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.  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. 

2. 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 

3. 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 

4. Intrinsic convergence of the homological Taylor tower for r-immersions in Rn , with G. Arone, to appear in Homology, Homotopy and Applications 

5. Connectivity estimates in the homological Taylor tower for the space of reduced embeddings in Rn. to appear in Special Editions of ANUBiH

Papers - submitted or in preparation

6. Weighted simple games and the topology of simplicial complexes, with A. Brooks and I. Volić, submitted. https://arxiv.org/abs/2210.09771 

7. The space of r-immersions of a union of discs in Rn, with G. Arone, submitted. https://arxiv.org/abs/2212.09809

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

Books

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

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

3. Osnove opće i algebarske topologije (in Croatian), in preparation.

Seminar/Colloquium/Conference Talks

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

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

3. 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)

4. "Geometry and topology of political structures and voting systems"; 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

5. "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

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

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

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

9. "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)

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

11. "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