
Click here for the quicklook schedule. Monday9:00 Registration 9:15 Welcome/Overview: Dan Margalit and Panel 10:45 CV / Web / Teaching Statements Jen Taback and Dan Margalit 12:00 Lunch 2:00 Seminar: Dilatation vs selfintersection number for pointpushing pseudoAnosovs, Spencer Dowdall This talk is about the dilatations of pseudoAnosov mapping classes obtained by pushing a marked point around a filling curve. After reviewing this "pointpushing" construction, I will give both upper and lower bounds on the dilatation in terms of the selfintersection number of the filling curve. I'll also give bounds on the least dilatation of any pseudoAnosov in the pointpushing subgroup and describe the asymptotic dependence on selfintersection number. All of the upper bounds involve analyzing explicit examples using train tracks, and the lower bound is obtained by lifting to the universal cover and studying the images of simple closed curves. 4:30 Abstracts, Priyam Patel 3:00 Tea 3:30 Beamer / Inkscape, Spencer Dowdall
Tuesday9:00 Etiquette, Kevin Wortman and Dan Margalit10:30 Tea 10:45 Talks I, Moon Duchin and Kevin Wortman 12:00 Lunch 2:00 Job Process, Moon Duchin and Jen Taback 3:00 Tea 3:30 Seminar: Automorphisms of higher rank lamplighter groups, Jen Taback I will describe the geometry of the higher rank lamplighter groups, whose Cayley graph with respect to a specified generating set is a DiestelLeader graph. I will mention why DiestelLeader graphs are of independent interest, but mainly focus on how the algebra and geometry of the group interact to produce a perhaps unexpected result about possible automorphisms. 4:30 Student Talk: Constant Mean Curvature Surfaces of Revolution versus Willmore Surfaces of Revolution: A Comparative Study with Physical Applications, Thanuja Paragoda This work is concerened with some special types of surfaces of revolution and their real world applications. The main two cases hereby considered are the constant mean curvature surfaces of revolution (also called Delaunay surfaces) and Willmore’s surfaces of revolution, respectively. We present the original construction of Delaunay surfaces, based on roulettes of conics, after which we characterize these geometric objects as solutions to specific ODEs. We present a few physical models of Delaunay surfaces arising as liquid bridges between two vertical walls  which are proved to be unduloidal surfaces, by using Calculus of Variations. We numerically computed the profile curves of these surfaces and provided some numerical models for them. By contrast, we studied Willmore surfaces as minimizers of the Willmore energy (or bending energy). In particular, we have studied some Willmore surfaces of revolution which come in as solutions to BVP problems consisting of the Willmore equation, together with some special Dirichlet type boundary conditions. 5:00 Student Talk: Generalized northsouth dynamics on the space of geodesic currents, Caglar Uyanik The study of outer automorphism group of a free group $Out(F_N)$ is closely related to study of Mapping Class Groups. The $Out(F_N)$ analog of a pseudoAnosov homeomorphism is called a fully irreducible or iwip (short for irreducible with irreducible powers). We will talk about types of iwips, geometric and hyperbolic, and prove that any iwip $\phi$ acts on the space of geodesic currents with a certain kind of northsouth dynamics. As an application, we will give a criterion for subgroups of $Out(F_N)$ to contain a hyperbolic iwip. 5:30 Student Talk: Pointpushing and Nielsen realization, Bena Tshishiku Let M be a manifold with mapping class group Mod(M). Any subgroup G subset Mod(M) can be represented by a collection of diffeomorphisms that form a group up to isotopy. The Nielsen realization problem asks whether or not G can be represented by an honest subgroup of diffeomorphisms. We will discuss a special case of this problem when M is a locally symmetric manifold and G = pi_1(M) is the pointpushing subgroup. This generalizes work of BestvinaChurchSouto.
Wednesday9:00 Careers, Panel10:30 Tea 10:45 Habits, Ravi Vakil and Kirsten Wickelgren 12:00 Lunch 1:00 Seminar: Random functions on finite sets, Vincent Lucarelli The first part of this talk decribes employment opportunities for mathematicians at the National Security Agency, the agency's primary missions, and the worklife balance for government employees. The second part of the talk introduces random functions on finite sets, properties of these functions, and concludes with an application. 2:00 Seminar: Hyperboliclike geodesics, Ruth Charney What is the difference between geodesics in a negatively curved space and geodesics in a nonpositively curved space? We will explore this question and why it matters. 3:00 Tea 3:30 Colloquium: Cutting and pasting in algebraic geometry, Ravi Vakil Given some class of ``geometric spaces'', we can make a ring as follows.
The tea and colloquium will be held in the Clary Theater at the Student Success Center. 4:30 Publishing Moon Duchin and Ruth Charney 6:30 Pizzaque Thursday9:00 Student Talk: Legendrian Knots, Augmentations, and Rulings, Caitlin LeversonA Legendrian knot in R^3 with the standard contact structure is a knot for which dzydx=0. Given a Legendrian knot, one can associate the ChekanovEliashberg differential graded algebra (DGA) over Z/2, a Legendrian knot invariant. Fuchs and Sabloff showed there is a correspondence between augmentations to Z/2 of the DGA and rulings of the knot diagram. Etnyre, Ng, and Sabloff showed that one can define a lift of the ChekanovEliashberg DGA over Z/2 to a DGA over Z[t,t^{1}], which is also a Legendrian knot invariant. This talk will give an extension of the relationship between rulings and augmentations for the DGA over Z/2, to the DGA over Z[t,t^{1}]. 9:30 Student Talk: One sledgehammer, many mosquitos, Jeffrey Carlson Equivariant cohomology is a tool for studying group actions that has been around since the 1950s and engendered occasional revivals of interest due to discoveries in physics and symplectic geometry. To demonstrate its power, I use two major results, due to Borel and AtiyahBott/BerlineVergne, here to recover some classical theorems with substantially less work. 10:00 Student Talk: Small dilatation pseudoanosovs on nonorientable surfaces, Balazs Strenner We present an implementation of a search algorithm for pseudoanosov homeomorphisms that works on any (not necessarily oriented) punctured surface, and of McMullen's algorithm for computing Teichm\"{u}ller polynomials from pseudoanosovs. This code helps us find nonorientable 3manifolds whose fibrations give rise to minimal dilatation pseudoanosovs on nonorientable surfaces. 10:30 Tea 10:45 Writing grants/Research statements, Ruth Charney and Moon Duchin 12:00 Lunch 2:00 Talks II, Ruth Charney, Moon Duchin, and Dan Margalit 3:00 Tea 3:30 Seminar: Quantifying Finiteness Properties of Hyperbolic Surface Groups and 3Manifold Groups, Priyam Patel The fundamental groups of hyperbolic surfaces and 3manifolds, referred to as surface groups and 3manifold groups, respectively, have various algebraic finiteness properties. Two of these properties, residual finiteness and subgroup separability, have played an important role in the recent resolution of some outstanding conjectures in 3manifold theory. To begin this talk, we will define residual finiteness and subgroup separability. We will then explain what it means to quantify these properties and the topological implications of such quantifications. Focusing on residual finiteness in the surface case, we will emphasize the use of hyperbolic geometry in tackling quantification problems, and if time permits, we will describe related methods used in joint work with K. BouRabee and M.F. Hagen to generalize the results to hyperbolic 3manifolds. 4:30 Student Talk: The leftorderability and the cyclic branched coverings, Ying Hu We give a sufficient condition for the fundamental group of the $n^{th}$ cyclic branched covering of S^3 along a prime knot K to be leftorderable in terms of representations of the knot group. As an application, we show that for any $(p,q)$ twobridge knot, with p = 3 mod 4, there are only finitely many cyclic branched coverings whose fundamental groups are not leftorderable. This answers a question posed by Dabkowski, Przytycki and Togha. 5:00 Student Talk: Generalizing Geometric Identities on Moduli Space, Andrew Yarmola We will start by introducing the identities of McShane and Basmajan on the moduli space of a finite area hyperbolic surface with boundary. Labourie and McShane have recently discussed how the former generalizes to Hitchin representations of the fundamental group. We will discuss a close relationship between the two identities that allows us to extend Basmajan's identity in a similar fashion. 5:30 Student Talk: The geometry of Hopf Fibrations, Priyanka Rajan We will study the geometry and symmetry of Hopf fibrations over complex numbers, quaternions, and the cayley numbers, and also give a sketch of proof that the symmetry group of the fibration S^15 \rightarrow S^8 (with fibers S^7) is isomorphic to Spin(9), the simply connected double cover of SO(9).
Friday9:00 Student Talk: Effective conjugacy in nilpotent groups, Mark Andrew PengitoreIn 1965 Blackburn showed that finitely generated nilpotent groups are conjugacy separable. Using the Conj function of Lawton, Louder, McReynolds one can measure the asymptotic behavior of conjugacy separability to understand the difficulty of solving the conjugacy problem for finitely generated groups. In particular we demonstrate for finitely generated nilpotent groups that the Conj function has polynomial upper and lower bounds using the ideas of Mal'cev and Blackburn. 9:30 Student Talk: Monodromy of Cyclic Covers, Lalit Jain We compute the Z/\ell monodromy of Hurwitz spaces corresponding to cyclic covers with specified ramification. Using techniques from topology, finite group theory and algebraic geometry we will show that as long as the genus of the parametrized curves is sufficiently large, the monodromy group is ``big.'' 10:00 Student Talk: Computing Khovanov Homology, Deniz Kutluay Khovanov homology is an invariant of oriented links which is strictly stronger than the Jones polynomial. The main aim of this talk is to illustrate the combinatorial construction of Khovanov homology on a generic computation. We will then highlight some of its properties and applications. This talk is for general audience – no familiarity on the subject is assumed. 10:30 Tea 11:00 Student Talk: McCulloughMiller 4Space is Not CAT(0), Charles Cunningham McCulloughMiller Space (MM) is virtually a geometric model for the Outer Automorphism Group of a Universal RightAngled Coxeter Group, Out(W). As it is currently an open question as to whether or not Out(W) is CAT(0) or not, it would be helpful to know whether MM can be equipped with an Out(W)equivariant CAT(0) metric. We show that the answer is in the negative. This is particularly interesting as there are very few examples of proving that a space of independent interest is NOT CAT(0). 11:30 Student Talk: Recognizing rightangled Coxeter groups, Andrew Eisenberg Despite the importance of rightangled Coxeter groups (RACGs) to combinatorial group theory, geometry and topology, there are very few methods known of identifying whether a given group is a RACG. We will discuss a new method and some applications. This is joint work (in progress) with Charlie Cunningham, Adam Piggott, and Kim Ruane. 12:00 Reflections and Farewell 