The FWZ seminar is an old-style seminar originally taking place in Freiburg, Vienna or Zürich each four months (in average) full of blackboard talk discussions to present new proofs, concepts, ideas, papers, ... but without fixed schedule. So far we met at 30.6.2015 (Zürich), 28.-29.10.2015 (Freiburg), 16.-18.12.2015 (Vienna), 23.2.2016 (Freiburg), 18.-19.5.2016 (Vienna), 30.11.-2.12.2016 (Freiburg), 10.-11.4.2017 (Zürich), 18.-19.9.2017 (Vienna), 15.-16.3.2018 (Zürich), 1.-4.7.2018 (Xth edition in Strobl at Wolfgangsee, see the **scheduled program**), 15.-16.1.2019 (Vienna) to meander by discussions, presentations, ideas around the following focus areas below provided with some hopefully inspiring references (which have triggered or will trigger discussions).

We are happy to announce that our triangle became a rectangle in May 2019: the group from Padova joint, now we listen to the name FPZW. See the schedule of the event. We met again at 10.-11.10.2019 (Zürich).

- Non-linear Filtering: a short collection of ideas connecting arbitrage and filtering.
- Robust Finance and Uncertainty: for instance from a pathwise point of view.
- New types of fundamental theorems of asset pricing towards Bayesian Finance: several new approaches evolved from new ideas how to prove small and large financial market FTAP. See also a talk on FTAP in LFM, or a talk on stochastic portfolio theory and LFM.
- Non-linear DEs and affine processes: Pierre-Henry Labordere's seminal article on branching diffusion approximations for semi-linear PDEs and the important follow-up paper on quasi-linear PDEs. And some new thoughts on connections of non-linear ODEs and self-exciting affine processes, or in a more polished form.
- Optimal Transport: a very recent generalization towards semi-martingale optimal transport.
- Term structure modeling: a very recent article on general defaultable term structure modeling.
- Affine and polynomial processes: pars pro toto recent progress on the polynomial processes.
- American Options: following seminal work by Benjamin Jourdain and Claude Martini on European Options mimicking American Options and our recent slight generalizations.
- Limit order book modeling: recent work on stochastic moving boundary problems or some "mean-field interpretation of LOB".
- Fractional processes, volatility modeling and affine processes: some recent work on fractional BM as infinite dimensional OU process.
- Regularity Structures in mathematical Finance: some recent work linking stochastic methods with methods from regularity structures.
- Stochastic Portfolio Theory: recent progress on the modeling side towards polynomial processes in SPT.
- Machine learning in mathematical Finance: ideas around machine-learning calibration functionals as presented in a seminal work by Andres Hernandez: Model Calibration with neural networks, SSRN.2812140 accompagnied by a talk on Bayesian Finance - a machine learning approach to a simple calibration problem, slides, 2017.
- Why does machine learning work so well: some recent work of Helmut Bölcskei, Philipp Grohs, Gitta Kutyniok, Philipp Petersen: Optimal Approximation with Sparsely Connected Deep Neural Networks, arxiv.1705.01714.
- Machine learning and non-linear PDEs: great recent work of Weinan E, Jiequn Han, Arnulf Jentzen: Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations, arxiv.1706.04702.
- Machine learning and the right parameterization of a problem: recent work of Terry Lyons, Rough paths, Signatures and the modelling of functions on streams, arxiv.1405.4537.
- Machine learning and unbiased estimation of risk: new ideas partly based on arxiv.1603.02615
- Affine semimartingales: recent progress, see e.g. the slides.