Seminars and Colloquia by Series

Tuesday, June 20, 2017 - 14:05 , Location: Skiles 006 , Dan Margalit and Justin Lanier , Georgia Tech , Organizer: Justin Lanier
We give a simple geometric criterion for an element to normally generate the mapping class group of a surface. As an application of this criterion, we show that when a surface has genus at least 3, every periodic mapping class except for the hyperelliptic involution normally generates. We also give examples of pseudo-Anosov elements that normally generate when genus is at least 2, answering a question of D. Long.
Monday, May 8, 2017 - 14:00 , Location: Skiles 006 , Tye Lidman , NCSU , Organizer: Jennifer Hom
We will discuss a relation between some notions in three-dimensional topology and four-dimensional aspects of knot theory.
Monday, April 24, 2017 - 14:30 , Location: UGA Room 303 , Alexandru Oancea and Basak Gurel , Jussieu and University of Central Florida , Organizer: Caitlin Leverson
Alexandru Oancea: Title: Symplectic homology for cobordisms Abstract: Symplectic homology for a Liouville cobordism - possibly filled at the negative end - generalizes simultaneously the symplectic homology of Liouville domains and the Rabinowitz-Floer homology of their boundaries. I will explain its definition, some of its properties, and give a sample application which shows how it can be used in order to obstruct cobordisms between contact manifolds. Based on joint work with Kai Cieliebak and Peter Albers. Basak Gürel: Title: From Lusternik-Schnirelmann theory to Conley conjecture Abstract: In this talk I will discuss a recent result showing that whenever a closed symplectic manifold admits a Hamiltonian diffeomorphism with finitely many simple periodic orbits, the manifold has a spherical homology class of degree two with positive symplectic area and positive integral of the first Chern class. This theorem encompasses all known cases of the Conley conjecture (symplectic CY and negative monotone manifolds) and also some new ones (e.g., weakly exact symplectic manifolds with non-vanishing first Chern class). The proof hinges on a general Lusternik–Schnirelmann type result that, under some natural additional conditions, the sequence of mean spectral invariants for the iterations of a Hamiltonian diffeomorphism never stabilizes. Based on joint work with Viktor Ginzburg.
Monday, April 17, 2017 - 14:05 , Location: Skiles 006 , Chaohui Zhang , Morehouse College , Organizer: Dan Margalit
Let S be a Riemann surface of type (p,1), p > 1.  Let f be a point-pushing pseudo-Anosov map of S.  Let t(f) denote the translation length of f on the curve complex for S.  According to Masur-Minsky, t(f) has a uniform positive lower bound c_p that only depends on the genus p.Let F be the subgroup of the mapping class group of S consisting of point-pushing mapping classes.  Denote by L(F) the infimum of t(f) for f in F pseudo-Anosov.  We know that L(F) is it least c_p.  In this talk we improve this result by establishing the inequalities .8 <= L(F) <= 1 for every genus p > 1. 
Friday, April 14, 2017 - 14:00 , Location: Skiles 006 , Henry Segerman , Oklahoma State University , Organizer: John Etnyre
This is joint work with Hyam Rubinstein. Matveev and Piergallini independently show that the set of triangulations of a three-manifold is connected under 2-3 and 3-2 Pachner moves, excepting triangulations with only one tetrahedron. We give a more direct proof of their result which (in work in progress) allows us to extend the result to triangulations of four-manifolds.
Wednesday, April 12, 2017 - 14:05 , Location: Skiles 006 , Jean Gutt , UGA , Organizer: Caitlin Leverson
I will present the recent result with P.Albers and D.Hein that every graphical hypersurface in a prequantization bundle over a symplectic manifold M pinched between two circle bundles whose ratio of radii is less than \sqrt{2} carries either one short simple periodic orbit or carries at least cuplength(M)+1 simple periodic Reeb orbits.
Monday, April 10, 2017 - 14:00 , Location: Skiles 006 , Peter Lambert-Cole , Indiana University , Organizer: John Etnyre
A foundational result in the study of contact geometry and Legendrian knots is Eliashberg and Fraser's classification of Legendrian unknots They showed that two homotopy-theoretic invariants - the Thurston-Bennequin number and rotation number - completely determine a Legendrian unknot up to isotopy. Legendrian spatial graphs are a natural generalization of Legendrian knots.  We prove an analogous result for planar Legendrian graphs. Using convex surface theory, we prove that the rotation invariant and Legendrian ribbon are a complete set of invariants for planar Legendrian graphs. We apply this result to completely classify planar Legendrian embeddings of the Theta graph. Surprisingly, this classification shows that Legendrian graphs violate some proven and conjectured properties of Legendrian knots. This is joint work with Danielle O'Donnol.​​
Monday, April 3, 2017 - 16:30 , Location: Skiles 006 , Sarah Rasmussen , University of Cambridge , Organizer: Caitlin Leverson
Exploring when a closed oriented 3-manifold has vanishing reduced Heegaard Floer homology---hence is a so-called L-space---lends insight into the deeper question of how Heegaard Floer homology can be used to enumerate and classify interesting geometric structures.  Two years ago, J. Rasmussen and I developed a tool to classify the L-space Dehn surgery slopes for knots in 3-manifolds, and I later built on these methods to classify all graph manifold L-spaces.  After briefly discussing these tools, I will describe my more recent computation of the region of rational L-space surgeries on any torus-link satellite of an L-space knot, with a result that precisely extends Hedden’s and Hom’s analogous result for cables.  More generally, I will discuss the region of L-space surgeries on iterated torus-link satellites and algebraic link satellites, along with implications for conjectures involving co-oriented taut foliations and left-orderable fundamental groups. 
Monday, April 3, 2017 - 15:15 , Location: Skiles 006 , Jo Nelson , Barnard College, Columbia University , Organizer: Caitlin Leverson
I will discuss joint work with Hutchings which gives a rigorousconstruction of cylindrical contact homology via geometric methods. Thistalk will highlight our use of non-equivariant constructions, automatictransversality, and obstruction bundle gluing. Together these yield anonequivariant homological contact invariant which is expected to beisomorphic to SH^+ under suitable assumptions. By making use of familyFloer theory we obtain an S^1-equivariant theory defined with coefficientsin Z, which when tensored with Q recovers the classical cylindrical contacthomology, now with the guarantee of well-definedness and invariance. Thisintegral lift of contact homology also contains interesting torsioninformation.
Monday, April 3, 2017 - 14:00 , Location: Skiles 006 , Josh Greene , Boston College , Organizer: John Etnyre
I will describe a diagrammatic classification of (1,1) knots in S^3 and lens spaces that admit non-trivial L-space surgeries. A corollary of the classification is that 1-bridge braids in these manifolds admit non-trivial L-space surgeries. This is joint work with Sam Lewallen and Faramarz Vafaee.

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