Problem of the Week
BUGCAT
Zassenhaus Conference
Hilton Memorial Lecture
BingAWM
Math Club
We meet Thursdays at 2:50–3:50 pm in Whitney Hall 100E. This semester's organizer is Cary Malkiewich. The seminar has an announcement mailing list open to all.
Topics include: geometric group theory, differential geometry and topology, low-dimensional topology, algebraic topology, and homotopy theory.
Abstract: We show the existence of an (infinitely generated) discrete subgroup of a Lie group (such as SL_n(R)) that has full limit set in its (Furstenberg) boundary and which is not a lattice, we also discuss the possibility of whether this is possible for finitely generated groups. All notions will be explained. Based on work in progress with Subhadip Dey.
Abstract: Regular trees of graphs are inverse limits of particularly simple
inverse systems of finite graphs. They form a 1-dimensional subclass
of the Markov compacta: a class of finitely describable inverse limits
of simplicial complexes, which includes all boundaries of hyperbolic
groups. I will discuss upcoming joint work with Jacek Swiatkowski in
which we use Bowditch's canonical JSJ decomposition to characterize
the 1-ended hyperbolic groups whose boundaries are (regular) trees of
graphs.
Abstract: Topological groupoids describe orbit structures of dynamical systems by capturing their local symmetries. The group of global symmetries, which are pieced together from local ones, is called the topological full group. This construction gives rise to new examples of groups with very interesting properties, solving outstanding open problems in group theory. This talk is about a new connection between groupoids and topological full groups on the one hand and algebraic K-theory spectra and infinite loop spaces on the other hand. Several applications will be discussed. Parts of this connection already feature in work of Szymik and Wahl on the homology of Higman-Thompson groups.
Abstract: In this talk we investigate invariants that count periodic points of a map. Given a self map $f$ of a compact manifold we could detect $n$-periodic points of $f$ by computing the Reidemeister trace of $f^n$ or by computing the equivariant Fuller trace. In 2020 Malkiewich and Ponto showed that the collection of Reidemeister traces of $f^k$ for varying $k|n$ and the equivariant Fuller trace are equivalent as periodic point invariants, and they conjecture that for families of endomorphisms the Fuller trace will be a strictly richer invariant for $n$-periodic points.
In this talk we will explain our new result which confirms Malkiewich and Ponto's conjecture. We do so by proving a new Pontryagin-Thom isomorphism between equivariant parameterized cobordism and the spectrum of sections of a particular parametrized spectrum and using this result to carry out geometric computations.
Abstract: In this talk, we study the algebraic structure of mapping class group Mod(M) of 3-manifolds M that fiber as a circle bundle over a surface. We prove an exact sequence, relate this to the Birman exact sequence, and determine when this sequence splits. We will also discuss the Nielsen realization problem for such manifolds and give a partial answer. This is joint work with Bena Tshishiku and Alina Beaini.
Abstract: TBA
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Abstract: Billiards in polygons can exhibit bizarre behavior, some of which can be explained by deep connections to several seemingly unrelated branches of mathematics. These include algebraic geometry, Teichmuller theory and ergodic theory on homogeneous spaces. The talk will be an introduction to these ideas, aimed at a general mathematical audience.
Abstract: TBA
Abstract: TBA