics and analytic Number Theory, Easter School, Durham Univer-sity, UK.

Sept.30-Oct.4,2013

Thue 150, conferences dedicated to the 150th anniversary of Axel Thue, Uni-versité Bordeaux 1, France.

1-5 July 2013 28th Journées Arythmétiques, Université Joseph Fourier , Grenoble, France.17-28 June

2013Number Theory and Dynamics, Summer School, Université Joseph Fourier,Grenoble, France.

18-22 March2013

Equidistribution in Number Theory and Dynamics, FIM - Institute forMathematical Research, ETH Zurich, Switzerland.

TalksInvited talks

1 -5 july 2019 On the ratio between ordinary and uniform exponent of Diophantineapproximation, Journées Arithmetiques, Istanbul, Turkey.

26-30 August2019

About the variational principle in parametric geometry of numbers,Baikal Number Theory, Baikal, Russie.

4-8December

2017

Transference between homogeneous and inhomogeneous Diophantineapproximation on manifolds, Fractals and Dimensions, Institut Mittag-Leffler, Stockholm.Sweden

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17-22 July2017

Transference between homogeneous and inhomogeneous Diophantineapproximation on manifolds, Combinatorics and Number theory, Vilnius,Lithuania.

5-9 sept.2016

On the spectrum of exponents of Diophantine approximation, ELAZ16, Elementary and analytic number theory, Strobl am Wolfgangsee, Austria.

13-17 July2015

Parametric Geometry of Numbers and uniform exponent, DiophantineApproximation and Related Topics, Aarhus.Danemark

13-15 Oct.2014

About Diophantine exponents, Rencontres Doctorales Lebesgues, Rennes,France.

Workshop18 March

2016Roy’s Theorem and its applications, Zahlentheoretisches Kolloquium, TUGraz, Graz, Austria.

SeminarsJanuary 2019 Uniform and ordinary Diophantine exponent, Number theory seminar,

Colorado University Boulder, USA.18 Octobre

2018Spectra of exponents of Diophantine approximation, Research Seminar,HRI, Allahabad, India.

10 Mai 2018 On spectra of Diophantine approximation exponents, Number TheorySeminar, Oxford, UK.

26 Feb. 2018 Principes de transfert diophantiens, Groupe d’Étude sur les ProblèmesDiophantiens, Jussieu, Paris, France.

12 Dec. 2016 About spectra of Diophantine approximation, Xmas special seminar,University of York, York, UK.

5 August2016

Parametric Geometry of Numbers, Seminar, TIFR, Mumbai, India.

26-29 April2016

Parametric Geometry of Numbers, Seminar and Lectures, LomonosovMoscow State University, Moscow, Russia.

27 Jan. 2016 On the spectra of Diophantine approximation, Seminar, JKU, Linz,Austria.

13 November2015

Parametric Geometry of Numbers, Seminar for Number Theory, TU, Graz,Austria.

13 March2015

Géométrie paramétrique des nombres, PhD Study Group, LMB, Besançon,France.

12 Feb. 2015 Géométrie paramétrique des nombres, Number Theory Study Group, In-stitut Fourrier, Grenoble, France.

29 Jan 2015 Géométrie paramétrique des nombres, Analysis seminar, LMIA, Mulhouse,France.

Feb. 2014 Exposants d’approximation diophantienne et spectre, PhD StudyGroup, Université de Strasbourg, France.

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2 Oct. 2013 Approximations diophantiennes et spectre des exposants en dimen-sion 2, Number Theory Study Group, Université de Bordeaux, France.

15 Mai 2013 Spectrum of diophantine exponents, twisted case, Seminar for NumberTheory and Algebra, University of Zagreb, Croatia.

VisitsNovember

2019Tata Institut of Fundamental Research (TIFR), invited by Anish Ghosh,Mumbay, India.

January 2019 Boulder University, invited by Wolfgang Schmidt, Boulder, CO, USA.October 2018 Tata Institut of Fundamental Research (TIFR), invited by Anish Ghosh,

Mumbay, India.3-16 June

2018Research in Pairs in Oberwolfach, with Nikolay Moshchevitin, Oberwolfach,Germany.

April 2017 Tata Institut of Fundamental Research (TIFR), invited by Anish Ghosh,Mumbay, India.

5-8 Dec.2016

University of York, invited by Victor Beresnevich and Sanju Velani, York,UK.

August 2016 Tata Institut of Fundamental Research (TIFR), invited by Anish Ghosh,Mumbay, India.

April 2016 Lomonosov Moscow State University, invited by Nikolay Moschchevitinand Oleg German, Moscow, Russia.

10-22 Mai2013

University of Zagreb, invited by Andrej Dujella, Croatia.

ReferencesYann Bugeaud, Nicolas Chevallier, Michel Laurent, Damien Roy, LeonhardSummerer, Robert Tichy, Nikolay Moshchevitin, Anish Ghosh, Sanju Velani

LanguagesNative FrenchFluent German & English Abitur & TOEIC 985

Notions Spanish & Russian Basic words and phrases only

Computing SkillsLATEX, HTML, Maple, SAGE, OCaml, C++

InterestsReading Sylvain Tesson, JRR Tolkien, Heinrich Heine, Charles Baudelaire, . . .

Sport Trail running and many mountain outdoor sports (cross-country and alpine ski,(ski) mountaineering, climbing, triathlon, . . . ), Team sports (Rugby, Ultimate,Soccer, . . . )

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I attempted French University Championship in Run&Bike (silver medalist),Crosscountry (8th Team), Mountainbike (21st), Downhillski (17th).My toughest race was the Eiger Ultra Trail (101km, 7000mD+) and Hard-moors110 (182km, 5500mD+), the highest mountain I climbed is Mera Peak ( 6467m)

Volonteering I am an active member of Mountain Wilderness France, and won the first prizeof Concours changez d’approche 2015. I am the initiator of the advertising 10idées de sorties sans voiture dans le massif des Vosges. I am a moderator of theonline topoguide camptocamp.org

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