This page contains notes from some seminar/reading group talks I've given/attended.

Research talks

  • Surface bundles with fiber-preserving group action. notes
  • The Wall conjecture and hyperbolic groups. video, notes, notes
  • Obstruction to Nielsen realization. notesnotes, video
  • Braid groups and Nielsen realization. notes
  • Minicourse on the topology of diffeomorphism groups. Notes
  • Point-pushing and Nielsen realization. notesslides
  • Pontryagin classes of locally symmetric spaces. notes

The Cremona group (Summer 2016, Stanford). Reading group organized by Alex Wright. Official website here. Below are some of my notes from the different lectures. 

  • Introduction (by Alex Wright). notes
  • Rational maps and blow ups (by Tony Feng). notes
  • Generating the Cremona group. notes

Foliations reading group (Winter 2016, Stanford). This reading group is organized by Sander Kupers, Katie Mann, and me. The official website is here. Below are my notes from the talks with some of my own additions/subtractions. In particular, any errors are probably mine (not the speakers'). 

Part 1. Basic results

  • Introduction to foliationsnotes
  • Holonomy and Reeb stability (by Weston Ungemach). notes
  • Haefliger's theorem on compact leaves (by Ben Dozier). notes
  • Thurston stability theorem (by Katie Mann). notes 
  • Poincare-Bendixson theorem (by Laura Starkson). notes

Part 2. Codimension-1 foliations of 3-manifolds

  • Introduction: topology of the space of foliations (by Katie Mann). notes
  • Thurston's theorem: existence of codimension-1 foliations (by Weston Ungemach). notes
  • Deformation of plane fields (by Cedric De Groote). 
  • Foliating solid tori (in families). notes

Farb and Friends Student Seminar (Chicago). 

  • The Borel conjecture, hyperbolic groups, and hyperbolization, May 2015. notes
  • Pontryagin classes for a locally symmetric manifold, Feb. 2014. notes
  • Some groups of mapping classes not realized by diffeomorphisms, Mar. 2013. notes
  • Mostow rigidity and bounded cohomology, Dec. 2012. notes
  • Homotopy types of diffeomorphism groups, May 2012.

Rigidity reading group (Summer 2014, Chicago). 

  • Goldman's theorem, Sept. 2014. notes
  • Volume rigidity, Aug. 2014. notes
  • Representation rigidity and Kneser's theorem, July 2014. notes
  • The degree theorem, July 2014. notes

Pizza seminar (Chicago). 

  • Holla if ya sphere me, Pizza seminar, Oct. 2014. notes 
  • Associations of a non-associative algebra, Pizza seminar, Nov. 2012. notes


  • Flat bundles, the Euler class, and Milnor-Wood, Harvard grad geometry seminar, Nov. 2016. notes
  • Poincare duality and local coefficients, PIMS Summer school on surgery, July 2016. notes
  • Surface bundles, branched covers, and arithmetic groups, Stanford topology progress seminar, May 2016. notes
  • Sullivan's theorem: arithmeticity and mapping class groups, Stanford student topology seminar, Nov. 2015. notes
  • Random walks on groups, Chicago student seminar on random walks, Jan. 2015. notes
  • Gelfand-Fuks cohomology, Chicago diffeomorphism groups seminar, Nov. 2014. notes
  • Applications of Ratner's theorem to hyper-Kaehler manifolds, Chicago applications of Ratner seminar, Oct. 2014. notes
  • Bott periodicity, Farb geometric literacy: Morse theory, Winter 2014. notes
  • Differential forms, Chicago WOMP 2014. notes
  • Introduction to Harer stability, Reading group, May 2015. notes