CURRICULUM VITAE. 1. Professor Frederick R. Cohen, Rochester University, NY, U. S. A.

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1 CURRICULUM VITAE Personnel Information: Last Name : Popescu First Name : Călin Date of Birth : September 26, calin.popescu@imar.ro Highest Degree and Source: Ph.D. in pure mathematics algebraic topology, received summa cum laudae (avec la plus grande distinction et les félicitations du jury) from Université Catholique de Louvain, Belgium, in January, Title of the Ph.D. Thesis: Characteristic zero loop space homology and universal enveloping algebras. Ph.D. Advisor: Professor Yves Félix of Université Catholique de Louvain, Belgium. Members of the Ph.D. Jury: 1. Professor Frederick R. Cohen, Rochester University, NY, U. S. A. 2. Professor Yves Félix, Université Catholique de Louvain, Belgium. 3. Professor Daniel Tanré, Université de Lille, France. Main Field of Interest: Loop space homology via homology of differential graded Lie algebras and their universal enveloping algebras; entwined and braided structures. Visits: October 17 December 19, 2001: Mathematics Section of the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy; invited by Professor M. A. Virasoro, director of the centre; talks and research on loop space homology in characteristic zero and universal enveloping algebras; computation of the loop space homology for the adjunction of a finite number of 4(p + 1)-cells to a wedge of two 2(p + 1)-spheres. 1

2 January 15-31, 2001: Department of Mathematics, University of Rochester, NY, U. S. A.; invited by Professor Frederick R. Cohen; talks and research on loop space homology in characteristic zero and universal enveloping algebras. Meetings: R-Quillen Theorems talk given at The Fourth International Joint Meeting of the American Mathematical Society and the Sociedad Matematica Mexicana, University of North Texas, Denton, TX, U. S. A., May 19-22, International Conference of Algebraic Topology, Angers, France, September, 1998 attendee. Career: Since 2003: Researcher with the Institute of Mathematics Simion Stoilow of the Romanian Academy talks and research on rational homotopy theory, and entwined and braided structures : Lecturer with the École Normale Supérieure de Bucarest lectures in general, algebraic and differential topology. Since 2004: Trainer of the Romanian team for the International Mathematics Olympiad. 2001: Short term postdoctoral visitor at the Mathematics Section of the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, and the Department of Mathematics, University of Rochester, NY, U. S. A. talks and research on loop space homology in characteristic zero and universal enveloping algebras. 1999: Temporary lecturer at the Summer School of Université Catholique de Louvain, Belgium introductory lectures on the topology of polyhedra. 1997: Research assistant with the Mathematics Institute of Université Catholique de Louvain, Belgium contract with Solvay Polyolefins Europe Belgium S.A.: numerical resolution of integral and differential equations : Assistant lecturer with the Department of Theoretical Electrical Engineering of the Polytechnic Institute of Bucharest, Romania seminars on mathematical field theory: variational and local approach : Mathematician-engineer with the Scientific Research Institute for Electrical Engineering, Bucharest, Romania theoretical research in mathematical field theory: variational and local approach. 2

3 Electronic Preprints: 1. Algebra Structures Arising from Yang-Baxter Systems (with Barbu R. Berceanu and Florin F. Nichita), arxiv: v1 [math.qa] 6 May, List of Publications: 1. Entwined Bicomplexes (with Florin F. Nichita), Bull. Math. Soc. Sci. Math. Roumanie, Tome 52(100), 2(2009), pp Abstract: We associate with each (co)algebra a bicomplex by encoding the (co)multiplication in one of the differentials, and the (co)unit in the other. Akin to the (co)bar construction, the construction enables us to encode a morphism entwining an algebra with a coalgebra as a bicomplex morphism entwining the associated bicomplexes. Next, we consider a related simplicial construction which associates a simplicial module with each (co)algebra. In this case, an entwining structure yields a simplicial map entwining the associated constructions, on one hand, and a chain map entwining the chain complexes on the constructions, on the other. Furthermore, the components of the simplicial entwining combine to yield another chain map between the chain complexes on the entwined products of constructions. The two chain maps thus obtained turn out to be compatible (they commute) up to chain homotopy with any pair of natural chain transformations for the Eilenberg-Zilber theorem which are the respective identities in dimension zero. 2. Characteristic Zero Loop Space Homology of Two-Cones, Bull. London Math. Soc., 32 (2000), pp Abstract: Given a principal ideal domain R of characteristic zero, containing 1/2, and a two-cone X of appropriate connectedness and dimension, we present sufficient algebraic conditions for the Hopf algebra F H(ΩX; R) to be isomorphic with the universal enveloping algebra of an R-free graded Lie algebra; here, F stands for free part (that is, quotient by the R-torsion), H for homology, and Ω for the Moore loop space functor. 3. On UHL and HUL, Bull. Belg. Math. Soc., 6 (1999), pp

4 Abstract: Let R be a principal ideal domain of characteristic zero, containing 1/2, and let ϱ = ϱ(r) be the least prime (or ) not invertible in R. Our main result is the following: Let (L, d) be a connected differential graded Lie algebra over R, whose underlying module is R- free of finite type. If ad ϱ 1 (x)(dx) = 0, for homogeneous x in L even, then the natural morphism UF H(L, d) F HU(L, d) is an isomorphism of graded Hopf algebras; here, F stands for free part (that is, quotient by the R-torsion), H for homology, and U for universal enveloping algebra. Related facts and numerous examples are also considered. 4. Characteristic zero loop space homology for certain two-cones, Comment. Math. Univ. Carolinae, 3 (1999), pp Abstract: Given a principal ideal domain R of characteristic zero, containing 1/2, and a two-cone X of appropriate connectedness and dimension, we present a sufficient algebraic condition, in terms of Adams-Hilton models, for the Hopf algebra F H(ΩX; R) to be isomorphic with the universal enveloping algebra of an R-free graded Lie algebra; here, F stands for free part (that is, quotient by the R- torsion), H for homology, and Ω for the Moore loop space functor. 5. On the homology of free Lie algebras, Comment. Math. Univ. Carolinae, 4 (1998), pp Abstract: Given a principal ideal domain R of characteristic zero, containing 1/2, and a connected differential graded free finite type R- module V, we prove that the natural arrow LF H(V ) F HL(V ) is an isomorphism of graded Lie algebras over R, and deduce thereby that arrow UF HL(V ) F HUL(V ) is an isomorphism of graded cocommutative Hopf algebras over R; here, F stands for free part (that is, quotient by the R-torsion), H for homology, L for free Lie algebra, and U for universal enveloping algebra. Related facts and examples are also considered. 6. Note on the Ptolemy theorem, Nieuw Arch. Wisk., 3 (1997), pp Abstract: The object of this note is to present an approach of the classical Ptolemy theorem and its generalization in terms of Ptolemaic equivalents for configurations consisting of more than four points in the Euclidean plane. 4

5 7. A proof of a theorem of Kaplanski, Sci. Bull. Polytech. Inst. Bucharest, Series C, vol. 55, 3-4 (1993), pp Abstract: The aim of this note is to present a proof of the Kaplansky structure theorem for submodules of free modules over a hereditary ring in terms of the Zorn lemma. 8. Note on the Tychonoff product theorem, Sci. Bull. Polytech. Inst. Bucharest, Chem. Mat. Sci., vol. 54, 1-2 (1992), pp Abstract: We prove the universal subnet theorem, the Alexander subbase theorem, and a Cauchy subnet theorem by appealing to a less standard equivalent of the axiom of choice: the Tychonoff compactness theorem. 9. Note on ordering, compactness and continuity, Sci. Bull. Polytech. Inst. Bucharest, Mech. Eng., vol. 52, 3-4 (1990), pp Abstract: We show that ordering ω-continuity is not sufficient to characterize topological continuity, by constructing a discontinuous function of a compact Hausdorff space into itself whose closure is ω-continuous (see entry 13 below). 10. Note on subset systems on the category of posets, Sci. Bull. Polytech. Inst. Bucharest, Mech. Eng., vol. 52, 2 (1990), pp Abstract: Given a subset system Z on the category of posets, we prove that some information on some Z-set in some poset enables identifying Z-sets in any poset. If, for instance, the cardinal number of some Z-set in some poset is greater than or equal to a positive integer n, then, in any poset, any chain of at most n elements is a Z-set. Consequently, if some poset contains an infinite Z-set, then any finite chain in any poset is a Z-set. 11. A non-trivial infinitely differentiable map, Sci. Bull. Polytech. Inst. Bucharest, Electr. Eng., vol. 52, 1 (1990), pp Abstract: We construct an infinitely differentiable real-valued map on the standard unit interval which is constant on no proper subinterval of its domain of definiton, whose zeros are located precisely at the points of the Cantor set. 5

6 12. A proof of the classical theorem of Tychonoff on the product of compact topological spaces, Bul. Inst. Politehn. Bucuresti, Seria Electron., tomul LI, 1989, pp Abstract: We prove the classical theorem of Tychonoff on the product of compact topological spaces by making use of some results on universal nets due to John L. Kelley. 13. Ordering, compactness, continuity (with Andrei Baranga), Bull. Math. Soc. Sci. Math. Roumanie, 31 (79), 2 (1987), pp Abstract: We characterize topological notions such as compactness, sequentially compactness, and continuity in terms of ordering notions such as -completeness, ω-completeness, -continuity, and ω- continuity. As an application, we derive Banach s fixed point theorem for contractions of compact metric spaces from Kleene s fixed point theorem. 14. Asupra simplexelor finit dimensionale, Bul. Inst. Politehn. Bucuresti, Seria Electrotehn., tomul XLVI-XLVII, , pp Abstract: We show that the orthogonal projection of an (n + 1)- parallelepiped on an n-dimensional hyperplane is the convex hull of a standard pattern obtained from an n-simplex in that hyperplane. Some related facts are also considered. 15. Asupra unor functii (with Florin Radulescu), Gazeta Mat., Seria A, 1-2 (1981). Abstract: Given a non-negative integer n, we construct a C n realvalued map on the standard unit interval which is constant on no proper subinterval of its domain of definiton, whose zeros are located precisely at the points of the Cantor set. 6