Difference between revisions of "Geometry and Topology Seminar"
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We will show how the first Betti number of a compact free boundary minimal hypersurface in an domain whose boundary satisfies weak convexity assumptions is controlled effectively by the Morse index of this hypersurface viewed as a critical point of the area functional (joint with A. Carlotto and B. Sharp). Among such domains, the unit three-ball is particularly interesting, as it contains many free boundary minimal surfaces, which one would like to classify. In particular, we will explain how to characterise the critical catenoid in terms of a pinching condition on the second fundamental form (joint with I. Nunes). | We will show how the first Betti number of a compact free boundary minimal hypersurface in an domain whose boundary satisfies weak convexity assumptions is controlled effectively by the Morse index of this hypersurface viewed as a critical point of the area functional (joint with A. Carlotto and B. Sharp). Among such domains, the unit three-ball is particularly interesting, as it contains many free boundary minimal surfaces, which one would like to classify. In particular, we will explain how to characterise the critical catenoid in terms of a pinching condition on the second fundamental form (joint with I. Nunes). | ||
+ | |||
+ | ===Paul Feehan=== | ||
+ | "TBA" | ||
===Rafael Montezuma=== | ===Rafael Montezuma=== |
Revision as of 07:49, 20 February 2017
The Geometry and Topology seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.
For more information, contact Alexandra Kjuchukova or Lu Wang .
Contents
Spring 2017
date | speaker | title | host(s) | |
---|---|---|---|---|
Jan 20 | Carmen Rovi (University of Indiana Bloomington) | "The mod 8 signature of a fiber bundle" | Maxim | |
Jan 27 | ||||
Feb 3 | Rafael Montezuma (University of Chicago) | "Metrics of positive scalar curvature and unbounded min-max widths" | Lu Wang | |
Feb 10 | ||||
Feb 17 | Yair Hartman (Northwestern University) | "Intersectional Invariant Random Subgroups and Furstenberg Entropy." | Dymarz | |
Feb 24 | Lucas Ambrozio (University of Chicago) | "Free boundary minimal hypersurfaces of Euclidean domains" | Lu Wang | |
March 3 | Mark Powell (Université du Québec à Montréal) | "Stable classification of 4-manifolds" | Kjuchukova | |
March 10 | Autumn Kent (Wisconsin) | Analytic functions from hyperbolic manifolds | local | |
March 17 | ||||
March 24 | Spring Break | |||
March 31 | Xiangwen Zhang (University of California-Irvine) | "TBA" | Lu Wang | |
April 7 | Paul Feehan (Rutgers) | "TBA" | Lu Wang | |
April 14 | Xianghong Gong (Wisconsin) | "TBA" | local | |
April 21 | Joseph Maher (CUNY) | "TBA" | Dymarz | |
April 28 | Bena Tshishiku (Harvard) | "TBA" | Dymarz | |
Spring Abstracts
Lucas Ambrozio
"Free boundary minimal hypersurfaces of Euclidean domains"
We will show how the first Betti number of a compact free boundary minimal hypersurface in an domain whose boundary satisfies weak convexity assumptions is controlled effectively by the Morse index of this hypersurface viewed as a critical point of the area functional (joint with A. Carlotto and B. Sharp). Among such domains, the unit three-ball is particularly interesting, as it contains many free boundary minimal surfaces, which one would like to classify. In particular, we will explain how to characterise the critical catenoid in terms of a pinching condition on the second fundamental form (joint with I. Nunes).
Paul Feehan
"TBA"
Rafael Montezuma
"Metrics of positive scalar curvature and unbounded min-max widths"
In this talk, I will construct a sequence of Riemannian metrics on the three-dimensional sphere with scalar curvature greater than or equal to 6, and arbitrarily large min-max widths. The search for such metrics is motivated by a rigidity result of min-max minimal spheres in three-manifolds obtained by Marques and Neves.
Carmen Rovi
The mod 8 signature of a fiber bundle
In this talk we shall be concerned with the residues modulo 4 and modulo 8 of the signature of a 4k-dimensional geometric Poincare complex. I will explain the relation between the signature modulo 8 and two other invariants: the Brown-Kervaire invariant and the Arf invariant. In my thesis I applied the relation between these invariants to the study of the signature modulo 8 of a fiber bundle. In 1973 Werner Meyer used group cohomology to show that a surface bundle has signature divisible by 4. I will discuss current work with David Benson, Caterina Campagnolo and Andrew Ranicki where we are using group cohomology and representation theory of finite groups to detect non-trivial signatures modulo 8 of surface bundles.
Yair Hartman
"Intersectional Invariant Random Subgroups and Furstenberg Entropy."
In this talk I'll present a joint work with Ariel Yadin, in which we solve the Furstenberg Entropy Realization Problem for finitely supported random walks (finite range jumps) on free groups and lamplighter groups. This generalizes a previous result of Bowen. The proof consists of several reductions which have geometric and probabilistic flavors of independent interests. All notions will be explained in the talk, no prior knowledge of Invariant Random Subgroups or Furstenberg Entropy is assumed.
Bena Tshishiku
"TBA"
Mark Powell
Stable classification of 4-manifolds
A stabilisation of a 4-manifold M is a connected sum of M with some number of copies of S^2 x S^2. Two 4-manifolds are said to be stably diffeomorphic if they admit diffeomorphic stabilisations. Since a necessary condition is that the fundamental groups be isomorphic, we study this equivalence relation for a fixed group. I will discuss recent progress in classifying 4-manifolds up to stable diffeomorphism for certain families of groups, arising from work with Daniel Kasprowski, Markus Land and Peter Teichner. As a by-product we also obtained a result on the analogous question with the complex projective plane CP^2 replacing S^2 x S^2.
Autumn Kent
Analytic functions from hyperbolic manifolds
At the heart of Thurston's proof of Geometrization for Haken manifolds is a family of analytic functions between Teichmuller spaces called "skinning maps." These maps carry geometric information about their associated hyperbolic manifolds, and I'll discuss what is presently known about their behavior. The ideas involved form a mix of geometry, algebra, and analysis.
Xiangwen Zhang
"TBA"
Archive of past Geometry seminars
2016-2017 Geometry_and_Topology_Seminar_2016-2017
2015-2016: Geometry_and_Topology_Seminar_2015-2016
2014-2015: Geometry_and_Topology_Seminar_2014-2015
2013-2014: Geometry_and_Topology_Seminar_2013-2014
2012-2013: Geometry_and_Topology_Seminar_2012-2013
2011-2012: Geometry_and_Topology_Seminar_2011-2012
2010: Fall-2010-Geometry-Topology