Danica Kosanović
Pronounce c as zz in pizza, and ć as ci in ciabatta.
Typeset the letter ć as \'c in LaTeX. ETH Zürich, Forschungsinstitut für Mathematik Rämistrasse 101, HG GO 68.2 8092 Zürich, Switzerland danica.kosanovic[at]math[dot]ethz[dot]ch |
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I am a Hermann Weyl Instructor at the Departement of Mathematics at ETH Zürich (Swiss Federal Institute of Technology in Zurich). My mentors are Peter Feller and Thomas Willwacher.
My interests include knot theory, 4-manifolds, knotted surfaces in 4-manifolds, homotopy types of embedding spaces, Goodwillie-Weiss embedding calculus, operads, graph complexes. For more details, see the slides from the public talk of my PhD defense, or have a look at the tabs on the left.
Before coming to ETH in 2021, I was a FSMP postdoc at Paris 13 (Université Sorbonne Paris Nord), working with Geoffroy Horel. 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. Previously, I studied in Belgrade (Serbia) and Cambridge (UK).
My partner Mihajlo Cekić is also a mathematician.
March 2024 | My preprint "Knotted families from graspers" is accepted by the Journal of Topology. |
Spring 2024 | I'm teaching Topology of Manifolds, see the tab "Teaching". |
May 22, 2024 | I will be giving a talk "Diffeomorphisms of 4-manifolds from graspers" @ Oberseminar Geometrie, Uni of Fribourg |
I like thinking about knots, 4-manifolds, surfaces inside, and in general about topology in low dimensions! However, I also believe that formalism and tools of higher topology, i.e. homotopy theory, higher categories, TQFT’s, operads, as well as combinatorics of Feynman diagrams and configuration spaces, can merge together to give even more insight about low-dimensional manifolds.
In my thesis I studied finite type knot invariants and their relation to the Goodwillie-Weiss embedding calculus.
Embedding calculus and grope cobordism of knots arxiv.org/abs/2010.05120 (submitted) |
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A space level light bulb theorem in all dimensions ~ Joint with Peter Teichner ~ arxiv.org/abs/2105.13032 accepted for publication in Commentarii Mathematici Helvetici |
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A new approach to light bulb tricks: Disks in 4-manifolds ~ Joint with Peter Teichner ~ arxiv.org/abs/2209.12015 accepted for publication in Duke Mathematical Journal |
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On homotopy groups of spaces of embeddings of an arc or a circle: the Dax invariant arxiv.org/abs/2111.03041 accepted for publication in Transactions of the American Mathematical Society |
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Knotted families from graspers arxiv.org/abs/2307.14028 accepted for publication in Journal of Topology |
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Homotopy versus isotopy: 2-spheres in 5-manifolds ~ Joint with Rob Schneiderman and Peter Teichner ~ arxiv.org/abs/2312.16905 (submitted) |
A geometric approach to the embedding calculus knot invariants. PhD Thesis. Download in Bonn Library. |
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.