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.
(with Jonas Stelzig) Bigraded notions of formality and Aeppli-Bott-Chern-Massey products, 2022. arxiv.org/abs/2202.08617.
Recorded talks
Geometria em Lisboa seminar, IST Lisbon, June 2022 (in person, one hour): link. Here is a related Oberwolfach report.
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 (same as above).
Stony Brook University capsule talks, thesis overview, May 2021 (online, fifteen minutes plus discussion): link
Some notes
(with Scott Wilson) Invariant Dolbeault cohomology for homogeneous almost complex manifolds, 2022. pdf.
(with Bora Ferlengez) A trichotomy of consequences of the existence of holomorphic charts on the six sphere, 2020. pdf; a note related to the paper "On the topology of the space of almost complex structures on the six sphere". Sections 1 and 2 feature alternative arguments for weaker versions of some results in the paper, and Section 3 is disjoint from the paper.
On the sixth k-invariant in the Postnikov tower for BSO(3), 2018. pdf
Some calculations of the rational homotopy type of the classifying space for fibrations up to fiber homotopy equivalence, 2018. pdf
A note on the difference between the sum of the Hodge numbers and Betti numbers on a non-Kähler complex manifold, 2018. pdf
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 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.