Beteiligte Dozenten: Jens Hornbostel, Sascha Orlik, Kay Rülling, Matthias Wendt.
Wenn nichts anderes angegeben ist, findet das Seminar mittwochs in F.13.11, 16:30 - 17:30 statt.
| 18. April, 15-16 Uhr in G.13.18! |
Jakob Scholbach | The integral motivic Satake equivalence The Satake equivalence is a cornerstone of the Langlands program. For a reductive group such as G = GL_n, it relates the topology of the so-called affine Grassmannian Gr_G, to the representation theory of the Langlands dual group of G. In this talk I will report on joint work with Richarz and Cass-van den Hove about this statement in the land of motives. I will attempt to make the talk as non-technical as possible. |
| 19. April | Sabrina Pauli | Tropical methods in refined enumerative geometry Using tropical geometry one can translate problems in enumerative geometry to combinatorial problems. Thus tropical geometry is a powerful tool in enumerative geometry over the complex and real numbers. In my talk I will give an introduction to tropical geometry and explain how one can use tropical methods to solve problems in refined enumerative geometry, that is how to get a refined answer in the Grothendieck-Witt ring of a field k to enumerative problems. |
| 26. April | Clémentine Lemarie-Rieusset | Motivic knot theory In this talk I will present a new application of motivic homotopy theory: motivic knot theory. More specifically, I will present the quadratic linking degree, which is a counterpart in algebraic geometry of the linking number of two oriented disjoint knots (the number of times one of the knots turns around the other knot). I will mostly talk about the quadratic linking degree of oriented couples of closed immersions of the affine plane minus the origin in the affine 4-space minus the origin (with several examples). I will then explain how one defines and studies the quadratic linking degree of oriented couples of closed immersions of smooth models of motivic spheres (which are counterparts in algebraic geometry of classical topological spheres). |
| 03. Mai | Kein Oberseminar (Symposium GRK2240/GRK2553) | - |
| 10. Mai | Vincent Gajda | Soergel's Conjecture and Finitely Cogenerated Modules In this talk I present a new approach to Soergel's conjecture. The conjecture can be considered a contribution to the Langlands' philosophy for real reductive groups, in the sense that it aims to relate certain categories of representations with geometry living on the Langlands' dual side. More precisely it aims to connect equivariant motives living on ABV-parameter spaces to finitely cogenerated (g,K)-modules related to representations of real reductive groups. I will discuss the results of my thesis, in which I introduce the relevant categories of (g,K)-modules and relate them to equivariant mixed Tate motives, thereby verifying a certain `degrading' version of the conjecture for special cases. |
| 17. Mai | - | - |
| 24. Mai | Christian Hess | Experiments on topological materials: topological insulators, Weyl semimetals, and quantum spin liquids The discovery of the quantum Hall state in 1980, represents the first experimental example of topological matter which is characterized by a topological invariant. Since then, topology has entered research in many aspects, and today the research on topological matter constitutes an important branch in solid state physics. In this talk, after introducing elementary concepts related to the quantum Hall state, I will discuss selected topology-related properties of topological insulators, Weyl semimetals, and quantum spin liquids together with pertinent experiments. |
| 31. Mai | Kein Oberseminar (Exkursionswoche Pfingsten) | - |
| 07. Juni | Emanuel Reinecke | Unipotent homotopy theory of schemes In this talk, I will present a notion of unipotent homotopy theory for schemes, which is based on Toen's work on affine stacks. I will discuss some general properties of the resulting unipotent homotopy group schemes and explain how over a field of characteristic p>0, they often recover the unipotent completion of the Nori fundamental group scheme, p-adic etale homotopy groups, and Artin-Mazur formal groups. As examples, we will see computations in the case of curves, abelian varieties, and Calabi-Yau varieties. Joint work with Shubhodip Mondal. |
| 14. Juni | - | - |
| 21. Juni | - | - |
| 28. Juni | Marcin Lara | - |
| 05. Juli | Nicolas Dupré | - |
| 12. Juli | - | - |