Members of the project group enjoy great reputation in mathematical community, witnessed also by their membership on editorial boards of 36 important mathematical journals and book series. We list the most important 10: 1. Advances in nonlinear analysis. Radulescu, Vicenţiu (editor-in-chief, 2012-). Repovš, Dušan (editor-in-chief of 2012-), Molica Bisci, Giovanni (editor-in-chief, 2015-). [Print ed.]. Berlin: De Gruyter, 2012-. ISSN 2191-9496. http://www.degruyter.com/view/j/anona. [COBISS.SI-ID 16253785] 2. Boundary value problems. Radulescu, Vincenţiu (editor-in-chief, 2009-). Repovš, Dušan (editor-in-chief of 2015), Molica Bisci, Giovanni (editor-in-chief, 2015-). Berlin: Springer, 2005-. ISSN 1687-2770. http://link.springer.com/journal/volumesAndIssues/13661, http://www.boundaryvalueproblems.com/archive. [COBISS.SI-ID 62113025] 3. Complex variables and elliptic equations. Radulescu, Vicenţiu (member of the editorial board of 2007-), Molica Bisci, Giovanni (member of the editorial board of 2016-), Repovš, Dušan (member of the editorial board 2019-). Abingdon: Taylor & Francis, 2006-. ISSN 1747-6933. http://www.tandfonline.com/loi/gcov20. [COBISS.SI-ID 513019929] 4. De Gruyter series and nonlinear analysis and applications. Radulescu, Vicenţiu (member of the editorial board 2018). Berlin; New York: De Gruyter. ISSN 0941-813X. https://www.degruyter.com/view/serial/16646. [COBISS.SI-ID 18404697] 5. Discrete and continuous dynamical systems. Papageorgiou, Nikolaos Socrates (member of the editorial board of 1995-). Springfield, MO: American Institute of Mathematical Sciences, 1995-. ISSN 1078-0947. http://www.aimsciences.org/journals/home.jsp?journalID=1. [COBISS.SI-ID 15865689] Journal of Mathematical Analysis and Applications. Radulescu, Vicenţiu (member of the editorial board of 2004-), Repovš, Dušan (member of the editorial board of 2017-). [Print ed.]. Orlando (FL): Elsevier, 1960-. ISSN 0022-247X. http://www.journals.elsevier.com/journal-of-mathematical-analysis-and-applications, http://www.sciencedirect.com/science/journal/0022247X. [COBISS.SI-ID 3081231] 7. Mathematical methods in applied sciences. Radulescu, Vicenţiu (member of the editorial board of 2018-). Stuttgart: Teubner; Chichester: Wiley, 1972-. ISSN 0170-4214. http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1476/issues. [COBISS.SI-ID 25911808] 8. Mathematics in Science and Engineering. Radulescu, Vicenţiu (member of the editorial board of 2016-). New York: Elsevier, 1961-. ISSN 0076-5392. [COBISS.SI-ID 17730905] 9. Mediterranean journal of mathematics. Repovš, Dušan (editor-in-chief, 2016-). Basel; Boston; Berlin: Birkhäuser, 2004-. ISSN 1660-5446. [COBISS.SI-ID 13561433] 10. Nonlinear Analysis, Theory, Methods and Applications. Radulescu, Vicenţiu (editor-in-chief, 2018-). [Print ed.]. Oxford; New York: Pergamon Press, 1976-. ISSN 0362-546X. [COBISS.SI-ID 26027520]

C.04 Editorial board of an international magazine

In his thesis, young researcher Govc (advisor Dr. Repovš) completely characterizes the unimodal category for functions f: R \to [0,\infty) using a decomposition theorem obtained by generalizing the sweeping algorithm of Baryshnikov and Ghrist. He also gives a characterization of the unimodal category for functions f: S^1 \to [0,\infty) and provides an algorithm to compute the unimodal category of such a function in the case of finitely many critical points. He then turns to the monotonicity conjecture of Baryshnikov and Ghrist. He shows that this conjecture is true for functions on R and S^1 using the above characterizations and that it is false on certain graphs and on the Euclidean plane by providing explicit counterexamples. He also shows that this holds for functions on the Euclidean plane whose Morse-Smale graph is a tree using a result of Hickok, Villatoro and Wang. He then presents several open questions indicating promising research directions. After this, he proves an approximate nerve theorem, which is a generalization of the nerve theorem from classical algebraic topology to the context of persistent homology. This is done by introducing the notion of an \varepsilon-acyclic cover of a filtered space. He uses spectral sequences to relate the persistent homologies of the various spaces involved. The approximation is stated in terms of the interleaving distance between persistence modules. To obtain a tight bound, the technical notions of left and right interleavings are introduced. Finally, examples are provided, which realize the bound and thus prove the tightness of the result.

D.09 Tutoring for postgraduate students

COBISS.SI-ID: 18139993