Gabe Angelini-Knoll

Papers Talks Teaching Resources Contact

I am a postdoctoral researcher at Michigan State University. My research focuses on interactions between algebraic K-theory and chromatic stable homotopy theory. As a postdoc, I am also happy to have the opportunity to teach courses and I am intersted in undergraduate research. I also enjoy organizing and participating in informal seminars.

Previously, I was a Ph.D. student working under the direction of Andrew Salch at Wayne State University. Outside of math, I enjoy hiking, biking, playing guitar and piano, and playing boardgames. I studied abroad in Quito, Ecuador as an undergraduate and I am often nostalgic and looking for opportunities to practice Spanish.

Papers

My work focuses on how algebraic K-theory interacts with periodicity in the homotopy groups of spheres. Specifically, I do computations of approximations to algebraic K-theory of structured ring spectra and analyze how chromatic complexity behaves in this context. I also work on developing tools for doing trace methods computations.

Submitted papers:

The Segal Conjecture for Topological Hochschild Homology of the Thom spectra X(n) and T(n) [pdf | arxiv]
We solve the homotopy limit problem for topological Hochschild homology of Ravenel's spectra X(n) and T(n) with respect to all cyclic p-groups. Joint with J.D. Quigley.
On topological Hochschild homology of the K(1)-local sphere [pdf| arxiv]
In this paper, I compute mod (p,v_1) topological Hochschild homology of the connective cover of the K(1)-local sphere spectrum using the THH-May spectral sequence.
A May-type spectral sequence for topological Hochschild homology [pdf| arxiv]
We constrtuct the THH-May spectral sequence for higher topological Hochschild homology and use it to give a bound on topological Hochshcild homology of connective ring spectra. Joint with Andrew Salch
Maps of simplicial spectra whose realizations are cofibrations [pdf| arxiv]
This paper provides user friendly conditions for checking when a map of simplicial spectra induces a cofibration on geometric realizations. Joint with Andrew Salch

Unpublished papers:

K(n)-local homotopy groups via Lie algebra cohomology [pdf]
We compute the homotopy groups of the K(1)-local mod p Moore spectrum at odd primes in order to illustrate a method that could be used to compute K(n) local homotopy of more general type n complexes.
Auslander-Reiten quiver of the category of unstable modules over a sub-Hopf algebra of the Steenrod algebra [pdf]
We provide partial results about the Auslander-Reiten quiver associated to the category of unstable E(1)-modules where E(1) is the sub-Hopf algebra of the Steenrod algebra generated by the first two Milnor primitives.
Galois cohomology and algebraic K-theory of finite fields [pdf]
We describe how to compute algebrqaic K-theory of finite fields mod l using the "motivic to algebraic K-theory" spectral sequence. This project was my master's thesis under the direction of Andrew Salch.

Talks

On the structure of the map from MU to BP [Link to notes]
Talbot Workshop on Obstruction Theory, May 2017 (Notes compiled by Eva Belmont and Sanath Devalapurkar)
Loday construction in functor categories [Slides]
AMS Sectional, Indiana University, April 2016
Stacks and Homotopy Theory [pdf]
West Coast Algebraic Topology Summer School 2016, University of Oregon (joint with Eva Belmont)
Periodicity in iterated algebraic K-theory [Slides]
Topology Seminar, Michigan State University, November 2016
On mod (p,v_1) homotopy of THH of the K(1)-local sphere and its homotopy fixed points [Slides]
K-theory Seminar, Ohio State University, February 2016
Fundamental Theorems of Algebraic K-theory [Notes ]
European Talbot Workshop 2015, Klosters, Switzerland
On the paper "Nilpotence and Stable Homotopy Theory II" [Notes]
MSRI Summer School: Algebraic Topology, Guanajuato, Mexico
The Topologist's Snowflake and the Rose [Abstract]
Kalamazoo College Undergraduate Seminar, Kalamazoo, Michigan

Teaching

This semester I am teaching two sections of Calculus I with a focus on applications to business and economics.

MTH 124: Survey of Calculus I Section 1

TIME: M W F 8:00 am - 9:50 am

ROOM: A208 WH

Course Webpage

WebWork

MTH 124: Survey of Calculus I Section 13

TIME: M W F 9:10 am - 10:00 am

ROOM: A330 WH

Course Webpage

WebWork

Resources

As a graduate student and postdoc I have been fortunate to attend conferences on many topics. If are interested in attending conferences in algebraic topology or algebraic K-theory as well, here are some links I have found useful for finding such conferences.

Niles Johnson maintains webpage which contains a useful conference list at MathMeetings

Bob Bruner maintains the Midwest Topology Seminar website.

Each year a small group of graduate students and postdocs is selected to participate in the Talbot workshop and it is held in a different remote location.

Almost every year there is a West Coast Algebraic Topology Summer School. I attended the chromatic homotopy theory and number theory WCATSS.