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Email: milivojevic[[at]]mpim-bonn.mpg.[[de]]
- (with Jiahao Hu) Infinite symmetric products of rational algebras and spaces, Comptes Rendus Mathématique. 2022. (arxiv: arxiv.org/abs/2108.09794)
- The weak form of Hirzebruch's prize question via rational surgery, Journal of Topology and Analysis, 2022. pdf.
- On the characterization of rational homotopy types and Chern classes of closed almost complex manifolds, Complex Manifolds, 2022. pdf. Based on a large part of my thesis; I gave an overview at the 2020 Oberwolfach mini-workshop "Almost complex geometry", with extended abstract here.
- (with Bora Ferlengez and Gustavo Granja) On the topology of the space of almost complex structures on the six sphere, New York Journal of Mathematics, 2021. (arxiv: https://arxiv.org/abs/2108.00750)
- (with Michael Albanese) Spinh and further generalisations of spin, Journal of Geometry and Physics, 2021. (arxiv: https://arxiv.org/abs/2008.04934)
- On the realization of symplectic algebras and rational homotopy types by closed symplectic manifolds, Proceedings of the American Mathematical Society, 2021. (arxiv: https://arxiv.org/abs/2011.02928)
- Another proof of the persistence of Serre symmetry in the Frölicher spectral sequence, a short note in Complex Manifolds, 2020.
- (with Spencer Cattalani) Verifying the Hilali conjecture up to formal dimension twenty, Journal of Homotopy and Related Structures, 2020. Research done as part of the undergraduate Directed Reading Program at Stony Brook.
- (with Michael Albanese) Connected sums of almost complex manifolds, products of rational homology spheres, and the twisted spinc Dirac operator, Topology and its Applications, 2019. (arxiv: https://arxiv.org/abs/1905.01760)
- (with Michael Albanese) On the minimal sum of Betti numbers of an almost complex manifold, Differential Geometry and its Applications, 2019. (arxiv: https://arxiv.org/abs/1805.04751)
- (with Scott Wilson) Invariant Dolbeault cohomology for homogeneous almost complex manifolds, 2022. pdf.
- (with Jonas Stelzig and Leopold Zoller) Poincaré dualization and formal domination, 2022. arxiv.org/abs/2203.15098.
- (with Jonas Stelzig) Bigraded notions of formality and Aeppli-Bott-Chern-Massey products, 2022. arxiv.org/abs/2202.08617.
- At the "Higher algebraic structures in algebra, topology and geometry" program at Institut Mittag-Leffler, Formality and non-zero degree maps, February 2022 (in person, half hour): link. Here is a related Oberwolfach report.
- Stony Brook University capsule talks, thesis overview, May 2021 (online, fifteen minutes plus discussion): link
Some notes
- On the sixth k-invariant in the Postnikov tower for BSO(3), pdf
- Some calculations of the rational homotopy type of the classifying space for fibrations up to fiber homotopy equivalence, pdf
- A note on the difference between the sum of the Hodge numbers and Betti numbers on a non-Kähler complex manifold, pdf
Expository, translations, miscellaneous
A symplectic non-Kähler complex threefold all of whose odd Betti numbers are even, and some almost-complex four manifolds with no complex structure. Here is an example of a non-integrable almost complex structure connected by a path to an integrable complex structure on a smooth manifold of even dimension four or greater.
A discussion on almost complex and stably almost complex structures, and the obstructions to such structures in low dimensions. You can find the minimal models of some relevant homogeneous spaces SO(2n)/U(n) here.
Notes for a talk I gave at the City University of New York Graduate Center K-Theory seminar in November 2018, on setting up and calculating the Frölicher spectral sequence.
Notes for a talk I gave at the Stony Brook Symplectic Geometry student seminar in August 2018, titled "Symplectic non-Kähler manifolds".
Notes for a talk I gave at the Stony Brook graduate student seminar in February 2018 as an introduction to rational homotopy theory.
A 1975 paper by Deligne and Sullivan, Complex vector bundles with discrete structure group, translated from French to English. Here you can find the original.
A 1956 paper by Haefliger, Sur l'extension du groupe structural d'un espace fibré, translated from French to English. The original can be found here in the Comptes Rendus archives, pp.558-560. This is the paper where the second Stiefel-Whitney class was first explicitly identified as the (only) obstruction for an oriented bundle to admit a spin structure.
I am occasionally on MathOverflow.
Question for visitor: is there a closed symplectic 2n-manifold such that the i-th Betti number is strictly greater than the (i+2)-nd Betti number, for some i+2 ≤ n?
Aleksandar Milivojević
I am a postdoctoral fellow at the Max Planck Institute for Mathematics in Bonn, where I will be from August 2021 to July 2023. In 2021 I obtained my PhD from Stony Brook University, under the guidance of Dennis Sullivan. I mostly think about rational homotopy theory and what it can say about the topology and geometry of manifolds, with an emphasis on almost complex manifolds. You can find my CV here.
Research
Publications and accepted:
Preprints:
Recorded talks
Photo courtesy of the Mathematisches Forschungsinstitut Oberwolfach