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Autumn Semester 2021

Date / Time Speaker Title Location
30 September 2021
16:15-17:15 		Dr. Benjamin Brück
ETH Zurich, Switzerland
Details

Geometry Graduate Colloquium

Title Poset topology and fibre theorems
Speaker, Affiliation Dr. Benjamin Brück, ETH Zurich, Switzerland
Date, Time 30 September 2021, 16:15-17:15
Location HG G 19.2
Livestream
Abstract To every partially ordered set (poset), one can associate a certain simplicial complex. This allows one on the one hand to use topological tools to study the combinatorics of posets and on the other hand to use combinatorial tools to study topological spaces. I will talk about how both of these sides arise in group theory: First, I will present examples of posets that give rise to "nice" spaces equipped with group actions. Then, I will talk about Quillen-type fibre theorems, which are important tools for studying the topology of spaces constructed from posets.
Poset topology and fibre theoremsread_more
HG G 19.2
Livestream
7 October 2021
16:15-17:15 		Dr. Alessio Pellegrini
ETH Zurich, Switzerland
Details

Geometry Graduate Colloquium

Title Novikov-Morse Homology and its friends
Speaker, Affiliation Dr. Alessio Pellegrini, ETH Zurich, Switzerland
Date, Time 7 October 2021, 16:15-17:15
Location HG G 19.2
Livestream
Abstract In this talk we introduce the notion of Novikov homology, which generalises Morse homology. We will compute some examples and see that Novikov homology can be viewed as a twisted version of Morse homology. If time permits, we will quickly glance over the importance of Novikov homology in symplectic geometry.
Novikov-Morse Homology and its friendsread_more
HG G 19.2
Livestream
14 October 2021
16:15-17:15 		Tommaso Goldhirsch
ETH Zurich, Switzerland
Details

Geometry Graduate Colloquium

Title A beginner’s Guide to Metric Currents
Speaker, Affiliation Tommaso Goldhirsch, ETH Zurich, Switzerland
Date, Time 14 October 2021, 16:15-17:15
Location HG G 19.2
Livestream
Abstract Introduced in the 60’s by Federer and Fleming, integral currents can be thought of as generalised surfaces and were used to solve Plateau’s problem of finding a surface of least area spanning a given boundary. In this talk we will survey some of the key features of this theory and give some insight into how it can be translated to metric spaces.
A beginner’s Guide to Metric Currentsread_more
HG G 19.2
Livestream
21 October 2021
16:15-17:15 		Luca De Rosa
ETH Zurich, Switzerland
Details

Geometry Graduate Colloquium

Title Geodesic Currents and the Intersection Form
Speaker, Affiliation Luca De Rosa, ETH Zurich, Switzerland
Date, Time 21 October 2021, 16:15-17:15
Location HG G 19.2
Livestream
Abstract Geodesic currents provide an elegant way to unify seemingly unrelated concepts such as hyperbolic structures, simple closed curves, and measured laminations. They were introduced by F. Bonahon in 1988, in the context of the compactification of Teichmüller space. In this talk we will define, starting from zero, what a geodesic current is, and we will survey the key aspects of the notion.
Geodesic Currents and the Intersection Formread_more
HG G 19.2
Livestream
28 October 2021
16:15-17:15 		Arnaud Maret
University of Heidelberg, Germany
Details

Geometry Graduate Colloquium

Title Character varieties, mapping class group action and ergodicity
Speaker, Affiliation Arnaud Maret, University of Heidelberg, Germany
Date, Time 28 October 2021, 16:15-17:15
Location HG G 19.2
Livestream
Abstract The goal of the talk is to first introduce the concept of character variety as a way to associate a symplectic manifold to a surface and a Lie group. We will then talk about the mapping class group of a surface and how it acts on the character variety. I will then mention some known results and conjectures about the nature of this action. The action turns out to be either pretty complicated, in fancy words ergodic, or much nicer, depending on the connected components of the character variety.
Character varieties, mapping class group action and ergodicityread_more
HG G 19.2
Livestream
4 November 2021
16:15-17:15 		Nicolas Mueller
ETH Zurich, Switzerland
Details

Geometry Graduate Colloquium

Title Analogies in the function field world
Speaker, Affiliation Nicolas Mueller, ETH Zurich, Switzerland
Date, Time 4 November 2021, 16:15-17:15
Location HG G 19.2
Livestream
Abstract There are several far reaching analogies between number theory and geometry in characteristic zero on the one hand and constructions using function fields over finite fields on the other hand. In this talk, we will see the concrete analogy between complex elliptic curves and Drinfeld modules which covers lattices, isogenies, torsion points and uniformization. No previous knowledge about Drinfeld modules is required.
Analogies in the function field worldread_more
HG G 19.2
Livestream
* 11 November 2021
16:15-17:15 		Gabriel Pallier
Sorbonne University, France
Details

Geometry Graduate Colloquium

Title Tilting at Euclid's windmill
Speaker, Affiliation Gabriel Pallier, Sorbonne University, France
Date, Time 11 November 2021, 16:15-17:15
Location HG F 26.3
Livestream
Abstract In his so-called windmill proof of Proposition I.47 (The Pythagorean theorem) Euclid makes use of an argument essentially equivalent to the fact that the area of triangles is invariant under rigid motion (especially, quarter-turns). Prochronistically speaking, this suggests that introducing a complex structure on a symplectic manifold determines a Hermitian (especially, Riemannian) metric there. Starting from this proof I will review more recent examples showing how finite and infinite-dimensional versions of this same principle have been able to bring some successes in XXth century mathematics.
Tilting at Euclid's windmillread_more
HG F 26.3
Livestream
25 November 2021
16:15-17:15 		Dr. Reynold Fregoli
Universität Zürich, Switzerland
Details

Geometry Graduate Colloquium

Title Dynamics and Diophantine Approximation: a fruitful interplay
Speaker, Affiliation Dr. Reynold Fregoli, Universität Zürich, Switzerland
Date, Time 25 November 2021, 16:15-17:15
Location HG G 19.2
Livestream
Abstract Around 1985, S.G. Dani introduced a novel and powerful tool to investigate "quantitative properties" of the embedding of rational numbers into the reals. Such tool, known today as Dani's Correspondence, allows to appreciate Diophantine properties of real numbers (or vectors) by observing their trajectory in a certain space and under the action of an appropriate flow. Together with Fractal Geometry and the Geometry of Numbers, Dani's Correspondence is a key ingredient in the most recent and striking advancements in the field of Diophantine Approximation. We will give and overview of Dani's Correspondence, starting from the basic concepts, and have a glimpse into the most recent developments of the fruitful interplay between Dynamics and Number Theory from this specific angle.
Dynamics and Diophantine Approximation: a fruitful interplayread_more
HG G 19.2
Livestream
2 December 2021
16:15-17:15 		Lauro Silini
ETH Zurich, Switzerland
Details

Geometry Graduate Colloquium

Title A sub-Riemannian promenade in the Heisenberg group
Speaker, Affiliation Lauro Silini, ETH Zurich, Switzerland
Date, Time 2 December 2021, 16:15-17:15
Location HG G 19.2
Livestream
Abstract Introduced at the beginning of 20th century by Charathéodory and Carnot, sub-Riemannian geometry is nowadays a very general and active area of research, both in applied and pure mathematics. In this talk we will explicitly construct from zero the model space carrying such a structure: the Heisenberg group. Time permitting, we will develop all the notions necessary to present the celebrated Pansu's 1982 conjecture.
A sub-Riemannian promenade in the Heisenberg groupread_more
HG G 19.2
Livestream
* 9 December 2021
16:15-17:15 		Dr. Bahar Acu
ETH Zurich, Switzerland
Details

Geometry Graduate Colloquium

Title A gentle introduction to open book decompositions
Speaker, Affiliation Dr. Bahar Acu, ETH Zurich, Switzerland
Date, Time 9 December 2021, 16:15-17:15
Location Zoom
Abstract A very useful strategy in studying topological manifolds is to factor them into “smaller" pieces. An "open book decomposition” of an n-manifold (the open book) is a type of fibration that helps us study our manifold in terms of its (n-1)-dim'l fibers (the pages) and (n-2)-dim'l boundary of these fibers (the binding). Open books provide a natural framework for studying topological properties of certain geometric structures on smooth manifolds such as contact structures. Thanks to open books, "contact manifolds", odd dimensional manifolds carrying these geometric structures, can be studied from an entirely topological viewpoint. For example, every contact 3-manifold can be presented as an open book whose pages are surfaces and binding is a knot/link. In this talk, we will talk about these objects in greater detail with examples.
A gentle introduction to open book decompositionsread_more
Zoom
16 December 2021
16:15-17:15 		Xenia Lorena Flamm
ETH Zurich, Switzerland
Details

Geometry Graduate Colloquium

Title Hilbert's 17th problem
Speaker, Affiliation Xenia Lorena Flamm, ETH Zurich, Switzerland
Date, Time 16 December 2021, 16:15-17:15
Location HG G 19.2
Livestream
Abstract Pick a polynomial of degree d in n variables which takes only non-negative values. Is it the sum of squares of polynomials? The answer was given by Hilbert in 1888 who showed that this is only true in three cases: n=1 and d arbitrary, n arbitrary and d=2, n=2 and d=4. We will prove the first two cases of this theorem and give Motzkin’s explicit counterexample of a non-negative polynomial which is not a sum of squares of polynomials. A refinement of the above question leads to what is now known as Hilbert’s 17th problem: Is every non-negative polynomial a sum of squares of rational functions? The answer to this question is yes, and was given by Artin in 1927. Its proof was very influential and fostered the development of real algebra. We will discuss the relevant concepts from real algebraic geometry, and finish by sketching a proof of Artin’s theorem.
Hilbert's 17th problemread_more
HG G 19.2
Livestream

Notes: events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location.

Organisers: Emilio Corso, Xenia Lorena Flamm, Francesco Fournier Facio, Paula Truöl

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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