Danica Kosanović
Pronounce c as zz in pizza, and ć as ci in ciabatta.
Typeset the letter ć as \'c in LaTeX. Hermann Weyl Instructor at the Departement of Mathematics at ETH Zürich ETH Zürich, Forschungsinstitut für MathematikRämistrasse 101, HG GO 68.2 8092 Zürich, Switzerland danica.kosanovic[at]math[dot]ethz[dot]ch
arxiv.org/a/kosanovic_d_1.html
Research interests: 4-manifolds, knotted surfaces in 4-manifolds, knot theory, homotopy types of embedding spaces, Goodwillie-Weiss embedding calculus, operads, graph complexes. |
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Before coming to ETH in 2021, I was a FSMP postdoc at LAGA, Paris 13 (Université Sorbonne Paris Nord). I obtained my PhD degree in September 2020 from the University of Bonn (Germany), working at the Max-Planck Insitut für Mathematik under the supervision of Peter Teichner. For a summary of my thesis, see the slides from the public talk of my PhD defense. Previously, I studied in Belgrade (Serbia) and Cambridge (UK).
People I have had pleasure to interact with mathematically include Pedro Boavida de Brito, Dušan Đorđević, Peter Feller, Daniel Hartman, Geoffroy Horel, Stefan Mihajlović, Jovana Nikolić, Zoran Petrić, Rob Schneiderman, Peter Teichner, Thomas Willwacher.
My partner Mihajlo Cekić is also a mathematician.
August 2024 |
My grant proposal "Embedding spaces: building bridges between geometric and algebraic viewpoints"
has been approved by the Swiss National Science Foundation and will commence in January 2025. This comes with a funding for a PhD student, click ☞ HERE ☜ to see details. |
Autumn 2024 | I am teaching The s-cobordism theorem and its 4d reincarnations @ CUSO graduate lectures in mathematics, Bern. See Teaching. |
22 Nov 2024 | I will give a talk at Séminaire Topologie @ Lille. |
25 Nov 2024 | I will take part in Journées de topologie quantique @ Paris. |
Embedding calculus and grope cobordism of knots 2020 preprint @ arxiv.org/abs/2010.05120 Published in the Advances in Mathematics @ doi.org/10.1016/j.aim.2024.109779 (open access). |
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On homotopy groups of spaces of embeddings of an arc or a circle: the Dax invariant 2021 preprint @ arxiv.org/abs/2111.03041 Published in the Transactions of the American Mathematical Society @ doi.org/10.1090/tran/8805 (subscription). |
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A space level light bulb theorem in all dimensions ~ Joint with Peter Teichner ~ 2021 preprint @ arxiv.org/abs/2105.13032 To appear in the Commentarii Mathematici Helvetici. |
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A new approach to light bulb tricks: Disks in 4-manifolds ~ Joint with Peter Teichner ~ 2022 preprint @ arxiv.org/abs/2209.12015 Published in the Duke Mathematical Journal @ doi.org/10.1215/00127094-2023-0036 (subscription). |
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Knotted families from graspers 2023 preprint @ arxiv.org/abs/2307.14028 Published in the Journal of Topology @ doi.org/10.1112/topo.12337 (open access). |
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Homotopy versus isotopy: 2-spheres in 5-manifolds ~ Joint with Rob Schneiderman and Peter Teichner ~ 2023 preprint @ arxiv.org/abs/2312.16905 To appear in the Pacific Journal of Mathematics. |
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Diffeomorphisms of 4-manifolds from degree one graspers 2024 preprint @ arxiv.org/abs/2405.05822 Submitted. |
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On fundamental groups of spaces of (framed) embeddings of the circle in 4-manifolds 2024 preprint @ arxiv.org/abs/2407.06923 Submitted. |
A geometric approach to the embedding calculus knot invariants. PhD Thesis. Download in Bonn Library. |
9.9.2024 | Diffeomorphisms of 4-manifolds @ Moduli spaces of curves, moduli spaces of graphs and graph complexes, ETH ITS Workshop |
19.8.2024 | Diffeomorphisms from degree one graspers @ Topology of moduli spaces, a conference in honour of Ulrike Tillmann's 60th birthday |
25.9.2024 | Diffeomorphisms of 4-manifolds from graspers @ Workshop Topologie in Oberwolfach |
22.05.2024 | Diffeomorphisms of 4-manifolds @ Oberseminar Geometrie, Uni of Fribourg |
29.11.2023 | Knotted families from graspers @ BIRS Workshop Spaces of Manifolds: Algebraic and Geometric Approaches, Banff, handwritten slides (~14MB) |
7.9.2023 | Knotted families from graspers @ Conference Swiss Knots 2023, Regensburg |
9.5.2023 | 2-knots with light bulbs and knotted families of arcs @ University of Neuchâtel, Colloquium |
5.5.2023 - Online | Homotopy groups of some embedding spaces Part II @ Kansas State University Topology Seminar |
28.4.2023 - Online | Homotopy groups of some embedding spaces @ Kansas State University Topology Seminar |
12.3.2023 - Online | A new approach to light bulb tricks @ Online Conference "Interactions of 3- & 4-dimensional Topology", webpage |
17.11.2022 | 2-knots and knotted families of arcs @ University of Zurich, room Y27-H-26, at 10:30 |
04.11.2022 - Online | A new approach to light bulb tricks @ BIRS Workshop Topology in Dimension 4.5, Banff |
24.-27.10.2022 | Homotopy groups of some embedding spaces @ Réunion annuelle du GDR, 24-27 October 2022, Université de Nantes, webpage, slides |
14.9.2022 | 2-knots and knotted families of arcs @ DMV (German Mathematical Society) Annual Meeting, Berlin, beamer slides |
16.7.2022 | 2-knots and knotted families of arcs @ AMS-EMS-SMF Congress of Mathematics, 18-22 July, 2022, Grenoble |
25.3.2022 - Online | A light bulb theorem for disks @ Algebraic Geometry and Differential Topology Seminar, Alfréd Rényi Institute of Mathematics, Budapest |
24.2.2022 | Smooth embeddings and their families @ Durham Geometry and Topology Seminar |
16.2.2022 | Smooth embeddings and their families @ Cambridge Differential Geometry and Topology Seminar |
11.2.2022 - Online | Smooth embeddings and their families @ UL Lafayette Topology Seminar |
7.10.2021 - Online | A light bulb theorem for disks @ Princeton Topology Seminar |
6.10.2021 | Light bulbs in 4-manifolds @ ETH Zürich Geometrie Seminar |
21.9.2021 - Online | A light bulb theorem for disks @ University of Virginia Geometry Seminar |
17.8.2021 | Учворени дискови у четири димензије @ Workshop on Symplectic Topology, University of Belgrade |
9.7.2021 - Online | Higher homotopy groups in low dimensional topology @ Young Topologists Meeting, beamer slides |
11.6.2021 - Online | A light bulb theorem for disks @ Georgia Topology Conference, beamer slides |
21.4.2021 - Online | Knotted families of arcs @ Münster Topology Seminar |
15.3.2021 - Online | Knotted families of arcs @ MIT Topology Seminar |
13.1.2021 - Online | Knot invariants from homotopy theory @ Higher Structures & Field Theory Seminar |
4.12.2020 - Online | Knot invariants from homotopy theory @ Colloquium LAGA Paris 13 |
3.12.2020 - Online | Knot invariants from homotopy theory @ Théorie des groupes, LAMFA Université d'Amiens |
26.11.2020 - Online | Knot invariants from homotopy theory @ Séminaire AGATA, Université de Montpellier, beamer slides |
17.11.2020 - Online | Knot invariants from homotopy theory @ Warwick algebraic topology seminar |
2.11.2020 - Online | Knot invariants from homotopy theory @ G&T Seminar Glasgow |
16.10.2020 | Knot invariants from homotopy theory @ Université de Lille |
31.7.2020 - Online | Embedding calculus for knot spaces @ Oberwolfach Workshop Topologie |
29.5.2020 - Online | Knot invariants from homotopy theory @ Topological Quantum Field Theory Seminar, Instituto Superior Técnico, Lisboa, video |
21.4.2020 - Online | Knot invariants from homotopy theory @ jointly Séminaire de l'équipe Topologie Algébrique, LAGA, Paris 13 and Séminaire de Topologie, IMJ-PRG, Paris 7 |
20.2.2020 | A geometric approach to the embedding calculus @ Oberwolfach Workshop Low-dimensional Topology |
30.1.2020 | Knot invariants from homotopy theory @ Topology Seminar Bochum |
20.1.2020 | Knot theory meets the embedding calculus @ Copenhagen Algebra/Topology Seminar |
16.1.2020 | Нове технике у теорији утапања (New techniques in the theory of embeddings) @ Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade |
2.12.2019 | Knot theory meets the embedding calculus @ MPIM Topology Seminar, Bonn |
16.10.2019 | Knots map onto components of the embedding calculus tower @ BIRS Workshop Spaces of Embeddings: Connections and Applications, Banff |
16.9.2019 | A gong show talk @ Workshop on 4-manifolds, MPIM Bonn |
13.5.2019 | A gong show talk @ Knots and Braids in Norway (KaBiN), Trondheim |
7.5.2019 | A geometric approach to embedding calculus @ Utrecht Geometry Center Seminar |
25.12.2018 | Инваријанте чворова и конфигурациони простори (Knot invariants and configuration spaces) @ Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade, slides (in Serbian) |
17.12.2018 | Revisiting the Arf invariant @ Topology Seminar, MPIM Bonn |
6.12.2018 | Extended evaluation maps from knots to the embedding tower @ Manifolds Workshop (part of Homotopy Harnessing Higher Structures Trimester) at Isaac Newton Institute, Cambridge |
28.11.2018 | Knot theory meets homotopy theory @ IMPRS Seminar, MPIM Bonn, slides |
24.7.2018 | Grope cobordism and the embedding tower for knots @ ICM 2018 Satellite Conference: Braid Groups, Configuration Spaces and Homotopy Theory, in Salvador, Brazil |
Feb 2018 - Poster | A homotopy theoretic approach to finite type knot invariants @ Winter Braids, CIRM, Luminy, France |
25.5.2022 | Freedman's work on 4-manifolds @ Actualité des mathématiques, Neuchâtel |
6.5.2021 | On a theorem of Kontsevich and Conant-Vogtmann @ Groupes de Grothendieck-Teichmüller et applications |
11.3.2021 | Chord diagram invariants of tangles @ Groupes de Grothendieck-Teichmüller et applications, notes |
13.2.2020 - Online | On the punctured knots model for embedding spaces @ Configuration Categories Learning Seminar |
19.12.2019 - Online | On link maps @ Mojito’s Seminar |
13.2.2020 - Online | On the paper by Bundey-Gabai about knotted 3-balls @ Online Student Seminar, notes |
19.12.2019 | Watanabe's counting formula for classes in Diff(S^4) @ Hot Topic Seminar, MPIM |
5.11.2019 | Milnor invariants and Whitney towers @ Milnor Invariants Learning Seminar, MPIM |
July 2019 | Introduction to Milnor link invariants and relation to Massey products @ Milnor Invariants Learning Seminar, MPIM |
May 2019 | Formality of little disks operads @ IMPRS seminar, MPIM |
Sep/Oct 2018 | Two talks about the paper of Ihara on automorphisms of pure sphere braid group @ GT learning seminar, MPIM |
Apr/May 2018 | Two talks on perturbative quantization and Chern-Simons theory for knots @ BV learning seminar, MPIM |
22.3.2018 | Complex oriented cohomology theories @ Peter’s Seminar in Berkeley |
06.12.2017 | Universal Knot Invariants @ The Chinese University of Hong Kong |
15.11.2017 | How to draw a smooth 4−manifold? @ IMPRS seminar, MPIM |
25.09.2017 | A categorical approach to quantum knot invariants @ Topology Seminar, MPIM |
04.08.2017 | A survey of Witten-Reshetikhin-Turaev invariants of 3-manifolds @ Special Topology Seminar, MPIM |
02.06.2017 | Topological reincarnations of the Arf invariant @ Cambridge Junior Geometry Tea Seminar, Cambridge, UK |
23.03.2017 | Topological reincarnations of the Arf invariant @ Berkeley seminar |
1. Here are the level sets of the Boy's surface.
2. Here is the proof that Bing double of any knot is a boundary link:
3. Here are solutions to some of the homework exercises we didn't have time to cover in the tutorials.
4. See also interior and boundary twists.
In the first part of the course we will discuss the proof of the s-cobordism theorem, for cobordisms between smooth manifolds of dimension at least 5 (in particular proving the Topological Generalised Poincaré Conjecture and the Schönflies Conjecture), and in the second part of the course we will see which arguments still apply for s-cobordisms between 4-manifolds, and how to push them further (touching on the work of Freedman and Quinn).