Learning Seminars

Venue: HIM lecture hall, Poppelsdorfer Allee 45 (unless stated otherwise)

Organizer: Jeff Meier

The aim was to give an introduction to the theory of trisections, with lots of examples and exercises, and describe some of the work that had been done so far and the current research directions.

Dates:

• Thursday, September 8, 13:15 - 14:45
  Jeff Meier: Introduction to trisections
• Thursday, September 15, 13:15 - 14:45
  Jeff Meier: Applications of trisections: Dehn surgery on links and generalized property R
• Thursday, September 22, 13:15 - 14:45
  Allison Miller: Bridge trisections of knotted surfaces in the four-sphere
• Thursday, September 29, 13:15 - 14:45
  Jeff Meier: Bridge trisections: Applications and examples
• Thursday, October 6, 16:30 - 18:00
  Venue: HIM seminar room (in the basement), Poppelsdorfer Allee 45
  Matthias Nagel: Trisections and Lefschetz fibrations
• Thursday, October 13, 13:15 - 14:45
  Alexander Zupan: Morse-2 functions and trisections
  Abstract: I will describe the basics of Morse-2 functions and present Gay and Kirby's original proof of the existence of trisections using these tools. Morse-2 functions also suggest a generalization of trisections which parallels the theory of generalized Heegaard splittings. Parts of this talk represent joint work with Amey Kaloti and Maggy Tomova.

Organizers: Chris Davis, Min Hoon Kim, Allison Miller, Aru Ray

The aim was to discuss filtrations of knot concordance, and the invariants used to detect non-triviality in the iterated graded steps, such as L⁽²⁾-invariants and Casson-Gordon signatures. We particularly encouraged discussion of conjectures relating to the global structure of knot concordance.

Dates:

• Tuesday, September 13, 14:30 - 16:00
  Allison Miller: Torsion Casson-Gordon invariants
• Tuesday, September 20, 14:30 - 16:00
  Allison Miller: Twisted Alexander polynomials and Casson-Gordon signatures
• Tuesday, September 27, 14:30 - 16:00
  Aru Ray: Higher order Alexander polynomials
• Monday, October 3, 14:30 - 16:00
  Chris Davis: The primary decomposition of the knot concordance group (part 1)
• Tuesday, October 11, 14:30 - 16:00
  Chris Davis: The primary decomposition of the knot concordance group (part 2)
• Tuesday, October 25, 13:00 - 14:30
  Jae Choon Cha: A quantitative approach to Cheeger-Gromov rho invariants and 4-dimensional bordism
  Abstract: I will discuss a quantitative approach to Cheeger-Gromov L² rho invariants of 3-manifolds, from a 4-dimensional viewpoint. Ingredients we develop include quantitative bordism theory and an algebraic notion of controlled chain homotopy, which seem interesting on their own. Applications will be discussed if time permits.
• Monday, October 31, 13:00 - 14:30
  Min Hoon Kim: On the bipolar filtration of knot concordance
• Monday, November 7, 16:30 - 18:00
  Venue: HIM seminar room (in the basement), Poppelsdorfer Allee 45
  Jung Hwan Park: Milnor's invariants and the solvable filtration

Organizers: Mark Powell, Patrick Orson

Knot concordance is closely related to surgery theory in dimension 4. The aim was to give an overview of the Browder-Novikov-Sullivan-Wall surgery theory, with focus on its connections to knot concordance and 4-manifolds. Also to describe the Farrell-Jones conjecture, with examples of using it for computations.

Dates:

• Tuesday, November 1, 14:30 - 16:00
  Patrick Orson: Introduction to surgery theory
• Tuesday, November 8, 14:00 - 15:45
  Venue: MPIM seminar room, Vivatsgasse 7
  Matthias Nagel, Duncan McCoy: The surgery obstruction map
• Tuesday, November 15, 13:00 - 14:45
  Matthias Nagel, Arunima Ray: Surgery in the middle dimension and L-groups
• Tuesday, November 22, 13:00 - 14:45
  Peter Feller: Normal invariants
• Tuesday, November 29, 13:00 - 14:45
  Allison Miller: Odd dimensional L-groups and the action on the structure set
• Tuesday, December 6, 13:00 - 14:45
  Min Hoon Kim: High dimensional concordance
• Tuesday, December 13, 14:00 - 16:00
  Chris Davis: The classification of simply-connected 4-manifolds
• Tuesday, December 20, 14:00 - 16:00
  Jeff Meier, Jung Hwan Park: Applications of surgery to knot concordance

Organizers: Peter Feller, Mark Powell

The idea was to explain some of what goes into Freedman's proof of the disc embedding theorem, and to talk about the attempts to understand the problem for all groups, and what one would want to show to prove or disprove surgery for free groups.

Dates:

• Thursday, November 3, 19:00
  Freedman movie night
• Friday, November 4, 9:00 - 10:45
  Mark Powell: Introduction to the disc embedding theorem in dimension 4
• Wednesday, November 9, 19:00
  Freedman movie night
• Friday, November 11, 14:15 - 16:00
  Marc Powell: From surgery input to capped gropes
• Wednesday, November 16, 19:00
  Freedman movie night (2013 Mike Freedman, shrinking of decomposition spaces)
• Friday, November 18, 13:00 - 14:45
  Peter Feller: Grope height raising and one story capped towers
• Wednesday, November 23, 19:00
  Freedman movie night
• Friday, November 25, 10:00 - 12:00
  Mark Powell: Tower height raising and geometric control
• Friday, November 25, 14:00 - 16:00
  Daniel Kasprowski: Shrinking of toroidal decomposition spaces
• Tuesday, November 29, 10:00 - 12:00
  Stefan Behrens: Infinite towers are 2-handles (part 1)
• Wednesday, November 30, 19:00
  Freedman movie night
• Thursday, December 1, 16:30 - 18:00
  Mark Powell: Infinite towers are 2-handles (part 2)
• Friday, December 2, 10:30 - 12:00
  Boldizsar Kalmar: The ball to ball theorem
• Friday, December 9, 10:00 - 12:00
  Mark Powell: Squeezing towers and red blood cells
• Friday, December 16, 10:00 - 12:00
  Allison Miller: Obstructing disc embedding for free groups: the AB slice and Round Handle problems
• Tuesday, December 20, 16:30 - 17:30
  Peter Teichner: Disc embedding theorem for subexponential growth groups