Garrett Credi

Garrett Credi

he/him

PhD Student at the University of Minnesota studying stable/equivariant homotopy theory

Posts by Collection

talks

The Serre Spectral Sequence and the Cohomology of BU(n)

Published:

PDF Available Here My first ever talk! For a final presentation for MATH 533 (Fiber Bundles) at the University of Illinois Urbana-Champaign, I gave a talk on the Serre Spectral Sequence and its use as a tool to compute cohomology groups of spaces related via some bundle structure. I spent the latter portions of the talk computing the cohomology groups of the classifying spaces of the unitary groups and constructing chern classes.

MU Theory

Published:

Recording Available Here This talk was a part of the reading group on chromatic homotopy theory organize by Yigal Kamel at the University of Illinois Urbana-Champaign. I discussed the geometry of MU theory, its construction as a spectrum, and then delved into the high level proof of Quillen’s theorem focusing heavily on Hopf Algebroid structures and their intuitive properties.

The Periodicity Theorem

Published:

Recording Available Here This was a talk on the proof and application of the Periodicity Theorem from the Orange Book. It was given as a part of a reading group on chromatic homotopy theory organized by Yigal Kamel.

Adams’ Vector Fields on Spheres

Published:

PDF Available Here This talk was given as a part of a Kan Seminar organized by Prof. Charles Rezk. I presented on “Vector Fields on Spheres” by Adams, going over the setup of the problem as well as Adams’ topological approach to obstructing the existence of nonvanishing vector fields via stunted projective spaces.

Adams’ On the Image J(X) IV

Published:

PDF Available Here This talk was part of a Kan Seminar organized by Prof. Charles Rezk. I spoke on Adams’ approach to analyzing the image of J using the precursor to periodicity phenomena later studied as a part of chromatic homotopy theory.

(Homotopy) Limits and Colimits in ∞ categories

Published:

I gave a talk on how the theory of infinity categories allows us to approach homotopy invariant limits and colimits, building off of the classical simplicial approach to homotopy (co)limits. This was a part of the University of Minnesota’s Topology Group’s Reading Group on infinity categories.

The Descent Spectral Sequence for Topological Modular Forms

Published:

As a part of the University of Minnesota’s Topology Group’s ArXiV seminar, wherein we would present weekly on a recent paper, I gave a talk on “The Descent Spectral Sequence for Topological Modular Forms” by Carrick et. al. I discussed synthetic spectra, their applications towards providing more structure for spectral sequences, and presented the author’s main ideas in how they tackled differentials in the aforementioned spectral sequence.

Fibrations and Straightening/Unstraightening in ∞-categories

Published:

This talk was given as a part of a seminar I organized on the paper “Descent Spectral Sequences Through Synthetic Spectra” by Carrick et. al. The first part of the seminar was dedicated to the infinity categorial prerequisites, of which fibrations and (un)straightening were a part.

Basic Equivariant Homotopy Theory

Published:

This talk was given as a part of a seminar I organized on the HHR solution to the Kervaire Invariant Problem. I discussed the basics of equivariant homotopy theory, G-CW Complexes, Mackey functor homotopy groups, and Elmendorf’s theorem among other topics.

teaching

MATH 2263 Multivariable Calculus

Undergraduate course, University of Minnesota Twin-Cities, Department of Mathematics, 2026

This was my first experience being an instructor for a course, instead of a TA, where I was responsible for all aspects of the course including but not limited to the:

  • Syllabus
  • Schedule
  • Lectures
  • Worksheets
  • Quizzes
  • Exams

MATH 1271 Calculus I

Undergraduate course, University of Minnesota Twin-Cities, Department of Mathematics, 2026