Mitul Islam

Research Interests

I am broadly interested in:

• Geometric structures on manifolds, their moduli spaces, and group actions preserving geometric structures,
• Discrete subgroups of Lie groups,
• Non-positive curvature phenomena and geometric group theory,
• Local and global rigidity of group actions on compact manifolds.

Publications and Preprints

1. Rigidity of compact rank one symmetric spaces (with Chris Connell, Thang Nguyen, and Ralf Spatzier)
   Submitted (15 pages). arxiv
2. Morse properties in convex projective geometry (with Theodore Weisman)
   Submitted (59 pages). arxiv
3. Boundary actions of lattices and C⁰ local semi-rigidity (with Chris Connell, Thang Nguyen, and Ralf Spatzier)
   Submitted (61 pages). arxiv
   (Video of a talk at IHP on this paper: video)
4. The structure of relatively hyperbolic groups in convex real projective geometry (with A. Zimmer)
   Submitted (31 pages). arxiv
5. Convex co-compact groups with one dimensional boundary faces (with A. Zimmer)
   Groups, Geometry, and Dynamics 18 (2024), No. 4, 1145–1183 (39 pages). arxiv
6. Convex co-compact representations of 3-manifold groups (with A. Zimmer)
   Journal of Topology (2024) Volume 17 Issue 2 (56 pages). arxiv
7. Rank one Hilbert geometries
   Geometry and Topology (to appear). arxiv
8. Convex co-compact actions of relatively hyperbolic groups (with A. Zimmer)
   Geometry and Topology 27 (2023) 417-511 (95 pages). arxiv
   (Here is a note that gives a simplified treatment of the paper, in the convex co-compact case: link)
9. A flat torus theorem for convex co-compact actions of projective linear groups (with A. Zimmer)
   Journal of the London Mathematical Society (2021) Volume 3 Issue 2 470-489 (19 pages). arxiv

Other writings

• Oberwolfach Report: Preliminaries on dynamics on geometrically finite hyperbolic manifolds article
  Oberwolfach Report No. 50/2021, pages 2732-2734.
  Arbeitsgemeinschaft (Thin groups and Super-approximation), October 2021.
• Ph.D. Thesis: Rank One Phenomena in Convex Projective Geometry UM Repository thesis
• An expository note on my paper number (2) from above: link to the note
  (This note is a simplified treatement of the paper, in the special case of convex co-compact groups; not intended for publication)

Mini-courses

Conference Talks

Invited Talks

Organizational Activities

Notes

These are a collection of expository notes that I have written up at various points. They are not original results, are not intended for publication, and have not been carefully proof-read.

• Hilbert geometry
• Cohomological characterization of higher rank symmetric spaces
• Geodesic flow on hyperbolic surfaces
• Rigidity theorems in geometry
• Volume entropy