Seminars, Colloquia, and Conferences
Geometric Group Theory and Topology Seminar
Geometric group theory and topology (GGTT) at Tufts includes
topics in geometric topology (especially in dimensions 2 and 3) and
the geometry of finitely generated groups. Areas of interest include
hyperbolicity and metric nonpositive curvature, braids and mapping
class groups, lattices and buildings, dynamics of group actions, and
asymptotic geometry.
The seminar meets weekly on Tuesdays at 4:30pm unless otherwise noted, in
Room 404, 574 Boston Ave.
This building is at the corner of Boston and Harvard. There is visitor parking in the lot on Boston Ave.
The Harvard Ave. door requires a Tufts University ID to open, the Boston Ave. (parking lot) door stays open until 5 pm.
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Spring 2016
February 2, 2016
A factorization theorem for Fuchsian groups
Hao Liang
(Tufts University)
Abstract:
A MakaninRazborov diagram (MRdiagram) for \(\Gamma\) is an important tool for understanding
sets of the form \(Hom(G, \Gamma)\). I will talk about a factorization theorem of Fuchsian groups,
which is a key step in the construction of the MRdiagram for Fuchsian groups. The proof uses ideas
from the construction of MRdiagrams for free groups.
February 18, 2016
*Thursday Talk  Room 202, 574 Boston Ave.
No finite index subgroup of a mapping class group embeds into the C^2 circle diffeomorphism group
Sanghyun Kim (Seoul National University)
Abstract:
One intriguing direction of research in surface theory is the analogy between mapping class groups
and higher rank lattices. However, current knowledge on finite index subgroups of mapping class
groups are still scarce. We prove the result in the title, which was originally asked by Farb,
and which is analogous to Ghys and BurgerMonod theorem on obstructions of higher rank lattice
actions on the circle. (Joint work with Hyungryul Baik and Thomas Koberda.)
February 23, 2016
Morse broken trajectories and hyperbolic volume
Hannah Alpert
(MIT)
Abstract:
A large family of theorems all state that if a space is topologically complex,
then the functions on that space must express that complexity, for instance by having many
singularities. For the theorem in this talk, our preferred measure of topological complexity
is the hyperbolic volume of a closed manifold admitting a hyperbolic metric (or more generally,
the Gromov simplicial volume of any space). A Morse function on a manifold with large
hyperbolic volume may still not have many critical points, but we show that there must
be many flow lines connecting those few critical points. Specifically, given a closed
\(n\)dimensional manifold and a MorseSmale function, the number of \(n\)part broken trajectories
is at least the Gromov simplicial volume. To prove this we adapt lemmas of Gromov that bound
the simplicial volume of a stratified space in terms of the complexity of the stratification.
A notable corollary: every Morse function on a closed hyperbolic manifold must have a critical
point of every index.
March 15, 2016
Intersections in the character variety of knot complements
Michelle Chu (University of Texas)
Abstract:
I will describe the \(SL_2(\mathbb{C})\) character variety for a family of two
bridge knot groups. In particular, these character varieties will have multiple
components which intersect at points associated to essential surfaces in the knot
complements. Along the way I will discuss how certain points in the character
variety are associated to splittings of the fundamental group via actions on trees.
March 29, 2016
*BromfieldPearson 6
Curves on hyperbolic surfaces
Viveka Erlandsson (Fribourg)
and
Coloring curves on surfaces
Nick Vlamis (Michigan)
Abstract:
Curves on hyperbolic surfaces
Viveka Erlandsson (Fribourg)
In this talk I will discuss the growth of the number of closed geodesics
of bounded length, as the length grows. More precisely, let \(c\) be a
closed curve on a hyperbolic surface \(S=S(g,n)\) and let \(N_c(L)\) denote
the number of curves in the mapping class orbit of \(c\) with length bounded
by \(L\). Due to Mirzakhani it is known that in the case that \(c\) is simple
this number is asymptotic to \(L^{6g6+2n}\). Here we consider the case when \(c\)
is an arbitrary closed curve, i.e. not necessarily simple. This is joint work with
Juan Souto.
April 19, 2016
Effective characterization of Morse geodesics and stable subgroups
Tarik Aougab (Brown)
Friday, April 29, 2016 — Department colloquium
*BromfieldPearson 101  4:005:00pm
Groups acting on the circle: Dynamics and topology
Katie Mann
(Berkeley)
The seminar organizer for Spring 2016 is
Genevieve Walsh.
GGTT Seminar archive >
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