Ernie E. Fontes's Mathematics

About me

I have now left academia. In my last academic position, I was a Ross Assistant Professor in mathematics at The Ohio State University. Before landing in Ohio, I obtained my PhD from UT Austin in May 2017. My PhD advisor was Andrew Blumberg. I have collaborated with Crichton Ogle, Niles Johnson, Nick Gurski, Christina Osborne, Aaron Royer, and Truls Raeder. I did my undergraduate work at Harvard in mathematics, where my senior thesis was advised by Michael Hopkins.

Most people call me Ernie but my undergraduate students tend to call me Dr. Ernie.

Outside of mathematics, I spend much of my time rock climbing, practicing yoga, baking sourdough bread, and cooking thin-crust pizzas.

My CV and research statements are available on request.

Research

I am an algebraic topologist and a homotopy theorist. My research focuses on algebraic K-theory and the complications that arise around it. I am interested in structural theorems: how does algebraic K-theory behave in the presence of other structures? I also explore computational results: where can we use trace methods to compute algebraic K-theory? These interests lead me to dabble in stable equivariant homotopy theory and the homotopy calculus of functors.

My broad research interest cover a variety of topics, including algebraic K-theory, topological Hochschild homology (THH), topological cyclic homology (TC), abstract homotopy theory, homotopy calculus of functors, equivariant (stable) homotopy theory, higher category theory, and computations in stable homotopy groups.

Papers

  • Algebraic K-theory for 2-categories: + = S-1S. With Niles Johnson and Nick Gurski. In preparation.
  • Partial modules and the splitting of A(ΣX). With Crichton Ogle. In preparation.
  • Topological cyclic homology of polynomial E∞-ring spectra. With Truls B. Raeder and Aaron M. Royer. In preparation.
  • A Fundamental Theorem for the K-theory of connective 𝕊-algebras. With Crichton Ogle. Under revision. Preprint available here.
  • Weight structures and algebraic K-theory of stable ∞-categories. My PhD thesis. Submitted. Preprint available here.

    Teaching

    I have enjoyed my teaching career and the way it let me enrich the lives of those around me. At OSU, I participated in the SEMINAL program to implement active learning techniques in large calculus classrooms (during Fall 2018 and again this semester). During graduate school, the UT Austin Mathematics Department recognized my teaching by awarding me with the Frank Gerth III Teaching Excellence Award in May 2014.

    In my past semesters at OSU, I taught the following courses:

  • Math 2153: Calculus III, Spring 2020.
  • Math 6802: Algebraic Topology II, Spring 2020.
  • Math 1152: Calculus II, Fall 2019.
  • Math 6801: Algebraic Topology I, Fall 2019.
  • Math 2153: Calculus III, Spring 2019.
  • Math 1151: Calculus I, Fall 2018.
  • Math 1151: Calculus I (Flipped & Flexible), Spring 2018.
  • Math 1151: Calculus I (Flipped & Flexible), Fall 2017.

    • In graduate school at UT, I was fortunate to be supported frequently by the RTG in Topology and Geometry. During other semesters, my teaching comprised:

  • Coordinator for undergraduate calculus learning assistants at UT, Spring 2016.
  • M 408N TA with Prof. Anna Spice, Fall 2013.
  • M 408S (Calculus II) TA with Prof. Mark M. Maxwell, Spring 2013.
  • M 408D (Calculus II/III) TA with Prof. Alex Rand, Spring 2012.
  • M 408L (Calculus II) TA with Prof. Diane Radin, Fall 2011.

    Service

    I am organizing no conferences currently.

    In the past, I helped organize:

  • The Workshop on Functor Calculus at OSU, March 16–17, 2019.
  • The Special session on Homotopy Theory at the Spring Central Sectional Meeting of the AMS at OSU, March 16–18, 2018.
  • In graduate school, I helped organize the 2016 and 2015 texTAG conferences, as well as the 2014 Graduate Student Topology & Geometry Conference.

    Seminars and talks

    I organize the Homotopy Seminar with John Harper, Vidhyananth Rao, Niles Johnson, and Christina Osborne here at OSU. The seminar calendar for the 2018–2019 year is now located here. I also heckle homotopy theory graduate students every week at the Student Homotopy Seminar. The following is a list of talks I've given outside local seminars at OSU and in graduate school.

  • "Weight structure and the algebraic K-theory of stable ∞-categories" - IU/PU/IUPUI Joint Topology Seminar at IUPUI. October 13, 2018.
  • "Weight structures and algebraic K-theory of stable ∞-categories" - Topology seminar at Johns Hopkins University. November 2015.
  • "Weight structures and algebraic K-theory of stable ∞-categories" - Topology seminar, University of Illinois at Urbana-Champaign. October 2015.
  • "Localization sequences in and around algebraic K-theory" - 'xkcd' seminar, UC Berkeley/Stanford. March 2014.
  • "Categories of modules and their equivalences" - MSRI: Algebraic Topology Summer School. June 2013.
  • "Applications to algebraic K-theory II" - MIT Talbot workshop on calculus of functors. May 2012.

    In Summer 2016, I ran a seminar for other graduate students on simplicial localization techniques. The website for that seminar is located here.

    Other resources

    Aside from this website and e-mail communication, I maintain a ghostlike presence on social media. I am active, but private, on Instagram. I am not active on Twitter and I have deactivated my Facebook account indefinitely.

    You might have stumbled on my website whilest looking for someone else. Perhaps you are seeking my sister, Lila or my father, Ernie.