Date | Time | Speaker | Title | Cookies, dinner, etc. |

Thursday, September 3(room B123)
| 4:00 p.m. | Isaac Goldbring, University of Illinois at Chicago | Hindman's theorem and idempotent types (abstract) | cookies/juice at 3:30/ dinner at 6 at Hopcat (222 W. Gorham St.) |

Friday, September 4(dept. coll.)
| 4:00 p.m. ( room B239)
| Isaac Goldbring, University of Illinois at Chicago | On Kirchberg's embedding problem (abstract) | |

Tuesday, September 8 (room B2??)
| 4:00 p.m. | Rutger Kuyper, UW | Medvedev and Muchnik reducibility: An introduction (abstract) | cookies/juice at 3:30 |

Wednesday, September 16(room B2??)
| 3:30 p.m. | Daniel Palacín, University of Münster, Germany | TBA | cookies/juice at 3/ dinner at 6 TBA |

4:30 p.m. | Nadja Hempel, University of Lyon-1, France | TBA | ||

Tuesday, September 22 | 4:00 p.m. | Mariya Soskova, visiting UW from University of Sofia, Bulgaria | TBA | cookies/juice at 3:30 |

Tuesday, September 29 | 4:00 p.m. | Vincent Guingona, Wesleyan University, Middletown, Connecticut | TBA | cookies/juice at 3:30/ dinner at 6 TBA |

Tuesday, October 6 | 4:00 p.m. | Henry Townser, University of Pennsylvania, Philadelphia | TBA | cookies/juice at 3:30/ dinner at 6 TBA |

Tuesday, October 13 | 4:00 p.m. | Joe Miller, UW | TBA | cookies/juice at 3:30 |

Tuesday, October 20 | 4:00 p.m. | Julia Knight, University of Notre Dame, Indiana | TBA | cookies/juice at 3:30/ dinner at 6 TBA |

Tuesday, October 27 | 4:00 p.m. | Reese Johnston, UW | TBA | cookies/juice at 3:30 |

**Prerequisites:** Math 770, and Math 773 or concurrent registration
in Math 773

**Time and Place:** MWF 13:20-14:10

**Textbook:** none

**Course Description:**
The Medvedev and Muchnik degrees are extensions of the Turing degrees studied
in computability theory. Both of these structures also have nice substructures,
namely, the degrees of the so-called effectively closed sets, which form an
analogue to the computably enumerable degrees studied in the Turing degrees.

We will discuss various aspects of these structures. In particular, we will cover the following topics, including their necessary prerequisites:

- Definability of substructures
- Automorphisms
- Embeddability
- Filters and ideals
- Density
- Connections to intuitionistic logic
- Complexity

On the other hand, Medvedev and Muchnik reducibility live "one level up" in the reducibility hierarchy: They are reducibilities on sets of functions from the natural numbers to the natural numbers. They were originally introduced by Medvedev in 1955 and Muchnik in 1963 as formalizations of an earlier informal idea of Kolmogorov, and were originally intended as a way to study intuitionistic logic. However, they are also very interesting from the viewpoint of computability theory, as people have started to realize in the last few decades.

This talk is intended as a gentle overview of the topic. We will discuss the definitions and their background, and will present some of the basic facts that are known about these structures. The topic will be treated in full detail in this semester's Math 873.

Prepared by Steffen Lempp (@math.wisc.edu">lemppmath.wisc.edu)