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ProgramMini-courses
Marco Golla: TBC
Adrien Abgrall: Geometry of Outer Space for RAAGs Untwisted Outer Space for right-angled Artin groups (RAAGs) has been constructed by Charney, Stambaugh, and Vogtmann in 2017. It is a contractible simplicial complex, and a geometric model of the group of coarse-median-preserving automorphisms of a RAAG. In this talk, I will give structural results about the geometry of this complex and its combinatorial automorphisms, as well as many explicit examples involving interesting tessellations of Euclidean space. Saraf Deepanshi: Fundamental n-quandles are residually finite Fundamental n-quandles are canonical quotients of the fundamental quandle of an oriented link in the 3-sphere, first introduced by Joyce. While they are coarser invariants than the fundamental quandle, they are often more tractable and admit deep connections to the the n-fold cyclic branched covers of the 3-sphere branched over the link. This connection has led to striking classification results, including a complete list of links with finite fundamental n-quandles, based on Thurston's geometrisation theorem and Dunbar's classification of spherical 3-orbifolds. In earlier work, Fish and Lisitsa developed an algorithm that uses fundamental 2-quandles to detect the unknot, and they conjectured that the fundamental 2-quandle of any knot is residually finite. This property not only supports the validity of their algorithm but also implies the solvability of the word problem for these algebraic structures. In this talk, I will present recent results showing that the fundamental n-quandle of any oriented link in the 3-sphere is residually finite for all integers n greater than or equal to 2. Along the way, we'll touch on connections to branched covers and classification results for when these quandles are finite. This work contributes to a growing bridge between low-dimensional topology and the algebraic theory of quandles. Achintya Dey: Bolza-like surfaces in Thurston set A surface in the Teichmüller space, where the systole function admits its maximum, is called a maximal surface. For genus two, a unique maximal surface exists, which is called the Bolza surface, whose systolic geodesics give a triangulation of the surface. We define a surface as Bolza-like if its systolic geodesics decompose the surface into (p, q, r)-triangles for some integers p, q, r. In this article, we construct a one-parameter family of hyperbolic surfaces within the Thurston set, which, in turn, yields Bolza-like surfaces for infinitely many genera g > 9. Next, we see an intriguing application of Bolza- like surfaces. In particular, we construct global maximal surfaces using these Bolza-like surfaces. Furthermore, we study a symmetric property satisfied by the systolic geodesics of our Bolza-like surfaces. We show that any simple closed geodesic intersects the systolic geodesics at an even number of points. Yohan Mandin-Hublé: TBC Moctar Traore: Ricci-Bourguignon with special vector field Sardor Yakupov: Moduli space of curves and achiral Lefschetz fibrations Lefschetz fibrations provide a powerful tool for studying symplectic 4-manifolds and contact 3-manifolds. Achiral Lefschetz fibrations extend this framework beyond the symplectic case, allowing us to address more general questions about 4-manifolds. On the other hand, the moduli space of complex curves is one of central objects in complex and Riemannian geometry of surfaces. The goal of this talk is to introduce these two concepts separately and explore their connection through the notion of the classifying map.
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