[Solomonov Seminar] 296. Solomonov seminar

[Mateja Škraba]

V sredo, 14. oktobra 2025 bo ob 14ih v Oranžni sobi (drugo nadstropje stavbe na Jamovi) 296. Solomonov seminar. Posnetki preteklih seminarjev so na http://videolectures.net/solomon/

Povezava za oddaljeno priključitev: https://meet.google.com/ymn-dsuw-wam
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Title: How to study probability in high and super-high dimensions in the future?
Speakers: Andrej Srakar

Abstract:

Problem of studying probability objects of any type in high dimensions is one of central open and unresolved topics in present-day probability theory (which strongly relates also to research in artificial intelligence). In my presentation I address the open and until my contribution unaddressed problem of generalization of Schramm-Loewner evolution to dimensions greater than 2.

Random geometry has transformed modern probability and mathematical physics. A paradigmatic example is Schramm–Loewner Evolution (SLE), which provides a stochastic description of random planar curves and has become a central object connecting probability, conformal geometry, statistical mechanics and field theory. There was and is, however, no comparably established theory of SLE in dimension d>2. This is not merely a technical obstacle. The geometric object that should replace a random planar curve is itself unclear. My presentation proposes that stochastic solutions of Beltrami-type equations in several complex variables should be interpreted as stochastic Kodaira–Spencer processes: random evolutions of complex structures generated by stochastic deformation tensors and represented geometrically on appropriate complex moduli spaces. They generalise the conceptual role of SLE from random curves to random complex structures and they, probably, combined with solutions to stochastic Loewner equation in high dimension provide the best while not unique generalization of SLE outside of plane.

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