seminars:topsem
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seminars:topsem [2025/09/17 11:54] malkiewich Keenan date |
seminars:topsem [2025/10/13 13:49] (current) lruffoni |
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| In this talk, I will discuss progress towards developing analogues of these tools in the C_2 equivariant setting. In particular, Guchuan Li, Sarah Petersen, and I have constructed models for C_2-equivariant analogues of the integral Brown-Gitler spectra, and used them to construct an analogue of the ku-splitting. \\ </WRAP> | In this talk, I will discuss progress towards developing analogues of these tools in the C_2 equivariant setting. In particular, Guchuan Li, Sarah Petersen, and I have constructed models for C_2-equivariant analogues of the integral Brown-Gitler spectra, and used them to construct an analogue of the ku-splitting. \\ </WRAP> | ||
| - | * **September 18th** \\ Speaker: ** ** \\ Title: ** ** <WRAP box>// Abstract: // \\ </WRAP> | + | * **September 18th** \\ Speaker: **Lorenzo Ruffoni (Binghamton) ** \\ Title: **A Pontryagin sphere at infinity in real hyperbolic space ** <WRAP box>// Abstract: // Given a discrete group of isometries of hyperbolic space, we can look at its limit set, i.e., the set of accumulation points of its orbits on the sphere at infinity. This is a compact metric space embedded in the sphere at infinity, and it often displays interesting geometric and topological features that can reveal algebraic information about the group itself. |
| + | In this talk, first we will discuss the general theory and present classical examples of limit sets, including some simple fractals (Cantor set, Sierpinski carpet). Then, we will present the construction of groups whose limit set is a Pontryagin sphere. These groups are obtained as reflection groups, and the construction is based on the existence of certain right-angled hyperbolic polyhedra. This is joint work with S. Douba, G.-S. Lee, and L. Marquis. \\ </WRAP> | ||
| - | * **September 25th** \\ Speaker: ** ** \\ Title: ** ** <WRAP box>// Abstract: // \\ </WRAP> | + | * **October 9th** \\ Speaker: ** Liam Keenan (Brown) ** \\ Title: ** On products of skeleta ** <WRAP box>// Abstract: // Given simplicial complexes, X and Y, a classical result of Eilenberg and Zilber tells us that the complex of integral chains on the product, X x Y, is quasi-isomorphic to the tensor product of complexes associated to X and Y. Their result relies on the basic observation that the product of an n-simplex with an m-simplex, can be built by gluing together simplices of dimension (n+m). Remarkably, this basic observation has much farther reaching-consequences than one might expect. In joint work with Maximilien Peroux, we showed that whenever you have two objects, X and Y, built up out of simplicies, the skeletal filtrations of X and Y can always be related to the skeletal filtration of X x Y, in an entirely canonical fashion. I will introduce this circle of ideas, explain my work with Peroux, and discuss its relation with the Dold-Kan correspondence. \\ </WRAP> |
| - | * **October 2nd** \\ No seminar \\ | + | * **October 14th (Tuesday 1:30-2:30pm -- cross-listed from the [[https://www2.math.binghamton.edu/p/seminars/comb/start|Combinatorics Seminar]])** \\ Speaker: ** Lee Kennard (Syracuse) ** \\ Title: ** Regular Matroids and Torus Representations ** <WRAP box>// Abstract: // Recent work with Michael Wiemeler and Burkhard Wilking presents a link between arbitrary finite graphs and torus representations all of whose isotropy groups are connected. The link is via combinatorial objects called regular matroids, which were classified in 1980 by Paul Seymour. We then apply Seymour’s deep result to classify and to compute geometric invariants of this class of torus representations. |
| + | The applications to geometry are significant. A highlight of our analysis of these representations is the first proof of Hopf’s 1930s Euler Characteristic Positivity Conjecture for metrics invariant under a torus action where the torus rank is independent of the manifold dimension. \\ </WRAP> | ||
| - | * **October 9th** \\ Speaker: ** Liam Keenan (Brown University) ** \\ Title: ** ** <WRAP box>// Abstract: // \\ </WRAP> | + | * **October 16th** \\ Speaker: ** John Abou-Rached (Binghamton) ** \\ Title: ** Integral models for non-Shimura curves and the Eichler-Shimura congruence relation ** <WRAP box>// Abstract: // We construct integral models for an infinite family of algebraic curves that includes noncongruence modular curves, as well as curves whose uniformizers are non-arithmetic Fuchsian groups. Most of these curves are not Shimura curves. We affirm a conjecture of Mukamel that the set of primes of good reduction of such curves have arithmetic significance and obtain an explicit description of this set. We conjecture that a version of Deligne-Rapoport's study of the reduction of modular curves holds in this context, and conjecture that a version of the Eichler-Shimura congruence relation holds in this setting, in resonance with Shimura curves. \\ </WRAP> |
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| - | * **October 16th** \\ Speaker: ** ** \\ Title: ** ** <WRAP box>// Abstract: // \\ </WRAP> | + | |
| * **October 23th** \\ Speaker: ** ** \\ Title: ** ** <WRAP box>// Abstract: // \\ </WRAP> | * **October 23th** \\ Speaker: ** ** \\ Title: ** ** <WRAP box>// Abstract: // \\ </WRAP> | ||
| - | * **October 30th** \\ Speaker: ** ** \\ Title: ** ** <WRAP box>// Abstract: // \\ </WRAP> | + | * **October 30th** \\ Speaker: ** Tam Cheetham-West (Yale) ** \\ Title: ** ** <WRAP box>// Abstract: // \\ </WRAP> |
| - | * **November 6th** \\ Speaker: ** Genevieve Walsh (Tufts University) ** \\ Title: ** ** <WRAP box>// Abstract: // \\ </WRAP> | + | * **November 6th** \\ Speaker: ** Genevieve Walsh (Tufts) ** \\ Title: ** ** <WRAP box>// Abstract: // \\ </WRAP> |
| * **November 13th** \\ Speaker: ** Maximilien Peroux (Michigan State University) ** \\ Title: ** ** <WRAP box>// Abstract: // \\ </WRAP> | * **November 13th** \\ Speaker: ** Maximilien Peroux (Michigan State University) ** \\ Title: ** ** <WRAP box>// Abstract: // \\ </WRAP> | ||
seminars/topsem.1758124454.txt · Last modified: 2025/09/17 11:54 by malkiewich