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ETH Zürich, Forschungsinstitut für Mathematik
Rämistrasse 101, HG GO 68.2
8092 Zürich, Switzerland
I am a Hermann Weyl Instructor at Eidgenössische Technische Hochschule Zürich (Swiss Federal Institute of Technology in Zürich).
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).
|-||I'm organizing a "Building Bridges" learning seminar (currently on an indefinite summer break). Here is its webpage.|
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
A space level light bulb theorem for disks
~ Joint with Peter Teichner ~
On homotopy groups of spaces of embeddings of an arc or a circle: the Dax invariant
A geometric approach to the embedding calculus knot invariants. PhD Thesis.
Download in Bonn Library.
|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 @ Spaces of Embeddings: Connections and Applications, Banff International Research Station, Canada|
|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|
|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||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 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|
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.