Rade T. Živaljević

Mathematical Institute SASA  ·  Belgrade

Scientific Biography

1   Education

Rade Živaljević was born on October 12, 1954 in Sarajevo. His Master's thesis (M.Sci) and Ph.D. degree thesis were defended at Belgrade University in 1979 and 1983 respectively. A second Ph.D. degree thesis was defended at the University of Wisconsin–Madison in 1985. He has been a member of the Mathematical Institute of the Serbian Academy of Sciences and Arts (SASA) since 1977, where he was appointed as a full research professor in 1995.

2   Scientific Activities

2.1   Selected Visits

Visiting associate professor at the University of Illinois at Urbana-Champaign in 1994; Mittag-Leffler Institute (Stockholm, Year of Combinatorics, 1991); Konrad Zuse Zentrum für Informationstechnik (ZIB), Berlin, 1994; Mathematical Institute Bern (1999). Shorter periods at Institut des Hautes Études (Paris), Mathematical Sciences Research Institute, Berkeley (2006, 1998, 1991), Moscow State University (MGU), Mathematics Forschungs Institut (Oberwolfach), Givat-Ram (Jerusalem), Technion (Haifa), KTH Stockholm, SISSA (Trieste), and others.

Recent visits include Moscow State University (April 2016), "Research in Pairs" program (Mathematisches Forschungsinstitut Oberwolfach, May 2016), Brown University — ICERM program "Topology in Motion" (Fall 2016), Saint Petersburg State University (June 2018), Research in Pairs at CIRM Marseille (Fall 2018), MFO Oberwolfach (2019), Research in Residence at CIRM (September 2022), and MFO Oberwolfach (February 2024).

2.2   Conferences

Selected lectures include: Seminar "Geometry, Topology and Mathematical Physics" (Steklov Mathematical Institute of RAS, October 2022); International School "Toric Topology, Combinatorics and Data Analysis" (Euler International Mathematical Institute, St. Petersburg, October 2022); Classical and Contemporary Geometry, Moscow (November 2021); "Toric Topology 2019 in Okayama" (invited lecture); Plenary lecture at conference in honor of Victor Buchstaber's 75th birthday (Steklov / SkolTech, Moscow, May 2018); Princeton Algebraic Topology Seminar and M.I.T. Topology Seminar (October 2016); Geometric and Algebraic Combinatorics, Oberwolfach 2015; Applied Algebraic Topology, Castro Urdiales 2014; Applied Topology Bedlewo 2013; Technical University Berlin and Free University Berlin, colloquium speaker (December 2005); Combinatorics Symposium in honor of Helge Tverberg, Bergen (March 2005); and many others.

R. Živaljević and Gil Kalai co-organized the conference Combinatorics and Topology, Jerusalem, June 2007.

2.3   National and International Projects

R. Živaljević is (together with Vladimir Dragović) the founder of the center "Dynamical Systems, Geometry and Combinatorics" as a research unit (center of excellence) within the Mathematical Institute SASA. The center coordinates international cooperation with groups at Steklov Institute Moscow, SISSA–ISAS Trieste, TU Berlin, DIMATIA Prague, and several regional groups.

R. Živaljević was co-coordinator (with Petar Pavešić, University of Ljubljana) of the Serbia–Slovenia bilateral project "Applied and Computational Algebraic Topology" (2016–2017).

2.4   Awards and Honors

In 1995, R. Živaljević was awarded (together with Siniša Vrećica) the City of Belgrade Award for the solution of the "Colored Tverberg Problem" — at the time the highest scientific award in Serbia.

2.5   Students

R. Živaljević was Ph.D. adviser (University of Belgrade) of Pavle Blagojević, Vladimir Grujić, Đorđe Baralić, Žana Kovijanić, Manuela Muzika-Dizdarević, Marinko Timotijević, and co-adviser of Duško Jojić. He was internship adviser of Stephan Hell (TU Berlin, 2006) and Leandro Vicente Mauri (São Paulo, 2022).

3   Research

3.1   Research Interests

Rade Živaljević is the author of more than 80 research papers and numerous review and expository publications. Papers have appeared in highly ranked international journals including Advances in Mathematics, Mathematische Annalen, J. Reine Angew. Math., Trans. Amer. Math. Soc., J. London Math. Soc., and Combinatorica. His main areas are topological and geometric combinatorics, discrete and computational geometry, and applied algebraic topology.

3.2   Selected Results

Main contributions fall in three thematic circles: Homotopy colimits and Ziegler–Živaljević formulae; the "Configuration space–test map" scheme with applications in computational topology; and Homotopic and cohomological methods in topological combinatorics.

  1. Solution of Vassiliev's problem (Berkeley 1997) on geometric resolutions expn(Sm) of spheres — Advances in Applied Mathematics, 1998.
  2. The Csorba–Živaljević universality theorem for Lovász graph complexes — J. Combinatorial Theory Ser. A, 2005.
  3. Solution of Grünbaum's 1960 problem on equipartitions of measures in 4-dimensional Euclidean space — Trans. Amer. Math. Soc., 2008.
  4. Multidimensional "Splitting Necklace" theorem extending Noga Alon's 1987 result — Advances in Mathematics, 2008.
  5. Combinatorial techniques for symmetric cohomology of algebras, solving a problem of Ault and Fiedorowicz — European J. Combinatorics, 2009 (with S. Vrećica).
  6. Differential and algebraic topology of "totally skew embeddings" — Trans. Amer. Math. Soc., 2011.
  7. Center Transversal Theorem — Bull. London Math. Soc., 1990 (with S. Vrećica).
  8. Ziegler–Živaljević formulae — Mathematische Annalen 1993; J. Reine Angew. Math., 1999.
  9. Colored Tverberg problem and chessboard complexes — J. Combin. Theory Ser. A (1992, 2011); J. London Math. Soc., 1994.
  10. Resolution (with D. Jojić and S. Vrećica) of the Blagojević–Frick–Ziegler conjecture on balanced Tverberg partitions — J. Algebraic Combin., 2017.

4   Publications

4.1   Five Most-Cited Papers (May 2026)

[1] R. Živaljević, S. Vrećica. The colored Tverberg's problem and complexes of injective functions. J. Combin. Theory, Ser. A 61(2), 1992, 309–318. Google Scholar: 205 citations
[2] G. Ziegler, R. Živaljević. Homotopy types of subspace arrangements via diagrams of spaces. Mathematische Annalen, 295:527–548, 1993. Google Scholar: 173 citations
[3] A. Björner, L. Lovász, S. Vrećica, R. Živaljević. Chessboard and matching complexes. J. London Math. Soc. (2), 49:25–39, 1994. Google Scholar: 175 citations
[4] V. Welker, G. Ziegler, R. Živaljević. Homotopy colimits – comparison lemmas for combinatorial applications. J. Reine Angew. Math., 509 (1999), 117–149. Google Scholar: 145 citations
[5] R. Živaljević. Topological methods, Chapter 11 in CRC Handbook of Discrete and Computational Geometry, J.E. Goodman, J. O'Rourke eds., CRC Press, New York, 1997. Google Scholar: 93 + 34 citations

md(H) = md(H)

4.2   Main Publications before 2003

  1. R. Živaljević. md(H) = md(H) Publ. Inst. Math. Belgrade, 26(40), 308–311, 1979.
  2. R. Živaljević. Note on H-convex functions. Publ. Inst. Math. Belgrade, 26(40), 313–317, 1979.
  3. R. Živaljević. Two examples of Q-topologies. Publ. Inst. Math. Belgrade, 35(49).
  4. R. Živaljević. The notions of w-net and Y-compact space viewed under infinitesimal microscope. Publ. Inst. Math. Belgrade, 34(48).
  5. R. Živaljević. A Loeb measure approach to the Riesz representation theorem. Publ. Inst. Math. Belgrade, 32(46), 175–177.
  6. M.M. Marjanović, S.T. Vrećica, R.T. Živaljević. Some properties of hyperspaces of higher rank. Bull. Acad. Serbe des Sciences et des Arts, LXXXIV, 1984.
  7. M. Rašković, R. Živaljević. Barwise completeness for some biprobability logics. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 32/2, 1986, 133–135.
  8. R. Živaljević. Loeb completion of vector valued measures. Mathematica Scandinavica, 56 (1985), 276–286.
  9. R. Živaljević. Infinitesimals, microsimplexes and elementary homology theory. Amer. Math. Monthly, Sept. 1987.
  10. R. Živaljević. On a cohomology theory based on hyperfinite sums of microsimplexes. Pacific J. Math., vol. 128, no. 1, 1987.
  11. R. Živaljević. A reversed Kakutani's fixed point theorem. Publ. Inst. Math., 44(58), 1989.
  12. R. Živaljević. Extremal Minkowski additive selections of compact convex sets. Proc. Amer. Math. Soc., vol. 105, no. 1, 1989.
  13. R. Živaljević, S. Vrećica. An extension of the ham sandwich theorem. Bull. London Math. Soc. 22, 1990, 183–186.
  14. A. Vučić, R. Živaljević. Dihedral hyperhomology of a chain algebra with involution. Publications de l'Institut Mathematique (Beograd), 49(63), 1991.
  15. S. Vrećica, R. Živaljević. The ham sandwich theorem revisited. Israel J. Math. 78, 1992, 21–32.
  16. N. Bokan, P. Gilkey, R. Živaljević. An inhomogeneous elliptic complex. Journal d'Analyse Mathematique, vol. 61, 1993, 367–393.
  17. A. Vučić, R. Živaljević. Note on a conjecture of Sierksma. Discrete and Computational Geometry, vol. 9, 339–349, 1993.
  18. S. Vrećica, R. Živaljević. New cases of the colored Tverberg theorem. Jerusalem Combinatorics '93, AMS Contemporary Mathematics, 1994.
  19. G. Ziegler, R. Živaljević. "Publikationsverbote für jugoslawische Mathematiker?" Mitteilungen der DMV, vol. 3, no. 2, 1995, 43–44.
  20. R. Živaljević. Colored Carathéodory–Bárány theorems. Publications de l'Institut Mathematique (Beograd), 49(63), 1996.
  21. R.T. Živaljević. User's guide to equivariant methods in combinatorics. Publ. Inst. Math. Belgrade, 59(73), 1996, 114–130.
  22. R. Živaljević. User's guide to equivariant methods in combinatorics II. Publications de l'Institut Mathematique (Beograd), 64(78), 1998.
  23. R. Živaljević. Combinatorics of topological posets: Homotopy complementation formulas. Advances in Applied Mathematics 21, 547–574 (1998).
  24. R. Živaljević. The Tverberg–Vrećica problem and the combinatorial geometry on vector bundles. Israel J. Math., 111 (1999), 53–76.
  25. E. Makai, S. Vrećica, R. Živaljević. Plane sections of convex bodies of maximal volume. Discrete Comput. Geometry 25, 2001, 33–49.
  26. S.T. Vrećica, R.T. Živaljević. Conical equipartitions of mass distributions. Discrete Comput. Geom. 25:339–350 (2001).
  27. R.T. Živaljević. An essay about geometric combinatorics. Bull. Soc. Math. Banja Luka 9 (2002), 80–93.
  28. P. Blagojević, V. Grujić, R. Živaljević. Symmetric products of surfaces; a unifying theme for topology and physics. Summer School in Modern Mathematical Physics, Belgrade 2002.

4.3   Main Publications after 2003

  1. S.T. Vrećica, R.T. Živaljević. Arrangements, equivariant maps and partitions by k-fans. In Discrete and Computational Geometry – The Goodman–Pollack Festschrift, Springer Verlag, Berlin, 2003.
  2. P. Blagojević, V. Grujić, R. Živaljević. Symmetric products of surfaces and the cycle index. Israel J. Math. 138 (2003) 61–72.
  3. R.T. Živaljević. Topological methods, Chapter 14 in Handbook of Discrete and Computational Geometry, Chapman & Hall/CRC 2004.
  4. P. Blagojević, V. Grujić, R. Živaljević. Arrangements of symmetric products of spaces. Topology and its Applications 148 (2005) 213–232.
  5. R.T. Živaljević. WI-posets, graph complexes and Z₂-equivalences. J. Combin. Theory, Ser. A, 111 (2005) 204–223.
  6. P. Mani–Levitska, S. Vrećica, R. Živaljević. Topology and combinatorics of partitions of masses by hyperplanes. Advances in Mathematics 207 (2006) 266–296.
  7. R. Živaljević. Groupoids in combinatorics – applications of a theory of local symmetries. AMS Contemporary Mathematics, Vol. 423, 305–324, 2007.
  8. R.T. Živaljević. Equipartitions of measures in ℝ⁴. Trans. Amer. Math. Soc. 360(1), 2008, 153–169.
  9. M. de Longueville, R.T. Živaljević. Splitting multidimensional necklaces. Advances in Mathematics, 2008.
  10. P.V.M. Blagojević, S.T. Vrećica, R.T. Živaljević. Computational topology of equivariant maps from spheres to complements of arrangements. Trans. Amer. Math. Soc. 361 (2009), 1007–1038.
  11. R. Živaljević. Combinatorial groupoids, cubical complexes, and the Lovász conjecture. Discrete & Computational Geometry, 41(1), 2009, 135–161.
  12. S. Vrećica, R. Živaljević. Cycle-free chessboard complexes and symmetric homology of algebras. European J. of Combinatorics 30(2), 2009, 542–554.
  13. R. Živaljević. Oriented matroids and Ky Fan's theorem. Combinatorica, 30(4), 2010, 471–484.
  14. S. Vrećica, R. Živaljević. Fulton–MacPherson compactification, cyclohedra, and the polygonal pegs problem. Israel J. Math., 184(1), 2011, 221–249.
  15. S. Vrećica, R. Živaljević. Chessboard complexes indomitable. J. Combinatorial Theory Ser. A, 118(7), 2011, 2157–2166.
  16. Đ. Baralić, B. Prvulović, G. Stojanović, S. Vrećica, R. Živaljević. Topological obstructions to totally skew embeddings. Trans. Amer. Math. Soc., 364, 2012, 2213–2226.
  17. R. Živaljević. Rotation number of a unimodular cycle: an elementary approach. Discrete Mathematics, 313, 2013, 2253–2261.
  18. R.T. Živaljević. Review of Mathematical Omnibus: Thirty Lectures on Classic Mathematics. Amer. Math. Monthly 120(3), 2013, 283–286.
  19. M. Muzika-Dizdarević, R. Živaljević. Symmetric polyomino tilings, tribones, ideals, and Gröbner bases. Publ. Inst. Math. (Beograd) 98(112), 2015, 1–23.
  20. R. Živaljević. Computational topology of equipartitions by hyperplanes. Topological Methods in Nonlinear Analysis, 45, 2015, 63–90.
  21. R. Živaljević. Illumination complexes, delta-zonotopes, and the polyhedral curtain theorem. Computational Geometry, 2015, 225–236.
  22. S. Vrećica, R. Živaljević. Measurable patterns, necklaces and sets indiscernible by measure. Topological Methods in Nonlinear Analysis, 45(1), 2015, 39–53.
  23. M. Muzika-Dizdarević, R. Živaljević. Signed polyomino tilings by n-in-line polyominoes and Gröbner bases. Publ. Inst. Math. (Beograd) 99(113), 2016, 31–42.
  24. R.T. Živaljević. A glimpse into continuous combinatorics of posets, polytopes, and matroids. Journal of Mathematical Sciences (Springer), 2016.
  25. D. Jojić, S.T. Vrećica, R.T. Živaljević. Multiple chessboard complexes and the colored Tverberg problem. J. Combin. Theory Ser. A, 145, 2017, 400–425.
  26. Đ. Baralić, R. Živaljević. Colorful versions of the Lebesgue, KKM, and Hex theorem. J. Combin. Theory Ser. A, 146, 2017, 295–211.
  27. D. Jojić, S.T. Vrećica, R.T. Živaljević. Symmetric multiple chessboard complexes and a new theorem of Tverberg type. J. Algebraic Combin., 46, 2017, 15–31.
  28. R. Živaljević. Topological methods in discrete geometry. Chapter 20 in Handbook of Discrete and Computational Geometry (3rd ed.), CRC Press, 2017.
  29. D. Jojić, I. Nekrasov, G. Panina, R. Živaljević. Alexander r-tuples and Bier complexes. Publ. Inst. Math. (Beograd) 104(118), 2018, 1–22.
  30. F.D. Jevtić, M. Jelić, R.T. Živaljević. Cyclohedron and Kantorovich–Rubinstein polytopes. Arnold Mathematical Journal, 4, 2018, 87–112.
  31. M. Jelić, D. Jojić, M. Timotijević, S.T. Vrećica, R.T. Živaljević. Combinatorics of unavoidable complexes. European J. of Combinatorics, 83, January 2020.
  32. F.D. Jevtić, M. Timotijević, R.T. Živaljević. Polytopal Bier spheres and Kantorovich–Rubinstein polytopes of weighted cycles. Discrete and Computational Geometry, 2019.
  33. D. Jojić, W. Marzantowicz, S.T. Vrećica, R.T. Živaljević. Topology of unavoidable complexes. J. Fixed Point Theory and Applications, 2020.
  34. D. Jojić, G. Panina, R. Živaljević. A Tverberg type theorem for collectively unavoidable complexes. Israel J. Math., 2019.
  35. F.D. Jevtić, R.T. Živaljević. Generalized Tonnetz and discrete Abel–Jacobi map. Topological Methods in Non-linear Analysis, 2020.
  36. Đ. Baralić, P-L. Curien, M. Milićević, J. Obradović, Z. Petrić, M. Zekić, R.T. Živaljević. Proofs and surfaces. Annals of Pure and Applied Logic, 171(9), 2020.
  37. D. Jojić, G. Panina, S.T. Vrećica, R.T. Živaljević. Generalized chessboard complexes and discrete Morse theory. Chebyshevskii Sb., 21:2, 2020, 207–227.
  38. D. Jojić, G. Panina, R. Živaljević. Colored Tverberg theorem; extensions and new results. Izvestiya Mathematics, 2021.
  39. D. Jojić, G. Panina, R. Živaljević. Optimal colored Tverberg theorems for prime powers. Homology, Homotopy and Applications, 2021.
  40. D. Jojić, G. Panina, R. Živaljević. Splitting necklaces with constraints. SIAM J. Discrete Math., 2021.
  41. M. Muzika Dizdarević, R.T. Živaljević. The unique balanced 4-bit Gray cycle, Hamiltonian surfaces and Venn diagrams. Publications de l'Institut Mathematique (N.S.) 111(125), 2022, 17–40.
  42. M. Muzika Dizdarević, M. Timotijević, R.T. Živaljević. Gröbner lattice-point enumerators and signed tiling by k-in-line polyominoes. Kragujevac J. of Mathematics, 49(3), 2025, 443–464.
  43. G. Panina, R.T. Živaljević. Envy-free division via configuration spaces. Topol. Methods Nonlinear Anal., 2022.
  44. G. Panina, R. Živaljević. Envy-free division in the presence of a dragon. J. Fixed Point Theory Appl. 24, 81, 2022.
  45. F.D. Jevtić, R.T. Živaljević. Bier spheres of extremal volume and generalized permutohedra. Applicable Analysis and Discrete Mathematics, 2022.
  46. D. Jojić, G. Panina, R. Živaljević. "Cooperative envy-free division." Zap. Nauchn. Sem. POMI, 528, 2023, 116–133.
  47. M. Timotijević, R.T. Živaljević, F.D. Jevtić. Polytopality of simple games. Experimental Mathematics, 2024.
  48. I. Limonchenko, M. Timotijević, R. Živaljević. Bier spheres and the problem of toric non-quasitoric manifolds. Rus. Math. Surveys, 2026 (to appear).
  49. F.D. Jevtić, M.Z. Timotijević, R.T. Živaljević. Indecomposability of the median hypersimplex and polytopality of the hemi-icosahedral Bier sphere. Filomat, 39(13), 2025.
  50. G. Panina, R. Živaljević. Ky Fan Theorem for sphere bundles. Russ. J. Math. Phys. 32, 141–149, 2025.
  51. I.Yu. Limonchenko, M. Timotijević, R.T. Živaljević. On a class of toric manifolds arising from simplicial complexes. Preprint, 2025; arXiv:2506.13547.
  52. I.Yu. Limonchenko, R.T. Živaljević. Bier spheres, Nevo–Petersen conjecture and polyhedral products. Results Math. 81(1), Paper No. 6, 32 pp., 2026.
  53. D. Jojić, G. Panina, R. Živaljević. Lower bounds on the number of envy-free divisions. arXiv:2504.18979.

4.4   International Visibility

1998 Total Citations
22 h-index
42 i10-index
490 Citations since 2021
10 h-index since 2021
16 i10-index since 2021
Math-Net.Ru personal page ZentralBlatt publications list Google Scholar profile MFO Oberwolfach profile CIRM Marseille