William SAREM

Email: william.sarem@imj-prg.fr

I am a FSMP post-doc at IMJ-PRG since september 2026, working in the team Complex Analysis and Geometry (ACG).

My office number is 16-26-526.

Previously, I was a PhD student (2023-2026) at Institut Fourier, Grenoble, under the supervision of Pierre Py. I defended my PhD thesis entitled Stein quotients via Patterson-Sullivan theory and the Shafarevich conjecture in December 2025. Here is the link to the manuscript.

My CV (Last update: June 2026).

Publications

• Holomorphic functions on geometrically finite quotients of the ball, Journal de l'École Polytechnique — Mathématiques, Tome 13 (2026), pp. 321-348. doi: 10.5802/jep.328. Journal version: pdf.
• Curvature properties and Shafarevich conjecture for toroidal compactifications of ball quotients, Journal of Differential Geometry 133 no. 3 (2026), pp. 443-478. doi: 10.4310/jdg/1779982479. arXiv version: 2306.07692.

Research seminar talks

• New trends in Complex Analysis, Geometry and Dynamics, Lille (June 2026). Entropy, holomorphic convexity, and locally symmetric spaces.
• Geometry Seminar (Anna Wienhard group), MPI MiS, Leipzig (June 2026). Entropy, holomorphic convexity, and locally symmetric spaces.
• Séminaire de Géométrie Complexe, IMT, Toulouse (April 2026). Entropy, holomorphic convexity, and locally symmetric spaces.
• Short talk: Complex analysis Workshop, Oberwolfach (April 2026). Locally symmetric spaces and Stein manifolds
• Séminaire Darboux, IMAG, Montpellier (April 2026). Entropie, convexité holomorphe et espaces localement symétriques.
• Séminaire Géométrie et Applications, IRMA, Strasbourg (February 2026). Entropy, holomorphic convexity, and locally symmetric spaces.
• Séminaire de Géométrie et Topologie, LMBA, Brest (December 2025). Entropie, convexité holomorphe et espaces localement symétriques.
• Séminaire de Géométrie et Topologie, IMJ-PRG, Paris (November 2025). Compact analytic subvarieties in quotient spaces.
• Séminaire de Géométrie, Groupes et Dynamique, UMPA, Lyon (October 2025). Sous-ensembles analytiques compacts dans des espaces quotients.
• Oberseminar (2 x 90min) , Mathematisches Institut, Bayreuth (July 2025). Toroidal compactifications of ball quotients and Shafarevich conjecture.
• Short talk: Geometric structures and discrete group actions, CIRM, Marseille (April 2025). Holomorphic properties of ball quotients: towards a higher rank generalization?
• Séminaire Géométrie Complexe, IECL, Nancy (March 2025). Propriétés holomorphes des quotients de la boule et exposant critique.
• Séminaire Algèbre, Topologie et Géométrie, LJAD, Nice (January 2025). Holomorphic properties of ball quotients.
• Séminaire Géométrie Analytique, IRMAR, Rennes (January 2025). Propriétés holomorphes des quotients de la boule.
• Séminaire Algèbre et Géométries, Institut Fourier, Grenoble (December 2024). Propriétés holomorphes des quotients de la boule.
• Séminaire Géométrie et Topologie, I2M, Marseille (November 2024). Propriétés holomorphes des quotients de la boule par un groupe d'exposant critique petit.
• Séminaire Géométrie, IMB, Bordeaux (October 2023). Compactifications toroïdales de quotients de la boule et conjecture de Shafarevich.
• Séminaire Algèbre et Géométries, Institut Fourier, Grenoble (October 2023). Conjecture de Shafarevich pour les compactifications toroïdales de quotients de la boule.
• Séminaire Géométrie Analytique, IRMAR, Rennes (June 2023). Propriétés de courbure et conjecture de Shafarevich pour les compactifications toroïdales de quotients de la boule.
• Short talk: Alpine meeting on nonpositive curvature in Kähler geometry, Aussois (June 2023). Curvature properties for toroidal compactifications of ball quotients.
• Séminaire GT3, IRMA, Strasbourg (June 2022). Variétés de Stein et sous-groupes de PU(n,1).

PhD seminar talks

• Séminaire Doctorants, UMPA, ENS de Lyon (June 2025). The Poincaré disk, its complex generalization and holomorphic functions.
• Séminaire Compréhensible, Institut Fourier, Grenoble (June 2025). The Poincaré disk, its complex generalization and holomorphic functions.
• Séminaire Doctorants, IRMA, Strasbourg (March 2025). The Poincaré disk, its complex generalization and holomorphic functions.
• Séminaire des doctorants, LMPA, Calais (May 2024). Le disque de Poincaré, sa généralisation complexe et leurs fonctions holomorphes.
• Rencontres Doctorales Lebesgue, Angers (April 2024). The complex hyperbolic space and its holomorphic functions.
• Séminaire Compréhensible, Institut Fourier, Grenoble (March 2024). The Poincaré disk, its complex generalization and holomorphic functions.
• Séminaire Pampers, IRMAR, Rennes, (March 2023). La formule de Matsushima.
• Geometry Graduate Colloquium, ETHZ, Zürich (December 2022). Harmonic forms and cohomology in smooth (complex) manifolds.

Research stays

• Visiting Benoît Cadorel, IECL, Nancy, 2 months (Jan-Feb 2026).
• Visiting Mihai Păun, Mathematisches Institut, Bayreuth, 1 week (July 2025).
• Visiting Christian Miebach, ULCO, Calais, 1 week (July 2025).
• Visiting Christian Miebach, ULCO, Calais, 3 days (May 2024).
• Visiting Simone Diverio, la Sapienza, Rome, 1 week (January 2024).

Attended conferences

• New trends in Complex Analysis, Geometry and Dynamics, Lille (June 2026).
• ANR GAG meeting, Orléans (June 2026).
• Complex Analysis Workshop, Oberwolfach (April 2026).
• Geometric structures and discrete group actions, CIRM, Marseille (April 2025).
• ANR GAG meeting: L² Invariants, Grenoble (February 2025).
• PhD meeting: Rencontres Doctorales Lebesgue, Angers (April 2024).
• ERC meeting: Groups of Algebraic Transformations, Rennes (January 2024).
• PhD meeting: Parole aux jeunes chercheuses et chercheurs du réseau Platon, Grenoble (November 2023).
• Lattices in Negative Curvature, Les Diablerets (July 2023).
• Alpine meeting on nonpositive curvature in Kähler geometry, Aussois (June 2023).
• Complex Hyperbolic Geometry and Related Topics, CIRM, Marseille (July 2022).

Distinction

• PhD prize of the Doctoral School MSTII, Grenoble Alpes University (2026).

Teaching assistant

At Grenoble Alpes University (2023-2025):

• Lie Groups and Lattices (Master 2 course), Tutorials, 8h, in English (Fall 2025).
• MAT101: Mathematical Language, Elementary Algebra and Geometry (L1 course):
  • Lectures and Tutorials, 56h, (Fall 2025).
  • Lectures and Tutorials, 32h (Fall 2024).
  • Lectures and Tutorials, 32h (Fall 2023).
• MAT206: Introduction to Mathematical Biology and Population Dynamics (L1 course):
  • Lectures and Tutorials, 32h (Spring 2025).
  • Lectures and Tutorials, 32h, in English (Spring 2024).

At CPES Multidisciplinary Undergraduate degree - PSL University (2026-...):

• General Mathematics for 2nd year scientists students (L2 course), Tutorials, 64h (2026).

Responsabilities

• PhD students' representative at the doctoral school MSTII.
• Organizer of the Séminaire Compréhensible, the PhD seminar of the Fourier Institute (2024-2025).
• Organizer of the PhD days of the Fourier Institute consisting in 4 days of talks given by PhD students (2024-2025).

Outreach

• (with Victor Issa) À la recherche des triplets pythagoriciens, Image des Maths (May 2021), link.
• (with Mathurin Passard) Pratique de la recherche en mathématiques, Journal de Mathématique de l'École, Lyon, special issue (May 2021), link.

Other scientific activities

• Reviewer service, zbMATH Open, 2025-present.

Last update: September 2026.