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Autumn Semester 2022

Date / Time Speaker Title Location
5 October 2022
15:45-16:45 		Stefan Mihajlović
Central European University, Budapest
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Geometry Seminar

Title Removing self-intersections of surfaces in 4-manifolds via multi-tubing
Speaker, Affiliation Stefan Mihajlović, Central European University, Budapest
Date, Time 5 October 2022, 15:45-16:45
Location HG G 43
Abstract Cup product in second (co)homology of a 4-manifold tells us a lot about its topology, even determining the manifold up to homeomorphism under certain assumptions. A geometrical question that asks what is the minimal genus of an embedded surface that represents a chosen class in the second homology, goes one step further, and gives essential information on the smooth structure. In joint work with Marco Marengon we present a simple but flexible method to remove multiple singularities of immersed surfaces in 4-manifolds. One concrete consequence is that 'many knots bound disks in 4-manifolds' - if we take a small ball in a 4-manifold, we can show that many knots on its boundary will bound disks in the interior of the manifold. Another consequence I will try to address is a work in progress regarding the above mentioned minimal genus problem in manifolds which are connected sums of complex projective planes.
Removing self-intersections of surfaces in 4-manifolds via multi-tubingread_more
HG G 43
19 October 2022
15:45-16:45 		Roman Sauer
Karlsruher Institut für Technologie
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Geometry Seminar

Title Action on Cantor spaces and macroscopic scalar curvature
Speaker, Affiliation Roman Sauer, Karlsruher Institut für Technologie
Date, Time 19 October 2022, 15:45-16:45
Location HG G 43
Abstract We prove the macroscopic cousins of three conjectures:
1) a conjectural bound of the simplicial volume of a Riemannian manifold in the presence of a lower scalar curvature bound,
2) the conjecture that rationally essential manifolds do not admit metrics of positive scalar curvature,
3) a conjectural bound of ℓ²-Betti numbers of a spherical Riemannian manifolds in the presence of a lower scalar curvature bound.
The macroscopic cousin is the statement one obtains by replacing a lower scalar curvature bound by an upper bound on the volumes of 1-balls in the universal cover. Group actions on Cantor spaces surprisingly play an important role in the proof.
The talk is based on joint work with Sabine Braun.
Action on Cantor spaces and macroscopic scalar curvatureread_more
HG G 43
26 October 2022
15:45-16:45 		Viacheslav Borovitskiy
ETH Zürich
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Geometry Seminar

Title Geometry-aware Gaussian Processes for Machine Learning
Speaker, Affiliation Viacheslav Borovitskiy, ETH Zürich
Date, Time 26 October 2022, 15:45-16:45
Location HG G 43
Abstract Gaussian random fields (Gaussian processes) are beautiful mathematical objects with many applications. In machine learning, they are widely accepted as models of choice in scenarios where decision making under uncertainty is required e.g. in black-box optimization and reinforcement learning. In this talk I will briefly overview Gaussian processes in this setting and my own work on Gaussian processes for modeling functions on non-Euclidean domains, including Riemannian manifolds and graphs.
Geometry-aware Gaussian Processes for Machine Learningread_more
HG G 43
2 November 2022
15:45-16:45 		Mireille Soergel
ETH Zurich, Switzerland
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Geometry Seminar

Title A generalized Davis-Moussong complex for Dyer groups
Speaker, Affiliation Mireille Soergel, ETH Zurich, Switzerland
Date, Time 2 November 2022, 15:45-16:45
Location HG G 43
Abstract One common feature of Coxeter groups and right-angled Artin groups is their solution to the word problem. In his study of reflection subgroups of Coxeter groups, Dyer introduces a family of groups, Dyer groups, which also have the same solution to the word problem as Coxeter groups. I will introduce this family of groups and give some of their properties. Then I explain how to construct actions of Dyer groups on CAT(0) spaces that extend those of Coxeter groups on Davis–Moussong complexes and those of right-angled Artin groups on Salvetti complexes.
A generalized Davis-Moussong complex for Dyer groupsread_more
HG G 43
23 November 2022
15:45-16:45 		Mihajlo Cekić
Universität Zürich
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Geometry Seminar

Title Resonant forms at zero for (dissipative) chaotic flows
Speaker, Affiliation Mihajlo Cekić, Universität Zürich
Date, Time 23 November 2022, 15:45-16:45
Location HG G 43
Abstract We consider a non-volume preserving Anosov flow generated by X on a compact 3-manifold M. The Ruelle Zeta Function (RZF) of this flow is a meromorphic function defined as a certain infinite product over closed orbits. Its behaviour at zero is conjectured to carry topological information of M and X, and is intimately related to certain resonant spaces of flow-invariant differential forms at zero. We introduce the notion of helicity (average self-linking) for X, and compute the dimension of resonant spaces as a function of helicity and the winding cycles of some natural flow-invariant measures. Finally, we illustrate this theory for thermostat flows associated to holomorphic quadratic differentials giving rise to quasi-Fuchsian flows of Ghys.
Resonant forms at zero for (dissipative) chaotic flowsread_more
HG G 43
21 December 2022
15:45-16:45 		Immanuel Van Santen
University of Basel
Details

Geometry Seminar

Title On algebraic and holomorphic embeddings into linear algebraic groups
Speaker, Affiliation Immanuel Van Santen, University of Basel
Date, Time 21 December 2022, 15:45-16:45
Location HG G 43
Abstract A starting point for the general study of embeddings of smooth real manifolds into highly symmetric smooth manifolds were the classical theorems of Whitney and Wu which assert that every smooth real manifold of dimension d≥1 properly embeds into the real Euclidean space of dimension R^(2d) and that two embeddings into R^(max(4,2d+1)) are the same up to diffeomorphisms. In this talk, we first address general embedding theorems for smooth affine algebraic varieties into complex Euclidean space due to Kaliman-Nori-Srinivas and Gromov-Eliashberg. Then we focus on the existence and uniqueness of embeddings of smooth affine varieties into complex linear algebraic groups up to algebraic (holomorphic) automorphisms of the underlying variety. This covers joint work with Peter Feller and Jérémy Blanc.
On algebraic and holomorphic embeddings into linear algebraic groupsread_more
HG G 43

Organisers:

Archive: AS 24 SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 AS 20 SS 20 AS 19 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11 SS 11 AS 10 SS 10 AS 09 SS 09

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