Research

My research is in algebraic topology, more precisely in the Goodwillie-Weiss manifold calculus of functors. I am also beginning to explore the topology of political structures modeled by simplicial complexes.

Papers - published or accepted for publication

1. Weighted simple games and the topology of simplicial complexes, with A. Brooks and I. Volić, Theory and Decision (2025)

DOI: 10.1007/s11238-025-10077-5

2. The space of r-immersions of a union of discs in Rn, with G. Arone, Mathematica Scandinavica 130 (2024),  no. 3, 487–503
   DOI: 10.7146/math.scand.a-148809 

3. Intrinsic convergence of the homological Taylor tower for r-immersions in Rn , with G. Arone, Homology, Homotopy and Applications 26 (2024), no. 2, 163–192.
   DOI: 10.4310/HHA.2024.v26.n2.a8 

4. Connectivity estimates in the homological Taylor tower for the space of reduced embeddings in Rn, in Proceedings of the Conference on March 14 – International Day Of Mathematics, Special Editions ANUBiH, Book CCXVI, OPMN Book 30 (2024), pp 33–37
   DOI: 10.5644/PI2024.216.05

5. Low stages of the Taylor tower for r-immersions, with B. Schreiner and I. Volić, Involve, A Journal of Mathematics 13 (2020), no. 1, 51–75. DOI: 10.2140/involve.2020.13.51

6. Toward finite models for the stages of the Taylor tower for embeddings of the 2-sphere, with A. Bolić and I. Volić, in Proceedings of the International Symposium on Innovative and Interdisciplinary Applications of Advanced Technologies (IAT 2019) pp 1-13.
   DOI: 10.1007/978-3-030-24986-1_1

7.  A streamlined proof of the convergence of the Taylor tower for embeddings in Rn , with I. Volić, Colloquium Mathematicum 156 (2019), no. 1, 91-122.
   DOI: 10.4064/cm7363-2-2018

Papers - submitted or in preparation

8. Mediation, splitting and shellability in political structures modeled by simplicial complexes, with D. Jojić, submitted. https://arxiv.org/abs/2509.04249

9. A model of preferential attachment in voting networks, with H. Šiljak and I. Volić, in preparation.

Books

1. Kratki uvod u topologiju (in Croatian), Univerzitet u Sarajevu - Prirodno-matematički fakultet, Synopsis, 2025.

2. Izvan stroja. Nacionalno, građansko i druge opsjene (in Croatian), Synopsis, Zagreb - Sarajevo, 2023.

3. Group actions, with I. Volić, in preparation.

Seminar/Colloquium/Conference Talks

1. "r-immersions and partial configuration spaces"; 3rd Young STEMM Researchers Meeting, Academy of Sciences and Arts of Bosnia and Herzegovina; October 2024 (Sarajevo, Bosnia). Awarded the first prize for the best presentation

2. Topology of political structures and voting games modeled by simplicial complexes; TU Graz (Graz University of Technology), May 2024 (Graz, Austria)

3. Convergence of the homological Taylor tower for r-immersions; University of Tuzla Colloquium, March 2024 (Tuzla, Bosnia)

4. Connectivity estimates in the homological Taylor tower for the space of reduced embeddings in Rn; Conference on March 14 - the International Day of Mathematics, Academy of Sciences and Arts of Bosnia and Herzegovina; March 2024 (Sarajevo, Bosnia)

5. "Geometry and topology of political structures and voting systems"; 2nd Young STEM Researchers Meeting, Academy of Sciences and Arts of Bosnia and Herzegovina; November 2023 (Sarajevo, Bosnia). Awarded the third prize for the best presentation

6. "r-Immersions from the point of view of functor calculus"; NMSU Geometry and Topology seminar, New Mexico State University; April 2023 (Las Cruces, USA), via Zoom. Lecture notes

7. "An intuitive introduction to Manifold calculus of functors"; Seminar of Algebra at Department of Algebra, University of Seville; September 2022 (Seville, Spain)

8. "Homological convergence of the manifold calculus Taylor tower for r-immersions"; talk at the Young Topologists Meeting 2019 at EPFL, July 2019 (Lausanne, Switzerland)

9. "Fixed-point theorems in topology", student seminar at Wellesley College, April 2019 (Wellesley, USA)

10. "Calculus of functors for r-immersions"; talk at the workshop Graph Complexes, Configuration Spaces and Manifold Calculus at Pacific Institute for the Mathematical Sciences, May 2018 (Vancouver, Canada)

11. "Calculus of functors for r-immersions"; University of Tuzla Colloquium, March 2018 (Tuzla, Bosnia)

12. "From Taylor series to Taylor tower: Calculus of functors and its applications"; University of Sarajevo Colloquium, March 2017 (Sarajevo, Bosnia)

Erasmus+ Staff Week

1. Polytechnic Institute of Tomar (Portugal), May 2022. Talks:

• An introduction to the main concepts of topology

• Some applications of topological methods in electrical engineering

2. The University of Graz (Austria), May 2024. Talks:

• A first introduction to Goodwillie calculus

• Towers of Goodwillie calculus