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 interested in undergraduate research. I also enjoy organizing and participating in seminars. For more information about me see my CV.

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 appreciate 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 Ravenel 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]
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Unpublished papers: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

Invited talks

Chromatic complexity of topological periodic cyclic homology of y(n)
AMS Sectional, Ohio State University, March 2018
The Segal Conjecture for topological Hochschild homology of Ravenel spectra
Topology Seminar, University of Kentucky, November 2017
Evidence for the Greek letter family red-shift conjecture
Midwest Topology Seminar, Wayne State University, November 2017
Loday construction in functor categories [Slides]
AMS Sectional, Indiana University, April 2017
Approximating algebraic K-theory of the image of J
Topology Seminar, University of Chicago, February 2017
Periodic Phenomena in iterated algebraic K-theory of finite fields
Topology Seminar, Notre Dame, December 2016
Periodicity in iterated algebraic K-theory [Slides]
Geometry and Topology Seminar, Michigan State University, November 2016
Red-shift type phenomena in iterated algebraic K-theory of finite fields
Topology Seminar, Indiana University, November 2016
Topological Hochschild homology of the connecitve cover of the K(1)-local sphere
Topology Seminar, University of illinois Urbana Champaign, 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

Conference 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)
Stacks and Homotopy Theory [pdf]
West Coast Algebraic Topology Summer School 2016, University of Oregon (joint with Eva Belmont)
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

Undergraduate talks

The Hopf map in classical mechanics
Math Club, University of Kentucky, November 2017
The Topologist's Snowflake and the Rose [Abstract]
Undergraduate Seminar, Kalamazoo College, February 2014

Teaching

Current courses:

MTH 310: Abstract Algebra I and Number Theory.

Course Website: MTH 310 Section 001

Past courses:

MTH 124: Business Calculus Section 001 Fall 2017 at Michigan State University

MTH 124: Business Calculus Section 013 Fall 2017 at Michigan State University

MAT 1050: Intermediate Algebra with Trigonometry Fall 2015 at Wayne State University

MAT 1050: Intermediate Algebra with Trigonometry Winter 2015 at Wayne State University

MAT 1050: Intermediate Algebra with Trigonometry Winter 2014 at Wayne State University

MAT 1800: Pre-Calculus Fall 2013 at Wayne State University

STAT 1020: Elementary Statistics Summer 2013 at Wayne State University

MAT 1000: Math in Today's World Summer 2013 at Wayne State University

MAT 1800: Pre-Calculus Winter 2013 at Wayne State University

MAT 1800: Pre-Calculus Fall 2012 at Wayne State University

MAT 1000: Math in Today's World Summer 2012 at Wayne State University

Resources

Here are some links I have found useful for attending conferences in algebraic topology or algebraic K-theory,

Niles Johnson maintains a useful conference list at MathMeetings

Bob Bruner maintains the Midwest Topology Seminar website.

Listing of algebraic K-theory seminars maintained by UIUC: K-theory Calander