Topology Reading Group (TRG) 2022

Fall 2022 Meeting Time and Place:

Tuesdays 3pm-4pm, Boston College Maloney Hall 560.

For Spring 2022 TRG info, head over to Fraser’s site, here; and for Fall 2021 TRG info, head over to Braeden’s site, here.

Together with Mujie Wang, I am organizing this year’s (Fall 2022 and Spring 2023) Topology Reading Group.

Topology Reading Group (TRG) is an informal seminar for graduate students and post-docs at Boston College and nearby universities. Participants can volunteer to speak about anything topology/geometry/dynamics-related that they’d like to.

If you’d like to speak, or to attend, please email either:

  • Kevin, at: kevin (dot) yeh (at) bc (dot) edu (that’s me!)
  • Mujie, at: mujiew (at) bc (dot) edu

Talks:

September 6th: Kevin Yeh

  • Title: An Introduction to the Classification of 4-Manifolds Part I
  • Abstract: The classification of 4-manifolds differs substantially from that of other dimensions. One such distinction is the crucial role the intersection form plays in their classification. In Kevin’s portion of the talk, we will introduce this algebraic object, together with several of its numerical invariants. We will end this portion with some classification results obtained via the intersection form in the topological category.

September 13th: Ali Naseri Sadr

  • Title: An Introduction to the Classification of 4-Manifolds Part II
  • Abstract: Ali will continue the thread by focusing on the smooth category; in particular the theorems of Freedman and Donaldson. We will see how the existence of a smooth structure on a 4-manifold can substantially restrict which intersection forms it can carry. Finally, we will finish by computing the intersection forms of certain manifolds using characteristic classes. Working knowledge in topological and smooth manifolds, and their homology and cohomology, will be assumed.

September 20th: Qingfeng Lyu

  • Title: An Introduction to the Classification of 3-Manifolds
  • Abstract: In this talk, we will ambitiously tell the story of how people developed a classification of 3 manifolds in the past century (in line with the past talks). We hope to mention prime decomposition, torus decomposition, hyperbolization and geometrization. Pure story. No actual proof included. All are welcome.

September 27th: Ali Naseri Sadr

  • Title: Construction of an Exotic R^4
  • Abstract: I will introduce instantons and show you how we can use the moduli space of instantons to prove 2E_8 is not smooth; Then we will use this to construct an exotic R^4 embedded in the connected sum of three copies of S^2 “cross” S^2.

October 4th: Joe Boninger

  • Title: Morse Theory and the Calculus of Variations
  • Abstract: We’ll give a rapid introduction to Morse theory, then discuss its relationship with the calculus of variations. This combination uses topology and differential geometry to study the path spaces of smooth manifolds. We’ll state the Morse Index Theorem, and give some fun applications if time permits. (One application is Bott Periodicity, which could be discussed in a future talk.) No background in differential geometry is needed.

October 11th: NO MEETING.

  • Title:N/A
  • Abstract:N/A

October 18th: Laura Seaberg

  • Title:TBD
  • Abstract:TBD

October 25th: Matthew Zevenbergen

  • Title:TBD
  • Abstract:TBD

November 1st: Joaquin Ignacio Lema Perez

  • Title:TBD
  • Abstract:TBD

November 8th: Braeden Reinoso

  • Title:
  • Abstract:

November 15th: Jacob Caudell

  • Title: (tentative) Lens Spaces in 3 and 4 Dimensions
  • Abstract:TBD

November 22nd:

  • Title:TBD
  • Abstract:TBD

December 6th:

  • Title:TBD
  • Abstract:TBD

December 13th:

  • Title:TBD
  • Abstract:TBD