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 Eidgenössische Technische Hochschule Zürich (Swiss Federal Institute of Technology in Zürich). 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.
March 2022  cancelled research visit @ Insitut MittagLeffler, Higher algebraic structures in algebra, topology and geometry 
  I'm organizing a "Building Bridges" learning seminar (currently on an indefinite summer break). Here is its webpage. 
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 for disks ~ Joint with Peter Teichner ~ arxiv.org/abs/2105.13032 (submitted) 

On homotopy groups of spaces of embeddings of an arc or a circle: the Dax invariant arxiv.org/abs/2111.03041 (submitted) 
A geometric approach to the embedding calculus knot invariants. PhD Thesis. Download in Bonn Library. 
24.02.2022  Smooth embeddings and their families @ Durham Geometry and Topology Seminar 
16.02.2022  Smooth embeddings and their families @ Cambridge Differential Geometry and Topology Seminar 
11.02.2022  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 @ Spaces of Embeddings: Connections and Applications, Banff International Research Station, Canada 
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 
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  On the punctured knots model for embedding spaces @ Configuration Categories Learning Seminar (Online) 
19.12.2019  On link maps @ Mojito’s Seminar (Online) 
13.2.2020  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 
See the tab seminar.
Geoffroy Horel and Bruno Vallette are organizing a learning seminar at Paris 13. See here.
Ben Ruppik and I were organising a series of talks on Milnor invariants. Ben made a cool website which contains our notes and references.
I was giving tutorials for this class. Here is the page with the class notes and homework assignments.
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.