The GT seminar meets on Fridays at 2:00pm Fridays in room 520. We also have an overflow room 622 from 11 to 1 Fridays for additional talks.

Organizer: Walter Neumann.

Other
area seminars. Our e-mail
list. Archive of previous semesters

## Spring 2019

Date | Speaker | Title |
---|---|---|

Jan 25 | Khalid Bou-Rabee, CUNY | On local residual finiteness of abstract commensurators of Fuchsian groups |

Feb 1 | David Futer, Temple | Effective theorems in hyperbolic Dehn surgery |

Feb 8 | Aaron Calderon, Yale | Mapping class groups and deformations of flat surfaces |

Feb 15 | Tarik Aougab, Brown | Origamis from minimally intersecting filling pairs |

Feb 22 | Hongbin Sun, Rutgers | A characterization of separable subgroups of 3-manifold groups |

Mar 1 | Rose Morris-Wright, Brandeis | Infinite Type Artin Groups and the Clique-Cube Complex |

Mar 8 | Jenja Sapir, Binghamton | TBA |

Mar 15 | Tim Susse | TBA |

Mar 29 | Ronno Das, Chicago | Points and lines on cubic surfaces |

Apr 5 | Caroline Abbott | TBA |

Apr 12 | Oishee Banerjee, Chicago | TBA |

Apr 19 | Laure Flapan, Northeastern | TBA |

Apr 26 | Daryl Cooper, UCSB | The Moduli Space of Generalized Cusps in Real Projective Manifolds |

May 3 | Shea Vela-Vick, LSU | TBA |

## Abstracts

**Khalid Bou-Rabee**, CUNY

January 25

**Title**: On local residual finiteness of abstract commensurators of Fuchsian groups

**Abstract**: The abstract commensurator (aka ``virtual automorphisms'') of a group encodes ``hidden
symmetries'', and is a natural generalization of the automorphism group. In this talk, I
will give an introduction to these mysterious and classical groups and then discuss their
residual finiteness. Recall that residual finiteness is a property enjoyed by linear groups
(by A. I. Malcev), mapping class groups of closed oriented surfaces (by EK Grossman), and
branch groups (by definition!). Moreover, by work of Armand Borel, Gregory Margulis, G. D.
Mostow, and Gopal Prasad, the abstract commensurator of any irreducible lattice in any
``nice enough'' semisimple Lie group is locally residually finite (a property is termed
``local'' if it is satisfied by every finitely generated subgroup of the group). ``Nice
enough'' is sufficiently broad that the only remaining unknown case is PSL_2(R). Are
abstract commensurators of lattices in PSL_2(R) locally residually finite? Lattices here
are commensurable with either a free group of rank 2 or the fundamental group of an
oriented surface of genus 2. I will present a complete answer to this decades old question
with a proof that is computer-assisted. Our answer and methods open up new questions and
research directions, so graduate students are especially encouraged to attend. This talk
covers joint work with Daniel Studenmund.

**David Futer**, Temple

February 1

**Title**: Effective theorems in hyperbolic Dehn surgery

**Abstract**: I will discuss two effective results about hyperbolic Dehn surgery. The first result is
about with cosmetic surgery: namely, distinct long Dehn fillings on a cusped manifold cannot
yield the same closed 3-manifold. The second result says that long Dehn fillings yield closed
3-manifolds with large Margulis numbers. These results are effective in the sense that all
hypotheses and conclusions (such as ``long'' and ``large'') are explicitly quantified. This is joint
work with Jessica Purcell and Saul Schleimer.

**Aaron Calderon**, Yale

February 8

**Title**: Mapping class groups and deformations of flat surfaces

**Abstract**:
Flat cone metrics on surfaces (often in the guise of translation
surfaces or holomorphic differentials) are a fundamental object of
study in Teichmueller theory, billiard dynamics, and complex
geometry. Fixing the number and angle of the cone points defines a
natural subvariety of the moduli space of flat surfaces called a
stratum, the global topology of which is quite enigmatic. In this
talk, I will explain which mapping classes are realized by
deformations contained in these strata, and how this result can be
applied to classify the connected components of Teichmueller spaces of
flat cone metrics.

**Tarik Aougab**, Brown

Feb 15

**Title**: Origamis from minimally intersecting filling pairs

**Abstract**: We consider square-tiled surfaces arising from pairs of simple closed curves on a surface of genus g with a single disk in the complement of their union. Our goal is to construct many
such surfaces up to the action of the mapping class group. We'll describe two constructions (one topological and one more combinatorial) which can be used to produce factorially many (in genus)
of these surfaces, improving dramatically over a previous result of the author and Huang. This represents joint work with Menasco and Nieland.

**Hongbin Sun**, Rutgers

February 22

**Title**: A characterization of separable subgroups of 3-manifold groups

**Abstract**: The subgroup separability is a property in group theory that is closely related to low dimensional topology, especially lifting \pi_1-injective
immersed objects in a space to be embedded in some finite cover and the virtual Haken conjecture of 3-manifolds resolved by Agol. We give a complete
characterization on which finitely generated subgroups of finitely generated 3-manifold groups are separable. Our characterization generalizes Liu's
spirality character on \pi_1-injective immersed surface subgroups of closed 3-manifold groups. A consequence of our characterization is that, for any
compact, orientable, irreducible and boundary-irreducible 3-manifold M with nontrivial torus decomposition, \pi_1(M) is LERF if and only if for any two
adjacent pieces in the torus decomposition of M, at least one of them has a boundary component with genus at least 2.

**Rose Morris-Wright**, Brandeis

March 1

**Title**: Infinite Type Artin Groups and the Clique-Cube Complex

**Abstract**: Artin groups form a large class of groups including braid groups,
free groups, and free abelian groups. Unlike their well understood cousins,
Coxeter groups, many basic questions about the properties of Artin groups
remain open. In this talk, I will discuss some of these open questions. Then
I will introduce the clique-cube complex, a CAT(0) cube complex constructed
from a given Artin group. I will discuss some of the properties of this cube
complex, as well as how it can be used to show that a large class of Artin
groups have trivial center and are acylindrically hyperbolic. This is joint
work with Ruth Charney.

**Jenja Sapir**, Binghamton

March 8

**Title**: TBA

**Abstract**: TBA

**Tim Susse**,

March 15

**Title**: TBA

**Abstract**

**Ronno Das**, Chicago

March 29

**Title**: Points and lines on cubic surfaces

**Abstract**:
The Cayley-Salmon theorem states that every smooth cubic surface S in
CP^3 has exactly 27 lines. Their proof is that marking a line on each
cubic surface produces a 27-sheeted cover of the moduli space M of
smooth cubic surfaces. Similarly, marking a point produces a
'universal family' of cubic surfaces over M. One difficulty in
understanding these spaces is that they are complements in affine
space of incredibly singular hypersurfaces. In this talk I will
explain how to compute the rational cohomology of these spaces. I'll
then explain how these purely topological theorems have (via the
machinery of the Weil Conjectures) purely arithmetic consequences: the
typical smooth cubic cubic surface over a finite field F_q contains 1
line and q^2 + q + 1 points.

**Caroline Abbott**,

April 5

**Title**: TBA

**Abstract**

**Oishee Banerjee**, Chicago

April 12

**Title**: TBA

**Abstract**: TBA

**Daryl Cooper**, UCSB

April 26

**Title**: The Moduli Space of Generalized Cusps in Real Projective Manifolds

**Abstract**: In the study of hyperbolic 3-manifolds cusps play an important role. The geometry of a cusp is determined by a similarity
structure on the boundary of the cusp. In the finite volume case, the boundary is a torus and the similarity structure is determined by a
complex number with positive imaginary part. Properly-convex real-projective manifolds are a generalization of hyperbolic manifolds. In
dimension 3 the moduli space of generalized cusps is a bundle over the space of similarity structures on the torus, with fiber a subspace of
the space of (real) cubic differentials. Conjecturally a similar statement is true in all dimensions for cusps with compact boundary. There
is a 9-dimensional cusp with fundamental group the integer Heisenberg group, and the classification of cusps with non-compact boundary is
unknown. Joint: Sam Ballas, Arielle Leitner.

**Laure Flapan**, Northeastern

April 19

**Title**: TBA

**Abstract**

**Shea Vela-Vick**, LSU

May 3

**Title**: TBA

**Abstract**: TBA

# Other relevant information.

## Previous semesters:

Fall 2018, Spring 2018, Fall 2017, Spring 2017, Fall 2016, Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, 2010/11, Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007, Spring 2007, Fall 2006.## Other area seminars.

- Columbia Symplectic Geometry/Gauge Theory Seminar
- All Columbia Math Dept Seminars
- CUNY Geometry and Topology Seminar
- CUNY Complex Analysis & Dynamics Seminar
- CUNY Magnus Seminar
- Princeton Topology Seminar.