**Lectures:**Tuesday, Thursday 11:30-12:30 PM EST on May 10, 12, 17, and 19.

**Problem sessions:**Wednesday 11:30-12:30 PM EST on May 18 and 25.

**Problem session leader:**Carissa Slone.

**Lecture Notes and videos:**

Lecture 1: | Notes | Video |

Lecture 2: | Notes | Video |

Lecture 3: | Notes | Video |

Lecture 4: | Notes | |

**Problem sets:**

**References:**

- [
**Dugger**]*An Atiyah-Hirzebruch spectral sequence for*. This is one of the starting points of the slice story.**KR**-theory - [
**Hill-Hopkins-Ravenel**]*On the nonexistence of elements of Kervaire invariant one*. This fully developed the equivariant slice filtration and brought it to prominence. - [
**Hill-Hopkins-Ravenel**] Equivariant stable homotopy theory and the Kervaire invariant problem (the Purple book). This is a textbook on their work on the Kervaire invariant. - [
**Hill-Hopkins-Ravenel**] The slice spectral sequence of Mackey functors for the C4-analog of real K-theory. You can find a discussion of the slice spectral sequence of**KR**here, in section 8. - [
**Hill**] The equivariant slice filtration: a primer. A good introduction of the (original) slice filtration, with a helpful discussion of geometric inflation (called pullback). -
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**Ullman**] On the slice spectral sequence. Introduces the regular slice filtration and proves Hill's conjecture about geometric inflation. -
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**Hill-Yarnall**] A new formulation of the equivariant slice filtration with applications to C_{p}-slices. Contains a description of slice-connectivity in terms of connectivity of fixed points or geometric fixed points. -
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**Angeltveit**] The slice spectral sequence for the cyclic group of order p. Includes a complete description of the slice filtration/spectral sequence for RO(G)-graded suspensions of Eilenberg-Mac Lane spectra. -
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**Dugger**] Coherence for invertible objects and multi-graded homotopy rings. Includes discussion of graded-commutativity in the RO(G)-graded setting. -
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**Lewis-Mandell**] Equivariant universal coefficients and Kunneth spectral sequences. See the appendix for a discussion of graded-commutativity in the RO(G)-graded setting. -
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**Ricka**] Equivariant Anderson duality and Mackey functor duality.