Daniil Dmitriev (ETH Zurich)
Robust Mixture Learning when Outliers Overwhelm Small Groups abstract
Abstract:
We study the problem of estimating the means of well-separated mixtures when an adversary may add arbitrary outliers. While strong guarantees are available when the outlier fraction is significantly smaller than the minimum mixing weight, much less is known when outliers may crowd out low-weight clusters - a setting we refer to as list-decodable mixture learning (LD-ML). In this case, adversarial outliers can simulate additional spurious mixture components. Hence, if all means of the mixture must be recovered up to a small error in the output list, the list size needs to be larger than the number of (true) components. We propose an algorithm that obtains order-optimal error guarantees for each mixture mean with a minimal list-size overhead, significantly improving upon list-decodable mean estimation, the only existing method that is applicable for LD-ML. Although improvements are observed even when the mixture is non-separated, our algorithm achieves particularly strong guarantees when the mixture is separated: it can leverage the mixture structure to partially cluster the samples before carefully iterating a base learner for list-decodable mean estimation at different scales.
14:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.1
Vladimir Dotsenko (Strasbourg)
Stable Lie algebra homology and wheeled operads abstract
Abstract:
I shall recall the definition of a wheeled operad and explain how homotopy invariants of wheeled operads appear naturally when computing stable homology of Lie algebras of derivations of free algebras. This a common generalization of the Loday-Quillen-Tsygan theorem on additive K-theory of an associative algebra, and the Fuchs\' stability theorem for homology of the Lie algebra of vector fields. I shall also discuss the (arguably more important) case of the Lie algebras of divergence zero derivations.
15:00 • Université de Genève, Conseil Général 7-9, Room 1-07
Anshul Adve (Princeton University)
Algebraic equations characterizing hyperbolic surface spectra abstract
Abstract:
Given a compact hyperbolic surface together with a suitable choice of orthonormal basis of Laplace eigenforms, one can consider two natural spectral invariants: 1) the Laplace spectrum Lambda, and 2) the 3-tensor C_{ijk} representing pointwise multiplication (as a densely defined map L^2 x L^2 -> L^2) in the given basis. Which pairs (Lambda,C) arise this way? Both Lambda and C are highly transcendental objects. Nevertheless, we will give a concrete and almost completely algebraic answer to this question, by writing down necessary and sufficient conditions in the form of equations satisfied by the Laplace eigenvalues and the C_{ijk}. This answer was conjectured by physicists, who introduced these equations (in an equivalent form) as a rigorous model for the crossing equations in conformal field theory.
15:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.2
Anton Khoroshkin (Haifa)
On Generating Series of Cohomology of Generalized Configuration Spaces abstract
Abstract:
A generalized configuration space on X consists of a collection of points on X with a prescribed rule determining which points may not coincide. I will introduce a new algebraic structure on the union of these spaces for X=R^n, which generalizes the concept of the little discs operad. I will demonstrate how one extracts information about the Hilbert series of cohomology rings out of this algebraic structure. Surprisingly, the same method can be applied to obtain generating series for various combinatorial data associated with graphs, such as the number of Hamiltonian paths, Hamiltonian cycles, acyclic orientations, and chromatic polynomials.If time permits, I will introduce certain compactifications of these configuration spaces for X=C that generalize the Deligne-Mumford compactification of the moduli spaces of rational curves with marked points, and I will present the formulas for the generating series of their cohomology.The talk is based on the joint work with my student D.Lyskov.
16:30 • Université de Genève, Conseil Général 7-9, Room 1-07
Robert Nowak (Universität Ulm)
What is... the arithmetic of curves and semistable reduction? abstract
Abstract:
Let Y be an algebraic curve over a number field K of genus at least 1. The reduction behavior of Y to characteristic p>0 can be used to compute arithmetic invariants of the curve. In this talk we will introduce notions of good, bad, and semistable reduction and discuss their connection to the L-series and the conductor of the curve. In the special case of hyperelliptic curves and p = 2, we will study the minimal extension over which the curve attains semistable reduction and the automorphism groups of the special fiber.
16:30 • UZH Zentrum, Building KO2, Room F 150
Abstract:
The quantum laws governing atoms and other tiny objects seem to defy common sense, and information encoded in quantum systems has weird properties that baffle our feeble human minds. John Preskill will explain why he loves quantum entanglement, the elusive feature making quantum information fundamentally different from information in the macroscopic world. By exploiting quantum entanglement, quantum computers should be able to solve otherwise intractable problems, with far-reaching applications to cryptology, materials, and fundamental physical science. Preskill is less weird than a quantum computer, and easier to understand.
17:00 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room F 30
Dr. Christian Urech (ETHZ)
Cubical geometry of Cremona groups abstract
Abstract:
Cremona groups are the groups of birational transformations of projective spaces. They have been the delight of algebraic geometers and group theorists in both, classical and modern times. Recently, geometric group theory and dynamics have opened up new viewpoints on the subject. In this talk, I will give a short introduction to Cremona groups and explain some natural constructions of isometric actions on negatively curved cube complexes. From those, we deduce old and new results. No prior knowledge of algebraic geometry nor geometric group theory will be assumed. This is joint work with Anne Lonjou.
17:15 • Université de Fribourg, room Phys 2.52