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 

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, 4manifolds, knotted surfaces in 4manifolds, homotopy types of embedding spaces, GoodwillieWeiss 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 MaxPlanck 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.
May 2023  I coorganised the workshop "Interactions of Lowdimensional Topology and Quantum Field Theory" 
July 2023  My new preprint "Knotted families of (long) knots from graspers" is on arXiv, see arxiv.org/abs/2307.14028. 
December 2023  The preprint "Homotopy versus isotopy: 2spheres in 5manifolds" of Rob Schneiderman and Peter Teichner and myself is on arXiv, see arxiv.org/abs/2312.16905. 
Spring 2024  I'll give lectures on Topology of Manifolds, see the tab "Teaching". 
I like thinking about knots, 4manifolds, 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 lowdimensional manifolds.
In my thesis I studied finite type knot invariants and their relation to the GoodwillieWeiss embedding calculus.
Embedding calculus and grope cobordism of knots arxiv.org/abs/2010.05120 (submitted) 

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 

A new approach to light bulb tricks: Disks in 4manifolds ~ Joint with Peter Teichner ~ arxiv.org/abs/2209.12015 accepted for publication in Duke Mathematical Journal 

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 

Knotted families of (long) knots from graspers arxiv.org/abs/2307.14028 (submitted) 

Homotopy versus isotopy: 2spheres in 5manifolds ~ 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, Banffhandwritten slides (~14MB) 
7.9.2023  Knotted families from graspers, Conference Swiss Knots 2023, Regensburg 
9.5.2023  2knots 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 & 4dimensional Topology", webpage 
17.11.2022  2knots and knotted families of arcs, University of Zurich, room Y27H26, 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, 2427 October 2022, Université de Nantes, webpage, slides 
14.9.2022  2knots and knotted families of arcs @ DMV (German Mathematical Society) Annual Meeting, Berlin, beamer slides 
16.7.2022  2knots and knotted families of arcs @ AMSEMSSMF Congress of Mathematics, 1822 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 4manifolds @ 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, IMJPRG, Paris 7 
20.2.2020  A geometric approach to the embedding calculus @ Oberwolfach Workshop Lowdimensional 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 4manifolds, 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 4manifolds @ Actualité des mathématiques, Neuchâtel 
6.5.2021  On a theorem of Kontsevich and ConantVogtmann @ Groupes de GrothendieckTeichmüller et applications 
11.3.2021  Chord diagram invariants of tangles @ Groupes de GrothendieckTeichmüller 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 BundeyGabai about knotted 3balls @ 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 ChernSimons 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 WittenReshetikhinTuraev invariants of 3manifolds @ 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.