# Disclaimer

I try to prepare a LaTex beamer presentation
for all talks. If I gave a LaTex beamer talk, then I will upload the corresponding
slides here. Talks without a LaTex beamer
presentation are not mentioned. Note that these are delivered as they are,
with no attempt at improving them.

Talk list: available here.

# TeX files

The TeX files for the talks are freely available at: https://github.com/dtubbenhauer/My-TeX-files.git

# A list of my talks

- Topic: Equivariant neural networks and representation theory - Or: Beyond linearity; Keywords: machine learning, deep learning, group actions, representation theory. Slides
- Topic: The mathematics of AI - Or: Learning = forward, loss, backward; Keywords: machine learning, deep learning. Slides
- Topic: Three colors suffice - Or: SO3 webs in action; Keywords: Four color theorem, diagrammatic algebra. Slides
- Topic: Magma in a nutshell - Or: Magma Mondays; Keywords: learning Magma, computer algebra system. Slides; Lecture notes: Click
- Topic: Piecewise linear representation theory - Or: Non-linear, but still rep theory; Keywords: representation theory, machine learning. Slides
- Topic: A primer on computer algebra - Or: Faster than expected; Keywords: Computer algebra, fast multiplication, fast Fourier transform. Slides
- Series with topic: Cell theory - Or: Representation theory of monoids, algebras and monoidal categories; Keywords: Monoids, Green's relations, sandwich cellular, cells, H reduction, classification theorems, categorification. Slides1, Slides2, Slides3
- Topic: Knots and algebra - Or: Quantum algebra = geometry + algebra; Keywords: Knots, knot invariants, Jones polynomial, quantum algebra. Slides
- Topic: Categorical representation theory and applications - Or: Functors, not matrices; Keywords: representation theory, categorification, categorical representation theory, applications. Slides
- Topic: Representation theory of monoids and monoidal categories - Or: Cells and actions; Keywords: Monoids, Green's relations, cells, H reduction, classification theorems, categorification. Slides
- Topic: Subfactors in a nutshell - Or: ADE and all that; Keywords: History, Temperley-Lieb algebra, Jones' subfactors, planar algebras, ADE classification. Slides
- Topic: Temperley-Lieb times four - Or: Invariant theory, magnetism, subfactors and skein; Keywords: History, Temperley-Lieb algebra, the Rumer-Teller-Weyl construction, Jones' subfactors, Kauffman calculus. Slides
- Topic: A brief, incomplete, and mostly wrong history of quantum groups - Or: From ice to R-matrices; Keywords: History, quantum groups, Yang-Baxter equation. Slides
- Topic: Why (categorical) representation theory? - Or: Representing symmetries; Keywords: Representation theory, categorical representation theory, 2-representation theory, categorification. Slides
- Topic: What is...finitary 2-representation theory? - Or: A (fairy) tale of matrices and functors; Keywords: Representation theory, integral representation theory, categorical representation theory, 2-representation theory, categorification. Slides
- Topic: What is...(2-)representation theory? - Or: A (fairy) tale of matrices and functors; Keywords: Representation theory, integral representation theory, categorical representation theory, 2-representation theory, categorification. Slides
- Topic: 2-representation theory in a nutshell - Or: \(\mathbb{N}_0\)-matrices, my love; Keywords: Representation theory, integral representation theory, categorical representation theory, 2-representation theory, categorification. Slides
- Topic: 2-representation theory in a nutshell - Or: A tale of matrices and functors; Keywords: Representation theory, integral representation theory, categorical representation theory, 2-representation theory, categorification. Slides
- Topic: Categorification: An introduction to \(\mathfrak{sl}_n\)-link homologies - Or: Webs and homology; Keywords: Webs, Khovanov homology, link homology. Slides
- Topic: Why category theory? - Or: Some history of category theory; Keywords: History, category theory, Eilenberg-Mac Lane, categorifcation. Slides

- Topic: Equivariant neural networks and representation theory - Or: Beyond linearity; Talk (in person) at the University of York (July 2024). Slides
- Topic: Analytic theory of monoidal categories - Or:
Strategies for avoiding counting; Talk (in person) at the University of York (July 2024).

Talk 5, monoidal categories: Slides

Talk 4, dual setting: Slides

Talk 3, SL2: Slides

Talk 2, finite groups: Slides

Talk 1, general setting: Slides - Topic: Fractal behavior in monoidal categories - Or: SL2, Cantor and Sierpinski; Talk (online) at Beijing Institute of Technology (June 2024). Slides
- Topic: Counting in tensor products - Or: Exponential growth everywhere; Talk (online) at Feza Gursey Research Center for Physics and Mathematics (May 2024). Slides
- Topic: The mathematics of AI - Or: Learning = forward, loss, backward; Talk (in person) at the University of Sydney (April 2024). Slides
- Topic: Three colors suffice - Or: SO3 webs in action; Talk (in person) at the University of Southern California (January 2024). Slides
- Topic: Growth and tensor products - Or: OMG exponential growth; Talk (in person) at Institute for Pure and Applied Mathematics (January 2024). Slides

- Topic: Magma in a nutshell - Or: Lecture 4 - Representation theory of finite dimensional algebras; Talk (in person) at the University of Sydney (November 2023). Slides
- Topic: Magma in a nutshell - Or: Lecture 0 - Types, conditionals and loops; Talk (in person) at the University of Sydney (October 2023). Slides
- Topic: Asymptotics and tensor products - Or: I love matrices; Talk (in person) at the University of Sydney (August 2023). Slides
- Topic: Matrices and moduli - Or: Almost all = boring?; Part 2; Talk (in person) at the University of Sydney (August 2023). Slides
- Topic: Matrices and quivers - Or: Complexity jumps; Part 1; Talk (in person) at the University of Sydney (August 2023). Slides
- Topic: Piecewise linear representation theory - Or: Non-linear, but still rep theory; Talk (in person) at the A.K.S.S. Foundation Schools of Spetses (July 2023). Slides
- Topic: Growth rates in tensor powers - Or: Jupiter and friends; Talk (in person) (July 2023). Slides
- Topic: Categorification: Objects and their shadows - Or: Homology and actions; Talk (online) at the University of New South Wales (June 2023). Slides
- Topic: Semisimplifications of tilting modules - Or: \(\mathcal{R}\mathrm{ep}(G)\) everywhere!?; Talk (in person) (June 2023). Slides
- Topic: Representations of braids and Howe duality - Or: Large = good; Talk (in person) at the Australian National University(May 2023). Slides
- Topic: A primer on computer algebra - Or: Faster than expected; Talk (in person) at the University of Sydney (April 2023). Slides
- Topic: Examples of analytic methods in tensor categories - Or: Assume n is large; Talk (in person) (April 2023). Slides

- Topic: Crystals and cellularity of wKLRW algebras - Or: String games; Talk (in person) at the National University of Singapore (December 2022). Slides
- Topic: From crystals to cellularity of wKLRW algebras - Or: From path to strings; Talk (in person) at the 66th Annual Meeting of the Australian Mathematical Society (December 2022). Slides
- Topic: Minimal representations of monoid - Or: The smallest nontrivial; Talk (in person) at the University of Sydney (December 2022). Slides
- Topic: Representations of monoidal categories - Or: Reps of categories of reps; Talk (online) at the Technische Universität Dresden (October 2022). Slides
- Topic: wKLRW algebras and crystals - Or: From path to strings; Talk (in person) at the Mathematisches Forschungsinstitut Oberwolfach (MFO) (September 2022). Slides
- Series with topic: Cell theory - Or: Representation theory of monoids, algebras and monoidal categories; Talk (in person) at the University of Oregon (August 2022). Slides1, Slides2, Slides3. Exercises: Part1, Part2, Part3
- Topic: Categorical representation theory and application - Or: Functors, not matrices; Talk (online) at the Technische Universität München (July 2022). Slides
- Topic: Representation theory of monoids and monoidal categories - Or: Cells and actions; Talk (in person) at the University of New South Wales (June 2022). Slides
- Topic: Subfactors in a nutshell - Or: ADE and all that; Talk (in person) at the University of Sydney (May 2022). Slides
- Topic: On weighted KLRW algebras - Or: Diagrammatic interpolation; Talk (online) at the Beijing Institute of Technology (April 2022). Slides
- Topic: Temperley-Lieb times four - Or: Invariant theory, magnetism, subfactors and skein; Talk (in person) at the University of Sydney (March 2022). Slides
- Topic: Some history of quantum groups - Or: From ice to R-matrices; Talk (in person) at the University of Sydney (March 2022). Slides
- Topic: Monoidal categories, representation gap and cryptography - Or: Why I like dimensions; Talk (in person) at the University of Sydney (March 2022). Slides
- Topic: On weighted KLRW algebras - Or: Mind the distance; Talk (online) at the Okinawa Institute of Science and Technology Graduate University (February 2022). Slides

- Topic: Diagrammatics and cryptography - Or: Not too small, please!; Talk (online) at Newcastle University (December 2021). Slides
- Topic: Monoidal categories and cryptography - Or: Monoids in action; Talk (online) at AustMS2021, the 2021 meeting of the Australian Mathematical Society (December 2021). Slides
- Topic: Aspects of (categorical) representation theory - Or: Topology, modular representations and categories; Talk (online) at Aarhus University (August 2021). Slides
- Topic: Why (categorical) representation theory? - Or: Representing symmetries; Talk (online) at the Okinawa Institute of Science and Technology Graduate University (August 2021). Slides
- Topic: Fusion rules for \(\mathrm{SL}_{2}\) - Or: A toy example of modular representation theory; Talk (online) at the RepNet Virtual Seminar (July 2021). Slides
- Topic: 2-representation of Soergel bimodules - Or: Take degree zero; Talk (online) at the Joint meeting of the British Mathematical Colloquium (BMC) and the British Applied Mathematics Colloquium (BAMC) (April 2021). Slides
- Topic: \(\mathrm{SL}_{2}\) and fractals - Or: Modular representation theory in a toy example, Talk (online) at the University of Birmingham and University of Warwick (March 2021). Slides (videos in the slides: Click and click)
- Topic: Why (modular) representation theory? - Or: Fractals and \(\mathrm{SL}_{2}\), Talk (online) at the University of Oklahoma (February 2021). Slides (videos in the slides: Click and click)
- Topic: Fractals and modular representations of \(\mathrm{SL}_{2}\) - Or: All I know about \(\mathrm{SL}_{2}\), Talk (online) at Newcastle University (February 2021). Slides (videos in the slides: Click and click)
- Topic: The double centralizer theorem categorified is...? - Or: Two different and yet similar answers, Talk (online) at the Universität Bonn (January 2021). Slides

- Topic: Green's theory of cells in categorification - Or: Mind your cells!, Talk (online) at Columbia University (December 2020). Slides
- Topic: On categories of tilting modules - Or: Mind your poles!, Talk (online) at the University of Georgia (October 2020). Slides
- Topic: What is...2-representation theory? - Or: Why do I care?, Talk (online) at the Hausdorff Institute of Mathematics (September 2020). Slides
- Topic: On categories of tilting modules - Or: Mind your poles!, Talk (online) at the University of Oregon (August 2020). Slides
- Topic: Why 2-representation theory? - Or: Representation theory of the 21th century!?, Talk (online) at Trinity College Dublin (April 2020). Slides, Slides2
- Topic: 2-representation of Soergel bimodules - Or: Mind your twists; Talk at the Joint meeting of the British Mathematical Colloquium (BMC) and the British Applied Mathematics Colloquium (BAMC) (April 2020, but postponed; here what I planned to talk about). Slides
- Topic: Why 2-representation theory? - Or: Representation theory of the 21th century!?, Talk at the Vrije Universiteit Brussel (March 2020). Slides, Slides2, Slides3
- Topic: All I know about Artin-Tits groups - Or: Why type A is so much easier...; Talk at Université Paris Diderot, (March 2020). Slides
- Topic: What is...2-representation theory? - Or: Of matrices and functors, Talk at the Universität Graz (January 2020). Slides, Slides2

- Topic: 2-representations of Soergel bimodules I - Or: \(\mathcal{H}\)-cells and asymptotes; Talk at Casa Matemática Oaxaca (CMO), (December 2019). Slides
- Topic: 2-representations of Soergel bimodules - Or: Mind your groups; Talk at Columbia University, (September 2019). Slides
- Topic: 2-representations of Soergel bimodules - dihedral case - Or: Who colored my Dynkin diagrams?; Talk at Columbia University, (September 2019). Slides
- Topic: Dihedral groups, \(\mathrm{SL}(2)_{q}\) and beyond - Or: Who colored my Dynkin diagrams?; Talk at the University of East Anglia, (July 2019). Slides
- Topic: 2-representation theory of Soergel bimodules - Or: Mind your groups; Talk at Karlsruhe Institute for Technology, (June 2019). Slides
- Topic: All I know about Artin-Tits groups - Or: Why type A is so much easier...; Talk at Uppsala universitet, (April 2019). Slides
- Topic: A tale of dihedral groups, \(\mathrm{SL}(2)_q\), and beyond - Or: Who colored my Dynkin diagrams?; Talk at the Vrije Universiteit Brussel (VUB) and the Université libre de Bruxelles (ULB) and the Université catholique de Louvain (UCL), (March 2019). Slides
- Topic: Handlebodies, Artin-Tits and HOMFLYPT - Or: All I know about Artin-Tits groups; and a filler for the remaining 59 minutes; Talk at the University of Sydney, (March 2019). Slides
- Topic: Handlebodies, Artin-Tits and HOMFLYPT - Or: All I know about Artin-Tits groups; and a filler for the remaining 59 minutes; Talk at the University of Melbourne, (March 2019). Slides
- Topic: What is...finitary 2-representation theory? - Or: A (fairy) tale of matrices and functor; Talk at the Australian National University (ANU), (February 2019). Slides
- Topic: A tale of dihedral groups, \(\mathrm{SL}(2)_q\), and beyond - Or: Who colored my Dynkin diagrams?; Talk at the Australian National University (ANU), (February 2019). Slides, Notes
- Topic: HOMFLYPT homology for links in handlebodies - Or: All I know about Artin-Tits groups; and a filler for the remaining 49 minutes, Talk at the Australian National University (ANU), (February 2019). Slides
- Topic: HOMFLYPT homology for links in handlebodies - Or: All I know about Artin-Tits groups; and a filler for the remaining 59 minutes, Talk at the Vrije Universiteit Brussel (VUB) and the Université libre de Bruxelles (ULB) and the Université catholique de Louvain (UCL), (January 2019). Slides
- Topic: A primer on finitary 2-representation theory - Or: \(\mathbb{N}_{0}\)-matrices, my love, Talk at the Erwin Schrödinger International Institute for Mathematics and Physics (January 2019). Slides

- Topic: Generalizing zigzag algebras - Or: It's all about polynomials, Talk at the University of Southern California (November 2018). Slides
- Topic: What is...(2-)representation theory? - Or: A (fairy) tale of matrices and functors, Colloquium talk at the ETH Zürich and the Universität Zürich (October 2018). Slides
- Topic: 2-representation theory in a nutshell - Or: \(\mathbb{N}_{0}\)-matrices, my love, Talk at the ETH Zürich (October 2018). Slides
- Topic: A tale of dihedral groups, \(\mathrm{SL}(2)\), and beyond - Or: \(\mathbb{N}_{0}\)-matrices, my love, Talk at the Universität Freiburg (July 2018). Slides
- Topic: Di- and trihedral (2-)representation theory I - Or: Who colored my Dynkin diagrams?, Talk at the Institute Mittag-Leffler (July 2018). Slides; Part II by Marco Mackaay: Slides
- Topic: 2-representation theory in a nutshell - Or: A tale of matrices and functors, Talk at the Universität Hamburg (June 2018). Slides
- Topic: Link invariants and orbifolds - Or: What makes types \(\mathrm{ABCD}\) special?, Talk in Aarhus at the QGM (April 2018). Slides
- Topic: Link invariants and \(\mathbb{Z}/2\mathbb{Z}\)-orbifolds - Or: What makes types \(\mathrm{ABCD}\) special?, Talk at a conference in Riederalp (January 2018). Slides

- Topic: Categorical representations of dihedral groups - Or: \(\mathbb{Z}_{\geq 0}\)-valued matrices, my love, Talk at the Universidade do Algarve (September 2017). Slides
- Topic: Webs and \(\mathrm{q}\)-Howe dualities in types \(\mathbf{BCD}\) - Or: “Howe” not to define link invariants, Talk at University of Cambridge (June 2017). Slides
- Topic: 2-representation theory of Coxeter groups: a biased survey - Or: The next generation of representation theory of Coxeter groups!?, Talk at Universität Zürich (April 2017). Slides
- Topic: Webs and \(\mathrm{q}\)-Howe dualities in types \(\mathbf{BCD}\) - Or: A story about “howe” I failed, Talk at Uppsala universitet (April 2017). Slides
- Topic: 2-representation theory of Coxeter groups: some first steps - Or: The next generation of representation theory of Coxeter groups!?, Talk at Columbia University (February 2017). Slides

- Topic: Some first steps towards 2-representation theory of Coxeter groups - Or: The next generation of representation theory of Coxeter groups!?, Talk at the Université catholique de Louvain (October 2016). Slides
- Topic: Some first steps towards 2-representation theory of Coxeter groups - Or: The next generation of representation theory of Coxeter groups!?, Talk at the Université de Montpellier (October 2016). Slides

- Topic: (Singular) TQFTs, link homologies and Lie theory 2 - Or: Fun with singular surfaces, Talk at the School of Mathematics of the University of Edinburgh (November 2015). Slides
- Topic: (Singular) TQFTs, link homologies and Lie theory 1 - Or: A story of foams and \(\mathcal{O}\), Talk at the School of Mathematics of the University of Edinburgh (November 2015). Slides
- Topic: Web calculi in representation theory - Or: The diagrammatic presentation machine, Talk at Mathematisch Instituut of the Universiteit Leiden (October 2015). Slides
- Topic: Cellular structures using \(\textbf{U}_q\)-tilting modules - Or: Centralizer algebras are fun!, Talk at the 2015 annual meeting of the Deutschen Mathematiker-Vereinigung (DMV), Hamburg (September 2015). Slides
- Topic: Web calculi in representation theory - Or: The diagrammatic presentation machine, Talk at Max-Planck-Institut for mathematics (MPIM) of the Universität Bonn (August 2015). Slides
- Topic: Cellular structures using \(\textbf{U}_q\)-tilting modules - Or: Centralizer algebras are fun!, Talk at the Mathematisches Institut of the Universität Freiburg (July 2015). Slides
- Topic: From dualities to diagrams - Or: The diagrammatic presentation machine, Talk at the Institut de Mathématiques de Jussieu (IMJ) in Paris (June 2015). Slides
- Topic: \(\textbf{U}_q(\mathfrak{gl}_N)\)-diagram categories via super \(q\)-Howe duality - Or: The diagrammatic presentation machine, Talk at the Mathematics Department of the Faculty of Sciences of the University of Porto (June 2015). Slides
- Topic: From dualities to diagrams - Or: The diagrammatic presentation machine, Talk at the Erwin Schrödinger Institute (ESI) in Vienna (May 2015). Slides
- Topic: Cellular structures using \(\textbf{U}_q\)-tilting modules - Or: Centralizer algebras are fun!, Talk at the Mathematisches Institut of the Universität Bonn (April 2015). Slides
- Topic: \(\textbf{U}_q(\mathfrak{sl}_n)\)-diagram categories via \(q\)-Howe duality - Or: From dualities to diagrams, Talk at the Hausdorff Research Institute for Mathematics (HIM) in Bonn (March 2015). Slides
- Topic: \(\textbf{U}_q(\mathfrak{sl}_n)\)-diagram categories via \(q\)-Howe duality - Or: “Howe” to make diagrammatic categories work!, Talk at the University of Sydney (February 2015). Slides
- Topic: \(\textbf{U}_q(\mathfrak{sl}_n)\)-diagram categories via \(q\)-Howe duality - Or: “Howe” to make diagrammatic categories work!, Talk at the Université catholique de Louvain (February 2015). Slides

- Topic: Diagram categories for \(\textbf{U}_q\)-tilting modules at roots of unity - Or: Fun with diagrams!, Talk at the QGM Nielsen Retreat 2014, Sandbjerg Estate (October 2014). Slides
- Topic: Categorification in topology - Or: Fun with highest weight modules!, Minitalk at the MFO, Oberwolfach (September 2014). Slides
- Topic: \(\dot{\mathbf{U}}_q(\mathfrak{sl}_m)\)-highest weight theory governs \(\mathfrak{sl}_n\)-link homology, Talk at the Université catholique de Louvain (May 2014). Slides
- Topic: \(\mathfrak{sl}_n\)-link homologies using \(\dot{\mathbf{U}}_q(\mathfrak{sl}_m)\)-highest weight theory - the \(m\) is not a typo!, Talk in Aarhus at the QGM (April 2014). Slides
- Topic: Categorification: An introduction to \(\mathfrak{sl}_n\)-link homologies, Talk at the Kerala School of Mathematics (KSOM), Kerala (March 2014). Slides
- Topic: \(\mathfrak{sl}_n\)-link homologies using \(\dot{\mathbf{U}}_q(\mathfrak{sl}_m)\)-highest weight theory, Summary of my research in the first quarter 2014 at the Kerala School of Mathematics (KSOM), Kerala (March 2014). Slides
- Topic: The diagrammatic beauty of \(\mathbf{Rep}(\mathbf{U}_q(\mathfrak{sl}_n))\) - Part II, Talk at the TATA Institute (TIFR), Mumbai (March 2014). Slides
- Topic: The diagrammatic beauty of \(\mathbf{Rep}(\mathbf{U}_q(\mathfrak{sl}_n))\) - Part I, Talk at the TATA Institute (TIFR), Mumbai (March 2014). Slides

- Topic: \(\mathfrak{sl}_3\)-web bases, categorification and link invariants, Talk in Aarhus (November 2013). Slides
- Topic: \(\mathfrak{sl}_3\)-web bases, intermediate crystal bases and categorification, Talk in Bonn (October 2013). Slides
- Topic: Web bases and categorification, Talk in Aarhus at the QGM (October 2013). Slides
- Topic: Categorification and applications in topology and representation theory, Talk in Göttingen (July 2013). Slides
- Topic: Categorification and (virtual) knots, Talk in San Francisco (February 2013). Slides
- Topic: The sl
_{3}web algebra, Talk in Goslar (October 2012). Slides