Title: TBA

Abstract: TBA

Title: ADE links and cyclic branched covers

Abstract: The Dynkin diagrams of types A,D and E arise in many classification problems in mathematics. We conjecture a modest addition to this list: the fibered links that induce the standard tight contact structure on S3 and have some cyclic branched cover an L-space. We will discuss progress towards a proof of this conjecture. This is joint work with Michel Boileau and Steve Boyer.

Title : Cyclic branched covers and the L-space conjecture

Abstract : We survey what is known about the L-space conjecture for manifolds obtained as cyclic branched covers of links in the 3-sphere and report, in particular, on joint work with Michel Boileau and Cameron Gordon and with Ying Hu.

Title: Euler class and taut foliations on surgered 3-manifolds

Abstract. This talk is motivated by the conjecture: the fundamental group of a QHS is left-orderable if and only if it admits a co-orientable taut foliation. It is known that if the Euler class of the taut foliation vanishes, then the fundamental group is left-orderable. In this talk, we will investigate the Euler class of co-orientable taut foliations on 3- manifolds which are obtained by Dehn surgery along a null-homologous knot.

Title: Distortion and the Bridge Distance of Knots

Title: Homology directions and veering triangulations

Abstract: The cone over a fibered face of a hyperbolic 3-manifold has a nice characterization as the dual of the so-called cone of homology directions of a certain pseudo-Anosov flow. We give a new characterization of this cone of homology directions in terms of Agols veering triangulations.

Title: Invariants of tangles from the Fukaya category of the 4-punctured sphere

Abstract: I will discuss a reinterpretation of Bar-Natans description of Khovanov homology in terms of immersed curves in the 4-punctured sphere. This point of view has some interesting algebraic consequences; the talk will focus on examples.

This is joint work with Artem Kotelskiy and Claudius Zibrowius.

Title: Taut foliations and Seiberg-Witten invariants

Title of talk: The Total Curvature and Betti Numbers of Complex Projective Manifolds

Abstract: We will prove an inequality between the total curvature of a complex projective manifold and the sum of its Betti numbers, and we will characterize the complex projective manifolds whose total curvature is minimal. These results extend the classical theorems of Chern and Lashof to complex projective space. As we prove these results, we will discuss several possible directions for future work.

What, where, when

Every year, UGA Department of Mathematics and Math Club hold an annual High School Varsity Math Tournament on the UGA campus, to foster the mathematical education in Georgia and neighboring states. The tournament consists of three challenging rounds: ciphering, written and team collaboration.

2019 Tournament

The 2019 tournament will be held on Saturday, October 26, 2019.