Mini-kurs „Tenzori u primenjenoj algebarskoj geometriji“

U ponedeljak i utorak, 3. i 4. decembra, na Matematičkom institutu SANU gostovaće Bernd Šturmfels, laureat Džordž Dejvid Birkhof nagrade 2018. za primenjenu matematiku, direktor Maks Plank Instituta za matematiku u nauci u Lajpcigu i profesor matematike i računarstva na Univerzitetu Kalifornija u Berkliju, dobitnik mnogih značajnih priznanja i jedan od vodećih naučnika u oblasti matematike i računarstva današnjice.

Prilikom posete, profesor Šturmfels će održati mini-kurs „Tenzori u primenjenoj algebarskoj geometriji“, kao serija od tri predavanja od kojih će se dva održati u ponedeljak 3.12 u sali 301f na Matematičkom institutu SANU, a treće u utorak 4.12 u Sali 2.

Program mini-kursa – Tensors in Applied Algebraic Geometry

Ponedeljak, 3. decembar, 12.00-13.00

Bernd Šturmfels – Eigenvectors of Tensors

Abstract: Eigenvectors of square matrices are central to linear algebra. Eigenvectors of tensors are a natural generalisation. The spectral theory of tensors was pioneered by Lim and Qi around 2005. It has numerous applications, and ties in closely with optimization and dynamical systems. We present an introduction that emphasizes algebraic and geometric aspects.

Ponedeljak, 3. decembar, 17.00-18.30

Bernd Šturmfels – Gaussian Mixtures and Their Tensors

Abstract: Mixtures of Gaussians are ubiquitous in data science. We discuss the geometry of these statistical models, with focus on the tensors that represent their higher moments. The familiar theory of rank and borderrank for symmetric tensors is recovered when all covariance matrices are zero. We seek to decide which Gaussian mixtures are identifiable from their moments.

Utorak, 4. decembar, 10.30-11.30

Bernd Šturmfels – Varieties of Signature Tensors

Abstract: We discuss recent developments in computational algebraic geometry that were motivated by the study of rough paths in stochastic analysis. Every path in a real vector space is encoded in a signature tensor whose entries are iterated integrals. As the path varies over a nice family we obtain an algebraic variety with interesting properties.