Powerpoint Presentations:

Seminar Talks

• The bo-Adams spectral sequence Joint wiht Agnes Beaudry, Prasit Bhattacharya, Dominic Culver, and Zhouli Xu. We give a new method for effectively computing the Adams spectral sequence based on the connective K-theory spectrum bo.
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• tmf cooperations Joint with Kyle Ormsby, Nathanial Stapleton, and Vesna Stojanoska. Following in the footsteps of Mahowald, Laures, and others, We study tmf_*tmf (at the prime 2) using bo-Brown-Gitler spectra, 2-variable modular forms, and isogenies of elliptic curves.
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• Exotic spheres and topological modular forms Joint with Mike Hill, Mike Hopkins, Mark Mahowald. Discusses state of affairs of resolving a question of Milnor: in which dimensions do exotic spheres exist?
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  Here is a more technical version of the talk, which explains our determination of the Hurewicz image of TMF. pptx pdf
• The Morava E-homology of the Goodwillie tower Joint with Charles Rezk. Computation of the Morava E-theory of the layers and k-invariants of the Goodwillie tower of the identity applied to odd dimensional spheres.
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• The EHP sequence and the Goodwillie tower
  Explains interaction between the Goodwillie tower and the EHP sequence in the computation of the 2-primary unstable homotopy groups of spheres, and uses the interaction to reproduce the computation in the Toda range.
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• The homotopy groups of the E(2)-local sphere, revisited
  Describes a conceptual reformulation of the Shimomura-Yabe calculation of the homotopy groups of the E(2)-local sphere for primes greater than or equal to 5.
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• Higher real K-theories and topological automorphic forms
  Joint with Mike Hopkins. Discusses the relationship between the Hopkins-Miller higher real K-theories EO_n and the spectra of topological automorphic forms on U(1,n-1).
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• Congruences amongst modular forms and the divided beta family
  Decribes a correspondence between the elements beta_i/j.k of Miller, Ravenel, and Wilson and certain congruences amongst modular forms.
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• v_2^32 periodicity at the prime 2
  Describes joint work with Mike Hill, Mike Hopkins, and Mark Mahowald, where we construct a v_2^32 self-map on the generalized Moore complex M(1,4) at the prime 2.
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Expository Talks

• Detectors in homotopy theory Colloquium talk explaining the Adams spectral sequence by using experimental high energy physics as an analogy.
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• Modular forms in topology
  This is a colloquium style talk decribing the notion of "topological modular forms" in the context of genera and associated algebraic invariants.
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• Wrapping spheres around spheres
  This is an expository talk on the homotopy groups of spheres for non-mathematicians.
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• Manifolds and Cobordism
  This is an expository talk on the theory of manifolds, cobordism, and surgery at a basic undergraduate level. It mostly focuses on the case of dimension 2, where pictures can be drawn.
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