* Seuraavan viikon tapahtumat merkitty tähdellä
Prof. Oscar Kivinen (Aalto University)
Motivic integration, singularities, and knots
* Tuesday 13 May 2025, 15:15, M1 (M232)
Motivic integration is a powerful technique in algebraic geometry developed by Kontsevich, Denef-Loeser, and others. For example, several interesting invariants can be attached to an isolated hypersurface singularity using motivic integration. In the Euler characteristic limit, these invariants are all related in a straightforward way, but the relationships between the motivic versions are more difficult to understand.
In the first half of this talk, I will give an introduction to motivic integration. In the second part, I will discuss the aforementioned singularity invariants in more detail, including connections to knot Floer homology, Hilbert schemes, and the Igusa zeta function. The second part of the talk is based on joint work with Oblomkov and Wyss.
Petteri Kaski
Kronecker scaling of tensors with applications to arithmetic circuits and algorithms
* Thursday 15 May 2025, 14:15, M2 (M233)
We show that sufficiently low tensor rank for the balanced tripartitioning tensor $P_d(x,y,z)=\sum_{A,B,C\in\binom{[3d]}{d}:A\cup B\cup C=[3d]}x_Ay_Bz_C$ for a large enough constant $d$ implies uniform arithmetic circuits for the matrix permanent that are exponentially smaller than circuits obtainable from Ryser's formula. We show that the same low-rank assumption implies exponential time improvements over the state of the art for a wide variety of other related counting and decision problems.
As our main methodological contribution, we show that the tensors $P_n$ have a desirable Kronecker scaling property: They can be decomposed efficiently into a small sum of restrictions of Kronecker powers of $P_d$ for constant $d$. We prove this with a new technique relying on Steinitz's lemma, which we hence call Steinitz balancing.
As a consequence of our methods, we show that the mentioned low rank assumption (and hence the improved algorithms) is implied by Strassen's asymptotic rank conjecture [Progr. Math. 120 (1994)], a bold conjecture that has recently seen intriguing progress.
Joint work with Andreas Björklund, Tomohiro Koana, and Jesper Nederlof; cf. https://arxiv.org/abs/2504.05772.
ADM Seminar
Markus Hakala (Aalto University)
Estimation of stochastic block models with nodal covariates (MSc thesis talk)
Monday 19 May 2025, 15:15, M237
Aalto Statistics Seminar / Lasse Leskelä
Antti Niemi (University of Oulu)
Buckling Stability of Cylindrical Shells: Classical Theory, Nonlinear Analysis, and Design Implications
Wednesday 21 May 2025, 14:00, M2 (M233)
Cylindrical shell structures display complex and sensitive buckling behavior that challenges both theoretical modeling and practical design. This presentation revisits classical asymptotic shell buckling theory and examines its numerical treatment, emphasizing nonlinear structural mechanics and the ability of modern computational tools to capture critical loads and deformation modes. The derivation and interpretation of design-oriented knockdown factors are discussed in relation to numerical results. Particular attention is given to the spatial characteristics of buckling modes and more interaction which are essential to accurately assess structural stability through numerical analysis.
Numerical Analysis seminar
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