Chris Gerig (Harvard): SW = Gr
Whenever the Seiberg-Witten (SW) invariants of a 4-manifold X are defined, there exist certain 2-forms on X which are symplectic away from some circles. When there are no circles, i.e. X is symplectic, Taubes' ``SW=Gr'' theorem asserts that the SW invariants are equal to well-defined counts of J-holomorphic curves (Taubes' Gromov invariants). In this talk I will describe an extension of Taubes' theorem to non-symplectic X: there are well-defined counts of J-holomorphic curves in the complement of these circles, which recover the SW invariants. This ``Gromov invariant'' interpretation was originally conjectured by Taubes in 1995.

Biji Wong (CIRGET Montreal): A Floer homology invariant for 3-orbifolds via bordered Floer theory
Using bordered Floer theory, we construct an invariant for 3-orbifolds with singular set a knot that generalizes the hat flavor of Heegaard Floer homology. We show that for a large class of 3-orbifolds the orbifold invariant behaves like HF-hat in that the orbifold invariant, together with a relative Z_2-grading, categorifies the order of H_1^orb. When the 3-orbifold arises as Dehn surgery on an integer-framed knot in S^3, we use the {-1,0,1}-valued knot invariant epsilon to determine the relationship between the orbifold invariant and HF-hat of the 3-manifold underlying the 3-orbifold.

We'll talk about grading strategies both for course graders (readers) and also for TAs who want to write quizzes that can be graded more efficiently.

From a group action on a space, define a variant of the configuration space by insisting that no two points inhabit the same orbit. When the action is almost free, this "orbit configuration space'' is the complement of an arrangement of subvarieties inside the cartesian product, and we use this structure to study its topology. We give an abstract combinatorial description of its poset of layers (connected components of intersections from the arrangement) which turns out to be of much independent interest as a generalization of partition and Dowling lattices. The close relationship to these classical posets is then exploited to give explicit cohomological calculations akin to those of (Totaro '96). Joint work with Nir Gadish.

In this session, we will cover the use of active learning techniques in the classroom to engage students in the learning process. We will begin with a short discussion on considerations for active learning, followed by how to create buy-in for students. Afterwards, we will go over different techniques depending on content goals and group sizes. We will finish by designing a lesson plan that integrates 1-2 active learning techniques that you can use in your own discussions. Participants interested in learning more are encouraged to visit the Division of Teaching Excellence and Innovation (DTEI) website at www.dtei.uci.edu.

Kan simplicial manifolds, also known as "Lie infinity-groupoids", are simplicial Banach manifolds which satisfy conditions similar to the horn lling conditions for Kan simplicial sets. Group-like Lie infinity-groupoids (a.k.a "Lie infinity-groups") have been used to construct geometric models for the higher stages of the Whitehead tower of the orthogonal group. With this goal in mind, Andre Henriques developed a smooth analog of Sullivan's realization functor from rational homotopy theory which produces a Lie infinity-group from certain commutative dg-algebras (i.e. L_infinity-algebras).

In this talk, I will present a homotopy theory for both these commutative dg-algebras and for Lie infinity-groups, and discuss some examples that demonstrate the compatibility between the two. Conceptually, this work can be interpreted either as a C^\infty-analog of classical results of Bouseld and Gugenheim in rational homotopy theory, or as a homotopy-theoretic analog of classical theorems from
Lie theory. This is based on joint work with A. Ozbek (UNR grad student) and C. Zhu (Gottingen).