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Spring Semester 2024

Date / Time Speaker Title Location
29 February 2024
16:15-17:15 		Marco Flaim
University of Bonn
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Geometry Graduate Colloquium

Title Optimal transport and Ricci flow
Speaker, Affiliation Marco Flaim, University of Bonn
Date, Time 29 February 2024, 16:15-17:15
Location HG G 19.1
Abstract By Bishop-Gromov theorem, a lower bound on the Ricci curvature allows to control the volume growth of a Riemannian manifold. In the first part of this talk we review some related properties of manifolds with nonnegative Ricci curvature, with particular interest in the behaviour of the heat flow. A central role is played by the Bakry-Émery inequality and by the contraction of the Wasserstein distance between two probability measures evolving under the heat flow. We then introduce the Ricci flow and see that some of these properties still hold in this setting. As an application, one can use these properties to reprove the monotonicity of Perelman’s W-entropy.
Optimal transport and Ricci flowread_more
HG G 19.1
7 March 2024
16:15-17:15 		Anna Roig Sanchis
Sorbonne Université
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Geometry Graduate Colloquium

Title Random hyperbolic 3-manifolds
Speaker, Affiliation Anna Roig Sanchis, Sorbonne Université
Date, Time 7 March 2024, 16:15-17:15
Location HG G 19.2
Abstract Among all geometric 3-manifolds, hyperbolic ones form the wildest class, and so there is still plenty of open questions about its geometric properties. Since due the their diversity, it is very complicated to prove results that are true for all of them, one natural approach is to try to find results that are valid for "most of them". This can take a mathematical meaning through the study of random manifolds. That is, we consider a set of hyperbolic manifolds, put a probability measure on it, and ask what is the probability that a random manifold has a certain property. There are several models of construction of random manifolds. In this talk, I will explain one of the principal probabilistic models for 3 dimensions, and I will state some geometric properties of a 3-manifold constructed under this model.
Random hyperbolic 3-manifoldsread_more
HG G 19.2
14 March 2024
16:15-17:15 		Filippo Gaia
ETH Zürich
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Geometry Graduate Colloquium

Title Hamiltonian Stationary Lagrangian Surfaces
Speaker, Affiliation Filippo Gaia, ETH Zürich
Date, Time 14 March 2024, 16:15-17:15
Location HG G 19.2
Abstract The seminar aims to discuss the following question: given a Lagrangian homotopy 2-class $\alpha$ in a Kähler-Einstein manifold, can we identify a distinguished representative of $\alpha$ by minimizing the area among Lagrangian surfaces in $\alpha$? We will introduce the concepts of Lagrangian surface, Lagrangian angle and Hamiltonian variations and present some of their properties. Subsequently we will address some existence and regularity aspects of the question above, drawing connections to the theories of minimal surfaces and harmonic maps.
Hamiltonian Stationary Lagrangian Surfacesread_more
HG G 19.2
21 March 2024
16:15-17:15 		Elias Dubno
Universität Zürich, Switzerland
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Geometry Graduate Colloquium

Title Apollonian Circle Packings
Speaker, Affiliation Elias Dubno, Universität Zürich, Switzerland
Date, Time 21 March 2024, 16:15-17:15
Location HG G 19.2
Abstract An Apollonian Circle Packing is a fractal construction (which goes back over 2000 years!) of iteratively adding new circles tangent to the previous ones. We will review the basic concepts, in particular focusing on some of the number-theoretic properties behind Apollonian Circle Packings. We will then explain a recent result of Haag-Kertzer-Rickards-Stange, where Quadratic Reciprocity played a crucial role to disprove a long-standing conjecture. If time permits we will also discuss further applications of this approach, e.g. to Zaremba's conjecture.
Apollonian Circle Packingsread_more
HG G 19.2
28 March 2024
16:15-17:15 		Blandine Galiay
ENS Paris Saclay
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Geometry Graduate Colloquium

Title The theory of divisible convex domains, and generalizations
Speaker, Affiliation Blandine Galiay, ENS Paris Saclay
Date, Time 28 March 2024, 16:15-17:15
Location HG G 19.2
Abstract A divisible convex set is a properly convexe open subset of the projective space admitting a cocompact action of a discrete subgroup of its automorphism group. The study of these geometric objects started in the 60s with the work of Benzecri and has seen significant developments since then. Many connections have been established with other research areas, ranging from geometric structures to dynamical systems, including geometric group theory and symmetric spaces. In this presentation, our goal is to introduce recent generalizations of the theory of divisible convex sets. To do so, we will first introduce the various objects and fundamental concepts of the theory.
The theory of divisible convex domains, and generalizationsread_more
HG G 19.2
11 April 2024
16:15-17:15 		Federico Trinca
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Geometry Graduate Colloquium

Title Riemannian Holonomy
Speaker, Affiliation Federico Trinca,
Date, Time 11 April 2024, 16:15-17:15
Location HG G 19.2
Abstract A century ago, Elie Cartan showed how to construct a group from a Riemannian manifold via parallel transport: the Riemannian holonomy group. He then used this group to study symmetric spaces. In 1953, Marcel Berger classified all the possible groups that can appear as the Riemannian holonomy of a Riemannian manifold. This result gives a list of interesting geometrical structures compatible with the Riemannian metric, including the classical Kähler geometry, Calabi--Yau geometry and Hyperkähler geometry. In this talk, I will provide an overview of Riemannian holonomy, including their connection with Einstein manifolds and minimal submanifolds. If time permits, I will discuss open problems and standard techniques used in the field.
Riemannian Holonomyread_more
HG G 19.2
18 April 2024
16:15-17:15 		Ata Deniz Aydin
ETH Zurich, Switzerland
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Geometry Graduate Colloquium

Title Quantization of measures and lattices
Speaker, Affiliation Ata Deniz Aydin, ETH Zurich, Switzerland
Date, Time 18 April 2024, 16:15-17:15
Location HG G 19.2
Abstract The quantization problem looks for finitely many points that best represent a given probability measure in space, in the sense of minimizing an L^p transport cost. Gersho’s conjecture posits that lattice configurations are asymptotically optimal for the quantization of uniform measures; this is known in dimensions 1 and 2, the optimal lattice for d = 2 being the regular hexagonal lattice. We will prove these known results and discuss their implications for the quantization of non-uniform measures and measures on 2-dimensional Riemannian manifolds. As a geometric application, we will finally discuss the approximation of convex bodies by polyhedra, whose faces are also known to form regular hexagons in the limit.
Quantization of measures and latticesread_more
HG G 19.2
25 April 2024
16:15-17:15 		Noa Vikman
Université de Fribourg
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Geometry Graduate Colloquium

Title Minimal Metric Spheres: Motivations and Recent Progress
Speaker, Affiliation Noa Vikman, Université de Fribourg
Date, Time 25 April 2024, 16:15-17:15
Location HG G 19.2
Minimal Metric Spheres: Motivations and Recent Progress
HG G 19.2
2 May 2024
16:15-17:15 		Merik Niemeyer
Max Plank Institut Leipzig
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Geometry Graduate Colloquium

Title Cluster Algebras in Geometry
Speaker, Affiliation Merik Niemeyer, Max Plank Institut Leipzig
Date, Time 2 May 2024, 16:15-17:15
Location HG G 19.2
Abstract Since their introduction in the early 2000s, cluster algebras have shown up all over mathematics, and notably also in geometry. This talk aims at giving a gentle introduction to cluster algebras, while staying close to (hyperbolic) geometry. Namely, we will take a look at (decorated) Teichmüller spaces for punctured surfaces, and describe coordinates on these that are endowed with a cluster structure. This exhibits a beautiful interplay of geometry, combinatorics and cluster theory. Time permitting, we will generalize this approach and give a rough overview of cluster algebras showing up in higher Teichmüller theory.
Cluster Algebras in Geometryread_more
HG G 19.2
16 May 2024
16:15-17:15 		Wooyeon Kim
ETH Zurich, Switzerland
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Geometry Graduate Colloquium

Title Oppenheim Conjecture
Speaker, Affiliation Wooyeon Kim, ETH Zurich, Switzerland
Date, Time 16 May 2024, 16:15-17:15
Location HG G 19.2
Abstract There have been several problems in number theory for which non-trivial progress has been made by reformulating them to a question on dynamics in homogeneous spaces. One famous example is the Oppenheim conjecture about representations of numbers by real quadratic forms in several variables. In 1986, Margulis settled the Oppenheim conjecture in full generality, using methods arising from ergodic theory and the study of discrete subgroups of Lie groups. We will review how the Oppenheim conjecture is converted to a dynamical statement in homogeneous space. If time permits, we will also discuss the orbit closure and measure rigidity theorems in a more general context.
Oppenheim Conjectureread_more
HG G 19.2
23 May 2024
16:15-17:15 		Ana Zegarac
ETH Zürich
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Geometry Graduate Colloquium

Title Applications of Geometry in Computer Graphics
Speaker, Affiliation Ana Zegarac, ETH Zürich
Date, Time 23 May 2024, 16:15-17:15
Location HG G 19.2
Abstract Computer graphics has been developing since the advent of first displays in the 1950s. Nowadays we're enjoying the results of this research daily through medical imaging, computer-generated imagery in movies and computer games, through interacting with objects designed with computer-aided design, etc. The aim of this talk is to demonstrate applications of geometry in different areas of computer graphics: mesh acquisition, geometry processing, and rendering.
Applications of Geometry in Computer Graphicsread_more
HG G 19.2

Archive: AS 24 SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 SS 21 AS 20 SS 20 AS 19 AS 18 SS 18

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