Antonin Prochazka

Maître de conférences

Équipe d’analyse fonctionnelle

Laboratoire de Mathématiques, UMR CNRS 6623,

Université de Franche Comté,

16, route de Gray,

25030 Besançon Cedex, FRANCE.

Tel : (+33) 3 81 66 63 50

Services d’enseignement

• 2019 Banach spaces and optimization : Conference on the occasion of Robert Deville’s 60th birthday
• 2018 Ecole de printemps du GdR AFHP
• 2017 Septièmes journées Besançon-Neuchâtel d’analyse fonctionnelle
• 2014 The special trimester "Geometric and noncommutative methods in functional analysis".

Research interests :

• Banach space geometry (linear and non-linear)
• embeddings from metric/Banach spaces into/onto Banach spaces
• differentiability and convexity
• convexity in metric spaces

Publications and talks :

• Injectivity of Lipschitz operators, (with Luis Carlos García Lirola and Colin Petitjean), Bull. Malays. Math. Sci. Soc. 46 (2023), no. 2, Paper No. 68.
• Purely 1-unrectifiable spaces and locally flat Lipschitz functions, (with Ramón Aliaga, Chris Gartland and Colin Petitjean), Trans. Amer. Math. Soc., Volume 375, Number 5, May 2022, Pages 3529–3567.

• Compact reduction in Lipschitz free spaces, (with Ramón Aliaga, C. Nous and Colin Petitjean), Studia Math. 260 (2021), no. 3, 341–359.
• Supports in Lipschitz-free spaces and applications to extremal structure, (with Ramón Aliaga, Eva Pernecká and Colin Petitjean), J. Math. Anal. Appl. 489 (2020) 124128.
• Embeddings of Lipschitz-free spaces into ℓ1, (with Ramón Aliaga and Colin Petitjean), Journal of Functional Analysis
  Volume 280, Issue 6, 15 March 2021, 108916.
  • Talk at Mini-Conference on Banach spaces Granada 2019 (does not contain the full results of v2 of the paper)
  • Talk at Séminaire virtuel d’analyse, Bordeaux 2020

• On exposed points of Lipschitz free spaces, (with Colin Petitjean), preprint, 2018.
• Pel​czyński space is isomorphic to the Lipschitz free space over a compact set, (with Luis Carlos García Lirola), Proc. Amer. Math. Soc. 147, no. 7 (2019), 3057-3060.
  • Talk at Congrès de la SMF, Lille 2018
• Extremal structure and duality of Lipschitz free spaces, (with Luis Carlos García Lirola, Colin Petitjean, and Abraham Rueda Zoca), Mediterr. J. Math. (2018) 15 : 69.
  • Due to page restrictions, some results of the arxiv version have been excluded from the journal version.
  • Talk at Function Theory on Infinite Dimensional Spaces XV, Madrid. February 2018.

• A characterisation of the Daugavet property in spaces of Lipschitz functions, (with Luis Carlos García Lirola and Abraham Rueda Zoca), J. Math. Anal. Appl. Volume 464, Issue 1 (2018), Pages 473-492.
  • Talk at Non Linear Functional Analysis, CIRM. March 2018.

• A characterisation of octahedrality in Lipschitz-free spaces, (with Abraham Rueda Zoca), Annales de l’institut Fourier, 68 no. 2 (2018), p. 569-588.
  • Talk at Institut de Mathématiques de Marseille, March 2017 (with a fairly long introduction to the basics of Lipschitz-free spaces)
  • Talk on "The long trapezoid property" at Winter school in abstract analysis, Svratka, January 2017
• Characterization of metric spaces whose free space is isometric to ℓ₁ (with Aude Dalet and Pedro Kaufmann), Bull. Belg. Math. Soc. Simon Stevin, Volume 23, Number 3 (2016), 391-400.
  • Talk at Congreso de Jóvenes Investigadores de la RSME, Murcia, September 2015

• On Kalton’s interlaced graphs and nonlinear embeddings into dual Banach spaces (with Bruno Braga, Gilles Lancien and Colin Petitjean), Journal of Topology and Analysis.
• On the coarse geometry of the James space (with Gilles Lancien and Colin Petitjean), 2018, to appear in Canadian Mathematical Bulletin.
  • Talk at XVI Encuentros análisis funcional Murcia Valencia 2018
• Linear properties of Banach spaces and low distortion embeddings of metric graphs, 2016, preprint.
  • Talk at Universidad de Granada, November 2016
  • Talk on "Low distortion characterization of reflexivity" at Function Theory on Infinite Dimensional Spaces, Madrid, February 2016
  • Talk on "Low distortion representation of ℓ₁ⁿ" at Relations Between Banach Space Theory and Geometric Measure Theory, Warwick, June 2015
• Low distortion embeddings of some metric graphs into Banach spaces (with Luis Sánchez González) Israel J. Math. 220 (2017), no. 2, 927–946.
• Low distortion embeddings between C(K) spaces (with Luis Sánchez González), 2014, preprint.
  • Talk at First Brazilian Workshop in Geometry of Banach Spaces, Maresias, August 2014
• Low distortion embeddings into Asplund Banach spaces (with Luis Sánchez González), 2013, preprint.
  • Talk at Function Theory on Infinite Dimensional Spaces, Madrid, February 2014

• Szlenk indices of convex hulls (with Gilles Lancien and Matías Raja), 2015, Journal of Functional Analysis 272 (2017) pp. 498-521.
  • Talk at Journées du GDR AFHP, CIRM, December 2015

• Weak* dentability index of spaces C([0,α]) (with Petr Hájek and Gilles Lancien),
  J. Math. Anal. Appl. 353 (2009), pp. 239-243.

• A parametric variational principle in metric spaces, (with Luis Sánchez González), in preparation.
• Parametric variational principle and residuality (with Robert Deville), J. Funct. Anal. 256 (11) 2009, pp. 3568-3587.

• Smooth version of Deville’s master lemma (with Petr Hájek), in preparation.
  • Poster for the Conference on 60th birthday of Gilles Godefroy, Mons, 2013
• C^k-smooth approximations of LUR norms (with Petr Hájek), Trans. Amer. Math. Soc. 366 (2014), 1973-1992.

• Delta-points and their implications for the geometry of Banach spaces (with Trond Abrahamsen, Ramon Aliaga, Vegard Lima, Andre Martiny, Yoel Perreau and Triinu Veeorg, preprint 2023.

• Winning tactics in a geometrical game,
  Proc. Amer. Math. Soc. 137 (2009), 1051-1061.

Intégrales et séries 2014/15 - cours magistral, L2 Math
Traitement du signal 2018/19 : TP1
Traitement du signal 2018/19 : TP3
Traitement du signal 2018/19 : TP4

Exposé sur le jeu de Hex donné au lycée Jules Haag (version française)
Talk on the Hex game at lycée Jules Haag (English version)
Tablier hex à imprimer&jouer à la maison/Hex board to print&play at home

San Francisco Declaration on Research Assessment
Exceptional MathReviews