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Geometry graduate colloquium

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Herbstsemester 2023

Datum / Zeit Referent:in Titel Ort
21. September 2023
15:00-16:00 		Luca Nalon
University of Fribourg, Switzerland
Details

Geometry Graduate Colloquium

Titel The Sard problem for the End-point map in step 2 Carnot groups
Referent:in, Affiliation Luca Nalon, University of Fribourg, Switzerland
Datum, Zeit 21. September 2023, 15:00-16:00
Ort HG G 19.1
Abstract The Sard theorem asserts that the set of critical values of a smooth map f:Rn → Rm has zero Lebesgue measure. The theorem has been disproved to various extents (see Bates 1993) when we replace the domain with an infinite-dimensional Banach space. The aim of the talk is to introduce the End-point map in the setting of step 2 Carnot groups and to prove an even stronger version of the Sard theorem for those kind of maps.
The Sard problem for the End-point map in step 2 Carnot groupsread_more
HG G 19.1
28. September 2023
15:00-16:00 		Denis Marti
University of Fribourg, Switzerland
Details

Geometry Graduate Colloquium

Titel The Plateau problem and currents
Referent:in, Affiliation Denis Marti, University of Fribourg, Switzerland
Datum, Zeit 28. September 2023, 15:00-16:00
Ort HG G 19.1
Abstract The Plateau problem asks for the existence of a minimal surface bounded by a given closed curve in Euclidean space. A surface is called minimal if it minimizes the area of all possible surfaces with the same boundary. In this talk we give an overview of the development from this classical version to higher dimensional analogues in Euclidean spaces and finally a generalized version in metric spaces. Along the way, we introduce currents, which were used to solve the problem, and discuss how this theory adapts to the different situations.
The Plateau problem and currentsread_more
HG G 19.1
5. Oktober 2023
15:00-16:00 		Andrea Drago
University of Rome, Italy
Details

Geometry Graduate Colloquium

Titel Entropy and curvature in low dimensional topology
Referent:in, Affiliation Andrea Drago, University of Rome, Italy
Datum, Zeit 5. Oktober 2023, 15:00-16:00
Ort HG G 19.1
Abstract In this talk we will explore the analogy between Ricci curvature and volume entropy. The Ricci curvature is a classical invariant in Riemannian geometry that has strong implications on the topology of manifolds. In particular, the topology of manifolds with a lower bound on the Ricci curvature are topologically finite, meaning that there are a finite number of diffeomorphism classes, and locally topologically rigid, meaning that two such manifolds with different topology cannot be too close. The volume entropy is an invariant of isometric group actions introduced in geometric group theory, which can be interpreted as an asymptotic, weak version of the Ricci curvature. In the spirit of this analogy, we will see two theorems, lying in the intersection between hyperbolic geometry, geometric group theory, and low dimensional topology, which show the topological finiteness and local topological rigidity for some classes of manifolds with volume entropy bounds.
Entropy and curvature in low dimensional topologyread_more
HG G 19.1
12. Oktober 2023
15:00-16:00 		Paula Truöl
MPIM Bonn
Details

Geometry Graduate Colloquium

Titel Relating knot theory to algebraic geometry
Referent:in, Affiliation Paula Truöl, MPIM Bonn
Datum, Zeit 12. Oktober 2023, 15:00-16:00
Ort HG G 19.1
Abstract Algebraic geometry studies solution sets of polynomial equations in multiple variables. For example, an algebraic plane curve is the zero set of a polynomial in two (say, complex) variables. Knot theory, on the other hand, studies 1-dimensional submanifolds of the 3-sphere from a topological perspective - up to continuous deformations. How are these two areas of mathematics related? We will draw connections between knot theory and the study of singularities of algebraic plane curves, assuming no knowledge of either area.
Relating knot theory to algebraic geometryread_more
HG G 19.1
19. Oktober 2023
15:00-16:00 		Alessio Cela
ETH Zürich
Details

Geometry Graduate Colloquium

Titel Geometric and tropical curves
Referent:in, Affiliation Alessio Cela, ETH Zürich
Datum, Zeit 19. Oktober 2023, 15:00-16:00
Ort HG G 19.1
Abstract Enumerative geometry aims to count geometric objects satisfying certain conditions. A major break-through in the subject happened in 1994, when, motivated by string theory, Kontsevich introduced the moduli spaces of stable maps. After Kontsevich, the area of enumerative geometry concerning curve counting problems has become a very active field of research, called Gromov-Witten theory. In 2003, Mikhalkin suggested a new approach to the curve counting problem, showing that there is a natural correspondence between algebraic and tropical curves and that, in certain nice situations, one can hope to obtain the count of algebraic curves via tropical methods. In this talk I will try to present both perspectives.
Geometric and tropical curvesread_more
HG G 19.1
26. Oktober 2023
15:00-16:00 		René Pfitscher
Université Sorbonne Paris Nord
Details

Geometry Graduate Colloquium

Titel Geometric aspects of diophantine approximation in flag varieties
Referent:in, Affiliation René Pfitscher, Université Sorbonne Paris Nord
Datum, Zeit 26. Oktober 2023, 15:00-16:00
Ort HG G 19.1
Abstract In this talk, we depart with the classical Schmidt Theorem in metric Diophantine approximation and use it as a guide to formulate a metric theory of Diophantine Approximation in the general setting of (generalized) flag varieties. Important examples of generalized flag varieties are the projective space, the n-sphere, projective quadrics, and Grassmannians. The underlying question is ``How well can a point, chosen at random, be approximated by rational points?''. We then focus on the asymptotic count of rational solutions to certain Diophantine inequalities. This can be reduced to counting primitive lattice points in a certain increasing family of Borel subsets in the ambient Euclidean space, and thus may be viewed as a problem in the realm of geometry of numbers. In the remainder of the talk, we explore various approaches ranging from homogeneous dynamics to spectral theory of Eisenstein series to accomplish such counts.
Geometric aspects of diophantine approximation in flag varietiesread_more
HG G 19.1
2. November 2023
15:00-16:00 		Hjalti Isleifsson
ETH Zurich, Switzerland
Details

Geometry Graduate Colloquium

Titel Asymptotic Plateau problems in Hadamard spaces
Referent:in, Affiliation Hjalti Isleifsson, ETH Zurich, Switzerland
Datum, Zeit 2. November 2023, 15:00-16:00
Ort HG G 19.1
Abstract I will explain what is is meant by an asymptotic Plateau problem in Hadamard spaces, give a survey of some classical results for such problems and also discuss more recent ones. Only very basic knowledge will be assumed so I will spend some time introducing the concepts and tools needed.
Asymptotic Plateau problems in Hadamard spacesread_more
HG G 19.1
9. November 2023
15:00-16:00 		Kevin Klinge
Karlsruher Institut für Technologie, KIT
Details

Geometry Graduate Colloquium

Titel Finiteness properties as geometric invariants
Referent:in, Affiliation Kevin Klinge, Karlsruher Institut für Technologie, KIT
Datum, Zeit 9. November 2023, 15:00-16:00
Ort HG G 19.2!
Abstract When using a constructive or algorithmic approach to group theoretic problems it is often important that the group has a finite description. While this property is well behaved under taking quotients, it is unfortunately not preserved by taking subgroups. For example, there are finitely generated groups that admit subgroups which are not finitely generated. The Σ-invariant gives the purely algebraic finiteness conditions a geometric interpretation. The goal of this talk is to understand how we can use this tool to translate between the algebraic and geometric viewpoints.
Finiteness properties as geometric invariantsread_more
HG G 19.2!
16. November 2023
15:00-16:00 		Baptiste Depouilly
ETH Zürich
Details

Geometry Graduate Colloquium

Titel An unexpected incursion of modular forms into geometry
Referent:in, Affiliation Baptiste Depouilly, ETH Zürich
Datum, Zeit 16. November 2023, 15:00-16:00
Ort HG G 19.1
Abstract In this talk, we'll explain how Milnor ingeniously (and surprisingly) used modular forms to give an answer to a purely geometrical question, namely ``Is there a pair of isospectral but non-isometric Riemannian manifolds?''. His proof leverages the finite-dimensionality of spaces of modular forms and the connexion between spectra of flat tori and Jacobi theta functions.
An unexpected incursion of modular forms into geometryread_more
HG G 19.1
23. November 2023
15:00-16:00 		Matilde Gianocca
ETH Zürich
Details

Geometry Graduate Colloquium

Titel Geometry of Harmonic Maps
Referent:in, Affiliation Matilde Gianocca, ETH Zürich
Datum, Zeit 23. November 2023, 15:00-16:00
Ort HG G 19.1
Abstract We will give an overview of the history and main results in the theory of harmonic maps in dimension two. We will in particular emphasise their relation to minimal surfaces.
Geometry of Harmonic Mapsread_more
HG G 19.1
30. November 2023
15:00-16:00 		Gerard Orriols
ETH Zürich
Details

Geometry Graduate Colloquium

Titel The conformal volume and its applications
Referent:in, Affiliation Gerard Orriols, ETH Zürich
Datum, Zeit 30. November 2023, 15:00-16:00
Ort HG G 19.1
Abstract In this talk we will define the conformal volume of a manifold endowed with a conformal class of Riemannian metrics. This invariant was introduced by Li and Yau in 1982 and since then has been very influential in the development of Geometric Analysis. After setting up the framework of conformal geometry and introducing the conformal volume, we will give some examples (mostly in dimension 2) and explore its connection to minimal surfaces, the Willmore functional and the Laplace eigenvalues.
The conformal volume and its applicationsread_more
HG G 19.1
7. Dezember 2023
15:00-16:00 		Isobel Davies
Otto-von-Guericke-Universität Magdeburg
Details

Geometry Graduate Colloquium

Titel Euclidean buildings and symmetric spaces of non-compact type
Referent:in, Affiliation Isobel Davies, Otto-von-Guericke-Universität Magdeburg
Datum, Zeit 7. Dezember 2023, 15:00-16:00
Ort HG G 19.2!
Abstract In this talk I will give an introduction to CAT(0) spaces with a particular focus on the geometry of Euclidean buildings and symmetric spaces of non-compact type.
Euclidean buildings and symmetric spaces of non-compact typeread_more
HG G 19.2!
14. Dezember 2023
15:00-16:00 		Frieder Jäckel
University Bonn, Germany
Details

Geometry Graduate Colloquium

Titel Effective hyperbolization of 3-manifolds
Referent:in, Affiliation Frieder Jäckel, University Bonn, Germany
Datum, Zeit 14. Dezember 2023, 15:00-16:00
Ort HG G 19.1
Abstract Because of Perelman‘s groundbreaking solution of the geometrization conjecture we know exactly which topological criteria a closed three-manifold needs to satisfy so that it admits a hyperbolic metric. However, one short-coming of Perelman’s Ricci flow approach is that even if the topology of the manifold is very well understood (e.g., if one knows how it is glued together from different pieces), it gives no information about geometric data (e.g., the hyperbolic volume) in terms of the topological data. The goal of this talk will be to explain how a lot of geometric information about the hyperbolic metric of the three-manifold can be read off a purely topological object called the curve graph. No prior knowledge about the geometrization conjecture or the curve graph will be assumed.
Effective hyperbolization of 3-manifoldsread_more
HG G 19.1

Organisatoren:innen: Konstantin Andritsch, Raphael Appenzeller, Martina Joergensen, Lauro Silini

Archiv: HS 24 FS 24 HS 23 FS 23 HS 22 FS 22 HS 21 FS 21 HS 20 FS 20 HS 19 HS 18 FS 18

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