Žiga Virk

Research interests

• PH Persistent homology and related topics

• A Applications of topology and geometry

• CG Coarse geometry

• W Topology of wild spaces

• Past: IL Inverse limits of multivalued functions, ET Extension theory, and NA Nonlinear Analysis

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Preprints

• PH H. Adams, S. Majhi, F. Manin, Ž. Virk, and N. Zava:
  Lower Bounding the Gromov-Hausdorff distance in Metric Graphs.
  A preprint on ArXiv.
  
  
• PH H. Adams, J. Bush, and Ž. Virk:
  The connectivity of Vietoris-Rips complexes of spheres.
  A preprint on ArXiv.
  
  
• PH CG A. Mitra and Ž. Virk:
  Geometric embeddings of spaces of persistence diagrams with explicit distortions.
  A preprint on ArXiv.
  
  
• CG A. Garber, Ž. Virk, and N. Zava:
  On the metric spaces of lattices and periodic point sets.
  A preprint on ArXiv.
  
  
• PH B. Lemež and Ž. Virk:
  Finite reconstruction with selective Rips complexes.
  A preprint on ArXiv.
  
  
• PH B. Jelenc and Ž. Virk:
  Detecting geodesic circles in hyperbolic surfaces with persistent homology.
  A preprint.
  
  

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Research papers

1. PH Ž. Virk:
   Contractibility of the Rips complexes of Integer lattices via local domination.
   Transactions of the American Mathematical Society, https://doi.org/10.1090/tran/9308.
   
   
2. PH Ž. Virk:
   Persistent Homology with Selective Rips complexes detects geodesic circles.
   Mediterr. J. Math. 21, 170 (2024), https://doi.org/10.1007/s00009-024-02706-0.
   
   
3. PH H. Adams and Ž. Virk:
   Lower bounds on the homology of Vietoris-Rips complexes of hypercube graphs.
   Bull. Malays. Math. Sci. Soc. 47, 72 (2024), https://doi.org/10.1007/s40840-024-01663-x.
   
   
4. PH P. Goričan and Ž. Virk:
   Critical edges in Rips complexes and persistence.
   Mediterr. J. Math. 20, 326 (2023), https://doi.org/10.1007/s00009-023-02533-9.
   
   
5. PH A. Franc and Ž. Virk:
   Rigidity of terminal simplices in persistent homology.
   Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 117, 141 (2023), https://doi.org/10.1007/s13398-023-01473-z.
   
   
6. PH M. Čufar and Ž. Virk:
   Fast computation of persistent homology representatives with involuted persistent homology.
   Foundations of Data Science, 2023, 5(4): 466-479, https://doi.org/10.3934/fods.2023006.
   
   
7. PH H. Adams, F. Frick, and Ž. Virk:
   Vietoris thickenings and complexes have isomorphic homotopy groups.
   J Appl. and Comput. Topology 7, 221–241 (2023), https://doi.org/10.1007/s41468-022-00106-5.
   
   
8. PH Ž. Virk:
   Contractions in persistence and metric graphs,
   Bull. Malays. Math. Sci. Soc. 45 (2022), 2003–2016, https://doi.org/10.1007/s40840-022-01368-z.
   Free official view-only version
   
   
9. PH Ž. Virk:
   Footprints of geodesics in persistent homology,
   Mediterranean Journal of Mathematics 19 (2022), https://doi.org/10.1007/s00009-022-02089-0.
   Free official view-only version
   
   
10. PH B. Lemež and Ž. Virk:
    Reconstruction properties of selective Rips complexes
    Glasnik Matematicki 57(2022), vol. 2, 73-88. https://doi.org/10.3336/gm.57.1.06.
    
    
11. PH Ž. Virk:
    A Counter-Example to Hausmann’s Conjecture
    Found Comput Math 22 (2022), 469-475. https://doi.org/10.1007/s10208-021-09510-2.
    Free official view-only version
    
    
12. PH CG A. Mitra and Ž. Virk:
    The Space of Persistence Diagrams on n Points Coarsely Embeds into Hilbert Space.
    Proc. Amer. Math. Soc. 149 (2021), 2693-2703. https://doi.org/10.1090/proc/15363.
    Updated version on ArXiv and Corrigendum to “The space of persistence diagrams on points coarsely embeds into Hilbert space”.
    
    
13. PH Ž. Virk:
    Rips complexes as nerves and a Functorial Dowker-Nerve Diagram.
    Mediterranean Journal of Mathematics 18 (2021). https://doi.org/10.1007/s00009-021-01699-4
    Free official view-only version
    
    
14. A Dejan Tomažinčič, Žiga Virk, Peter Marijan Kink, Gregor Jerše, and Jernej Klemenc:
    Predicting the Fatigue Life of an AlSi9Cu3 Porous Alloy Using a Vector-Segmentation Technique for a Geometric Parameterisation of the Macro Pores.
    Metals 2021, 11(1), 72. https://doi.org/10.3390/met11010072
    
    
15. PH H. Edelsbrunner, Ž. Virk, and H. Wagner:
    Topological data analysis in information space.
    In ``Proc. 35th Ann. Sympos. Comput. Geom., 2019''. http://doi.org/10.4230/LIPIcs.SoCG.2019.31
    
    
16. PH Ž. Virk:
    1-Dimensional Intrinsic Persistence of Geodesic Spaces
    Journal of Topology and Analysis 12 (2020), 169-207. https://doi.org/10.1142/S1793525319500444
    Updated version on ArXiv.
    
    
17. PH Ž. Virk:
    Approximations of 1-Dimensional Intrinsic Persistence of Geodesic Spaces and Their Stability
    Revista Matemática Complutense 32 (2019), 195-213. https://doi.org/10.1007/s13163-018-0275-4
    Free official view-only version
    
    
18. PH H. Edelsbrunner, Ž. Virk, and H. Wagner:
    Smallest enclosing spheres and Chernoff points in Bregman geometry.
    In ``Proc. 34th Ann. Sympos. Comput. Geom., 2018''. http://doi.org/10.4230/LIPIcs.SoCG.2018.35
    
    
19. W Ž. Virk and A. Zastrow:
    A new topology on the universal path space.
    Topology and its Applications 231(2017), 186-196. https://doi.org/10.1016/j.topol.2017.09.015
    
    
20. CG K. Austin and Ž. Virk:
    Higson Compactification and Dimension Raising.
    Topology and its Applications 215(2017), 45-57. http://dx.doi.org/10.1016/j.topol.2016.10.005
    Updated version on ArXiv.
    
    
21. CG K. Austin and Ž. Virk:
    Coarse metric approximation.
    Topology and its Applications 202(2016), 194-204. http://dx.doi.org/10.1016/j.topol.2016.01.010
    
    
22. CG J. Dydak, and Ž. Virk:
    Preserving coarse properties.
    Revista Matemática Complutense 29(2016), 191-206.
    https://doi.org/10.1007/s13163-015-0182-x
    
    
23. CG J. Dydak, and Ž. Virk:
    Inducing maps between Gromov boundaries.
    Mediterranean Journal of Mathematics 13(2016), 2733-2752. https://doi.org/10.1007/s00009-015-0650-z
    Free official view-only version
    
    
24. IL A. Vavpetič and Ž. Virk:
    The right homotopy shift in the fundamental group of inverse limits.
    Topology and its Applications 208(2016), 40-54 http://dx.doi.org/10.1016/j.topol.2016.05.007.
    
    
25. IL A. Vavpetič and Ž. Virk:
    On the fundamental group of inverse limits.
    Bulletin of the Malaysian Mathematical Sciences Society 40(2017), 941-957. https://doi.org/10.1007/s40840-016-0327-1
    Free official view-only version
    
    
26. NA M. Cencelj, D. Repovš, and Ž. Virk:
    Multiple perturbations of a singular eigenvalue problem.
    Nonlinear Analysis: Theory, Methods and Applications 119(2015), 37-45. http://dx.doi.org/10.1016/j.na.2014.07.015
    
    
27. W Ž. Virk and A. Zastrow:
    The comparison of topologies related to various concepts of generalized covering spaces.
    Topology and its Applications 170C(2014), 52-62. http://dx.doi.org/10.1016/j.topol.2014.03.011
    
    
28. CG T. Miyata and Ž. Virk:
    Dimension-Raising Maps in a Large Scale.
    Fundamenta Mathematicae 223 (2013), 83-97.
    https://www.impan.pl/en/publishing-house/journals-and-series/fundamenta-mathematicae/all/223/1/88840/dimension-raising-maps-in-a-large-scale
    
    
29. W Ž. Virk and A. Zastrow:
    A homotopically Hausdorff space which does not admit a generalized universal covering space.
    Topology and its Applications 160(2013), 656-666. http://dx.doi.org/10.1016/j.topol.2013.01.011
    
    
30. W Ž. Virk:
    Realizations of Countable Groups as Fundamental Groups of Compacta.
    Mediterranean Journal of Mathematics 10(2013), 1573-1589. http://dx.doi.org/10.1007/s00009-013-0274-0
    
    
31. W D. Repovš, W. Rosicki, Ž. Virk, and A. Zastrow:
    On Minc' sheltered middle path.
    Topology and its Applications 159(2012), 2609-2620. http://dx.doi.org/10.1016/j.topol.2012.04.008
    
    
32. CG M. Cencelj, J. Dydak, A. Vavpetič, and Ž. Virk:
    A combinatorial approach to coarse geometry.
    Topology and its Applications 159(2012), 646-658. http://dx.doi.org/10.1016/j.topol.2011.10.012
    
    
33. ET Ž. Virk:
    A generalization of the Levin-Rubin-Schapiro factorization theorem.
    Topology and its Applications 159(2012), 695-703. http://dx.doi.org/10.1016/j.topol.2011.10.018
    
    
34. W Ž. Virk:
    Homotopical smallness and closeness.
    Topology and its Applications 158(2011), 360-378. http://dx.doi.org/10.1016/j.topol.2010.11.010
    
    
35. W H. Fischer, D. Repovš, Ž. Virk, and A. Zastrow:
    On semilocally simply connected spaces.
    Topology and its Applications 158(2011), 397-408. http://dx.doi.org/10.1016/j.topol.2010.11.017
    
    
36. CG J. Dydak and Ž. Virk:
    An alternate proof that the fundamental group of a Peano continuum is finitely presented if the group is countable.
    Glasnik Matematicki 46(2011), no.2,
    http://web.math.hr/glasnik/vol_46/vol46no2.html
    
    
37. W Ž. Virk:
    Small loop spaces.
    Topology and its Applications 157(2010), 451-455. http://dx.doi.org/10.1016/j.topol.2009.10.003
    
    
38. ET M. Cencelj, J. Dydak, J. Smrekar, A. Vavpetič, and Ž. Virk:
    Algebraic properties of quasi-finite complexes.
    Fundamenta Mathematicae 197(2007), 67-80.
    
    
39. ET M. Cencelj, J. Dydak, J. Smrekar, A. Vavpetič, and Ž. Virk:
    Compact maps and quasi-finite complexes.
    Topology and its Applications 154(2007), 3005-3020. http://dx.doi.org/10.1016/j.topol.2007.06.015
    
    

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