seminars:topsem
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seminars:topsem [2026/02/26 16:27] malkiewich Wang TA |
seminars:topsem [2026/03/04 16:21] (current) malkiewich Mann date |
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| Recently, Stover and Toledo proved that analogous complex hyperbolic branched cover manifolds exist. They also proved that these manifolds do not admit a locally symmetric metric, and a result of Zheng shows that these manifolds are Kahler. In this talk I will present recent work proving the existence of pinched negatively curved metrics, as well as the existence of negatively curved Kahler-Einstein metrics (due to Guenancia and Hamenstadt) on these complex hyperbolic branched cover manifolds. Part of my presented work is joint with Lafont. \\ </WRAP> | Recently, Stover and Toledo proved that analogous complex hyperbolic branched cover manifolds exist. They also proved that these manifolds do not admit a locally symmetric metric, and a result of Zheng shows that these manifolds are Kahler. In this talk I will present recent work proving the existence of pinched negatively curved metrics, as well as the existence of negatively curved Kahler-Einstein metrics (due to Guenancia and Hamenstadt) on these complex hyperbolic branched cover manifolds. Part of my presented work is joint with Lafont. \\ </WRAP> | ||
| - | * **February 12th** \\ Speaker: ** ** \\ Title: ** ** <WRAP box>// Abstract: // \\ </WRAP> | + | * **February 12th** \\ Speaker: ** Francis Wagner (Cornell University) ** \\ Title: ** Isoperimetric functions and the Word Problem ** <WRAP box>// Abstract: // A fundamental algorithmic question in group theory is the Word Problem for finitely generated groups, which asks whether there exists an algorithm to decide whether two words on the generators represent the same group element. A related notion is the Dehn function of a finitely presented group, the smallest isoperimetric function of the presentation's Cayley complex. While the Dehn function gives an upper bound for the complexity of the Word Problem for that group, this bound is only meaningful in the class of finitely presented groups and is very far from sharp even in this class. We resolve this disconnect by instead considering the Dehn functions of the finitely presented groups into which a group embeds, demonstrating a refinement of the Higman embedding theorem that gives a potentially quasi-optimal bound on the Dehn function of the ambient group. \\ </WRAP> |
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| * **February 19th** \\ Speaker: ** Satya Howladar (University of Florida) ** \\ Title: ** Gromov’s Conjecture for Product of Baumslag-Solitar Groups and some other One relator groups ** <WRAP box>// Abstract: // Gromov introduced macroscopic dimension of metric spaces in order to study large scale properties of manifolds. He conjectured that a closed $n$-manifold which admits Positive Scaler Curvature metric, should have its universal cover to be of macroscopic dimension at most $n-2$, with respect to the pull back metric on it. This conjecture depends a lot on the fundamental group of the base manifold. For $n>4$, closed spin $n$-manifolds $M$, we developed sufficient condition on $\pi_1(M)$, to verify the conjecture. When $\pi_1(M)$ is product of $2$-dimensional groups (i.e. groups with classifying space a $2$-dimensional CW complex), $\mathbb Z_2$-summands in their homology creates a problem for application of our technique. We could resolve this in the case of certain one-relator groups, including Baumslag-Solitar, and certain others, by passing to some finite index subgroup of them not admitting $\mathbb Z_2$-torsion in homology. This is done by the well-known technique of Fox calculus, to analyze boundary maps of cells of finite index covers. I will try to revisit this technique and sketch a proof our result. \\ </WRAP> | * **February 19th** \\ Speaker: ** Satya Howladar (University of Florida) ** \\ Title: ** Gromov’s Conjecture for Product of Baumslag-Solitar Groups and some other One relator groups ** <WRAP box>// Abstract: // Gromov introduced macroscopic dimension of metric spaces in order to study large scale properties of manifolds. He conjectured that a closed $n$-manifold which admits Positive Scaler Curvature metric, should have its universal cover to be of macroscopic dimension at most $n-2$, with respect to the pull back metric on it. This conjecture depends a lot on the fundamental group of the base manifold. For $n>4$, closed spin $n$-manifolds $M$, we developed sufficient condition on $\pi_1(M)$, to verify the conjecture. When $\pi_1(M)$ is product of $2$-dimensional groups (i.e. groups with classifying space a $2$-dimensional CW complex), $\mathbb Z_2$-summands in their homology creates a problem for application of our technique. We could resolve this in the case of certain one-relator groups, including Baumslag-Solitar, and certain others, by passing to some finite index subgroup of them not admitting $\mathbb Z_2$-torsion in homology. This is done by the well-known technique of Fox calculus, to analyze boundary maps of cells of finite index covers. I will try to revisit this technique and sketch a proof our result. \\ </WRAP> | ||
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| - | * **March 19th** \\ Speaker: ** Francesco Lin (Columbia) ** \\ Title: ** ** <WRAP box>// Abstract: // \\ </WRAP> | + | * **March 19th** \\ Speaker: ** Francesco Lin (Columbia) ** \\ Title: ** Coexact 1-form spectral gaps of hyperbolic rational homology spheres ** <WRAP box>// Abstract: // The spectral gap of the Hodge Laplacian of functions (or, |
| + | equivalently, exact 1-forms) is a very well-studied fundamental | ||
| + | quantity associated to a hyperbolic three-manifold. In recent years, | ||
| + | the problem of understanding its counterpart on coexact 1-forms has | ||
| + | also spurred a lot of activity because of its relation with questions | ||
| + | in number theory and low-dimensional topology. In this talk, after | ||
| + | introducing the geometric setup and highlighting some fundamental | ||
| + | differences between these two quantities, I will focus on some | ||
| + | structural properties of the set of coexact 1-form spectral gaps of | ||
| + | hyperbolic rational homology spheres. In particular, I will discuss a | ||
| + | construction that allows to determine somewhat explicitly some | ||
| + | interesting accumulation points of the set of such spectral gaps. This | ||
| + | is joint work with M. Lipnowski. \\ </WRAP> | ||
| - | * **March 26th** \\ Speaker: ** ** \\ Title: ** ** <WRAP box>// Abstract: // \\ </WRAP> | + | * **March 26th** \\ Speaker: ** Varinderjit Mann (Cornell University) ** \\ Title: ** ** <WRAP box>// Abstract: // \\ </WRAP> |
| * **April 2nd** <WRAP box>// // (Spring break - no seminar) \\ </WRAP> | * **April 2nd** <WRAP box>// // (Spring break - no seminar) \\ </WRAP> | ||
seminars/topsem.1772141227.txt · Last modified: 2026/02/26 16:27 by malkiewich