Talks

Patterns and complex textures are ubiquitous in astronomical data but challenging to quantify. I will present a new powerful statistic called the “scattering transform”. It borrows ideas from convolutional neural nets (CNNs) while retaining the advantages of traditional statistics. As an example, I will show its application to weak lensing cosmology, where it outperforms classic statistics and is on a par with CNNs. I will also show interesting visual interpretations of the scattering statistics and possible extensions of this “mathematical neural network” idea. I argue that the scattering transform provides a powerful new approach in cosmology and beyond.

Related papers:

https://arxiv.org/abs/2112.01288

https://arxiv.org/abs/2103.09247

https://arxiv.org/abs/2006.08561

Zoom Link: https://pitp.zoom.us/j/91612161747?pwd=bnQrVmo4ZjBjaUdQMDBNZGhFS2NPQT09

In this talk, I will discuss a new duality that was recently discovered in joint work with David Ayala and Nick Rozenblyum, which we refer to as reflection.

In essence, reflection amounts to two dual methods for reconstructing objects, based on a stratification of the category that they live in. As a classical example, an abelian group can be reconstructed on the one hand in terms of its p-completions and its rationalization, or on the other (reflected) hand in terms of its p-torsion components and its corationalization; and these both come from a certain "closed-open decomposition" of the category of abelian groups.

Examples and applications of reflection are abundant, because stratifications are abundant. In algebra, reflection recovers the derived equivalences of quivers coming from BGP reflection functors (hence the terminology "reflection"). In topology, reflection is closely related to Verdier duality, a generalization of Poincaré duality that applies to singular spaces. Moreover, an explicit description of reflection leads to a categorification of the classical Möbius inversion formula, a Fourier inversion theorem for functions on posets.

Zoom Link: https://pitp.zoom.us/j/92439401154?pwd=cGZsUGJGcmNXdFZuclREL3gyYnhQdz09

The vast and growing number of publications in all disciplines of science cannot be comprehended by a single human researcher. As a consequence, researchers have to specialize in narrow subdisciplines, which makes it challenging to uncover scientific connections beyond the own field of research.

In my talk, I will present a possible solution: I demonstrate the development of a semantic network for quantum physics (SemNet), using 750,000 scientific papers and knowledge from books and Wikipedia. I use it in conjunction with an artificial neural network for predicting future research directions. Finally, I show first indications how individual scientists can use SemNet for suggesting and inspiring personalized, out-of-the-box ideas.

I believe that computer-inspired scientific ideas will play a significant role in accelerating scientific progress, and am looking forward hearing your thoughts and ideas about this crucial question.

References
[1] Mario Krenn, Anton Zeilinger, Predicting research trends with semantic and neural networks with an application in quantum physics, PNAS 117(4) 1910-1916 (2020).
[2] IEEE BigData 2021 competition: Science4Cast: https://github.com/iarai/science4cast

Zoom Link: https://pitp.zoom.us/j/92240839439?pwd=LytUTHlMWE9ycjlsUXJkdHRta2c1UT09