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For more information about the Seminar, or to suggest speakers, contact Jim Hoste , Dave Bachman , Sam Nelson , Erica Flapan or Vin de Silva.
Date  Speaker  Title and Abstract 
Tuesday
Sept 10 3:00 pm 
Organizational Meeting  Meet at Some Crust Bakery for organizational meeting. 
Tuesday
Sept 17 3:00 pm 


Tuesday
Sept 24 3:00 pm 


Tuesday
Oct 1 3:00 pm 


Tuesday
Oct 8 3:00 pm 


Tuesday
Oct 15 4:15 in Mudd 125 
Renata Gerecke  Title: Factor Groups of Knot and LOT Groups Abstract: It is difficult to determine whether, given a finite, balanced group presentation, the group is finite or infinite. We study this problem in the context of knot groups and label orientated tree (LOT) groups. More specifically, we are looking at factor groups of knot and LOT groups by powers of meridians. This is in the spirit of Coxeter's work on the factor groups of braid groups. Indeed, our findings generalize Coxeter's work from the threestrand braid groups to knot groups. 
Tuesday
Oct 22 3:00 pm 
No Meeting  Fall Break 
Tuesday
Oct 29 3:00 pm 
Sam Nelson Claremont McKenna College 
Title: Augmented Birack Homology Abstract: We introduce a homology theory for augmented biracks. 2cocyles in the cohomology of a coloring birack define enhancements of the birack counting invariant; we will see some examples. 
Tuesday
Nov 5 3:00 pm 


Tuesday
Nov 12 3:00 pm 
Henry Segerman University of Melbourne 
Title: Regular triangulations and the index of a cusped hyperbolic 3manifold Abstract: Recent work by Dimofte, Gaiotto and Gukov defines the "index" (a collection of Laurent series) associated to an ideal triangulation of an oriented cusped hyperbolic 3manifold. "Physics tells us" that this index should be a topological invariant of the manifold, not just of the triangulation of it. The problem is that the index is not well defined on all triangulations. We define a class of triangulations of a 3manifold, depending only on the topology of the manifold, such that the index is welldefined and has the same value for each triangulation in the class. A key requirement is that the class of triangulations be connected by local moves on the triangulations, since we can prove invariance of the index under these moves. To achieve this requirement we import a result from the theory of regular triangulations of Euclidean point configurations due to Gelfand, Kapranov and Zelevinsky. 
Tuesday
Nov 19 3:00 pm 


Tuesday
Nov 26 4:15 at CMC, room TBA 
Karly Brint Pitzer College 
Title: Stick Number of Torrified Rational Links Abstract: Using the idea of supercoiling of DNA, it is possible to represent knots and links containing large numbers of twists with relatively small numbers of sticks. We use this approach to place an upper bound on stick number for a large class of links we call torrified rational links. 
Tuesday
Dec 3 3:00 pm 
Dave Bachman Pitzer College 
Title: Limits on concentrated instability Abstract: Minimal surfaces typically have places where their instability is concentrated. We show that if all of this instability is concentrated in one place, then there is a limit to how unstable the surface is. 
Tuesday
Dec 10 3:00 pm 

Date  Speaker  Title and Abstract 
Tuesday
Jan 28 3:00 pm 
Eleni Panagiotou UCSB 
Title: Entanglement in systems of curves with Periodic Boundary Conditions Abstract: Periodic Boundary Conditions (PBC) are often used for the simulation of complex physical systems of open and closed curve models of polymers or vortex lines in a fluid flow. Using the Gauss linking number, we define the periodic linking number as a measure of entanglement for two oriented curves in a system employing PBC. In the case of closed curves in PBC, the periodic linking number is a topological invariant that depends on a finite number of components in the periodic system. For open curves, the periodic linking number depends upon the entire infinite system and we prove that it converges to a real number that varies continuously with the configuration. Finally, we define two cutoffs of the periodic linking number and we compare these measures when applied to a PBC model of polyethylene melts. 
Tuesday
Feb 4 3:00 pm 


Tuesday
Feb 11 3:00 pm 


Tuesday
Feb 18 3:00 pm 
Yin Tian USC 
Title: a categorification of a Clifford algebra via 3dimensional contact topology Abstract: Categorification, initiated in the work of Crane and Frenkel, describes richer ``higherlevel" structures which aim to clarify objects on the decategorification level and to provide finer invariants. A celebrated example is Khovanov homology which categorifies the Jones polynomial. In this talk we describe a categorifcation of a Clifford algebra. The motivation is from the contact category C(D^2) of a disk D^2 introduced by Honda which describe contact structures on D^2 \times [0,1]. 
Tuesday
Feb 25 3:00 pm 


Tuesday
Mar 4 3:00 pm 
Kristen Hendricks UCLA 
Title: Periodic Knots and Heegaard Floer Homology Abstract: We introduce periodic knots and discuss two classical obstructions to periodicity, Murasugi's condition on the Alexander polynomial of a periodic knot and Edmonds' condition on the genus. We then describe a generalization of these two results in the case of doublyperiodic knots which arises from the modern link invariant Heegaard Floer homology. We finish with an example in which our construction gives more information that the two classical theorems. 
Tuesday
Mar 11 3:00 pm 
Hugh Howards Wake Forrest University 
Title: Linked spheres in Higher dimensions and how it all shapes up. Abstract: The Borromean Rings are one of the most famous links. A result of Freedman and Skora shows that they cannot be formed out of circles, but they can be formed from two circles and an ellipse. They, however, are the only Brunnian link of 3, 4, or 5 components that can be formed out of convex curves. We look at generalizations of Brunnian Links to higher dimensions and ask if it is possible to form these genralized Brunnian Links out of round spheres or convex components answering the first question in the negative and the second in the positive. 
Tuesday
Mar 18 
No Meeting  Spring Break 
Tuesday
Mar 25 3:00 pm 
Allison Gilmore UCLA 
Title: Knot Floer homology and constituent knots of graphs Abstract: Knot Floer homology for singular knots was developed by Ozsvath, Szabo, and Stipsicz using the usual techniques of Heegaard diagrams and counts of holomorphic disks. Much of the talk will be devoted to introducing this theory and discussing its basic properties. The remainder of the talk will discuss joint work in progress with Kristen Hendricks. We will describe spectral sequences from the knot Floer homology of a singular knot to the knot Floer homology of any of its oriented constituent knots. If time permits, some preliminary computations will be presented and potential implications sketched. 
Tuesday
Apr 1 3:00 pm 
Ryan Blair CSU Long Beach 
Title: Knots with compressible thin levels. Abstract: Width is an integer invariant of knots that is affected by the number of maxima and minima of a knot as well as the relative heights of these critical points. Width has been a particularly useful invariant due to deep connections between a width minimizing embedding of a knot and the topology of the knot exterior. In particular, Wu showed that a thinnest thin level for a width minimizing embedding is incompressible. In this talk, I will present joint work with Alex Zupan in which we construct the first examples of a width minimizing embedding with compressible thin levels. 
Tuesday
Apr 8 3:00 pm 
Jeremy Pecharich Pomona College 
Title: A class of associative algebras arising from quantum mechanics Abstract: Classical mechanics, i.e., all of physics up to 1900, can be described by a Poisson manifold. After 1900, quantum mechanics happened and pandemonium ensues. The pandemonium was caused by a series of experiments which showed that the mathematics of the quantum level is no longer a Poisson manifold. The mathematics of the quantum world is still up for debate, but we will discuss one possibility which constructs an associative algebra from any Poisson manifold. We will then constructs modules over this associative algebra and give applications to intersections of Lagrangian submanifolds. Part of this is joint work with Baranovsky, Ginzburg, and Kaledin. 
Tuesday
Apr 15 3:00 pm 


Tuesday
Apr 22 3:00 pm 
Ellie Grano Pepperdine University 
Title: The popswitch planar algebra and the JonesWenzl projections Abstract: The TemperleyLieb planar algebra brought us the Jones' polynomial. We will discuss this planar algebra and then define the JonesWenzl projections, important elements of the TemperleyLieb planar algebra. Next we will present the popswitch planar algebra, a new planar algebra containing the TemperleyLieb planar algebra. It is motivated by Jones' idea of the "graph planar algebra" of type $A_n$. Complicated calculations using the graph planar algebra can be done pictorially in this new planar algebra. Furthermore, the JonesWenzl projections are traditionally very complicated to write down. Viewing the popswitch planar algebra as a matrix category, the JonesWenzl projections are direct sums of very simple diagrams. We will discuss this method of viewing the JonesWenzl projections. 
Tuesday
Apr 29 4:155:15 Shanahan B460, HMC 
Tim Hsu San Jose State Univ. 
Title: Cube Complexes, 3manifolds, and the Virtual Haken Theorem Abstract: The Virtual Haken Conjecture was, until recently, probably the biggest open problem in 3manifolds (3dimensional geometry). Then in March 2012, Ian Agol proved the conjecture by completing a key part of Dani Wise's program of studying nonpositively curved cube complexes. So how did questions in 3dimensional geometry end up being resolved using spaces made from (very highdimensional) cubes? We'll give an overview explaining the connection and describe the speaker's joint work with Wise that is part of the emerging and rapidly growing subject of cube complexes. 
Tuesday
May 6 3:00 pm 
Erkao Bao UCLA 
Title: Hofer energy and Gromov's Monotonicity of pseudoholomorphic curves Abstract: I will introduce the notion of pseudoholomorphic curve, and the Hofer energy of pseudoholomorphic curves in symplectization of contact manifolds. Then as a direct corollary, we prove the Gromov's Monotonicity with multiplicity. I will make it accessible to general audience. 