Ernie in an impromptu picture. Ernest (Ernie) E. Fontes

Email: efontes [at] math dot utexas [.] edu
Office: RLM 13.150

Department of Mathematics
University of Texas at Austin
1 University Station C1200
Austin, TX 78712-0257
United States of America

About me

I am a PhD student in mathematics at the University of Texas at Austin and will be graduating in May 2017. I will be a Ross Assistant Professor at The Ohio State University starting this fall. My PhD advisor is Andrew Blumberg and I collaborate with Aaron Royer and Truls Raeder. I am a member of the Geometry group at UT and a beneficiary of the Geometry/Topology RTG. I did my undergraduate work at Harvard in mathematics, where my senior thesis was advised by Michael Hopkins.

Most people call me Ernie. Please feel free to do so as well.

My CV is available here and my research statement is 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 in progress

  • Weight structures and algebraic K-theory of stable ∞-categories. My PhD thesis.
  • Topological cyclic homology of polynomial E-ring spectra. With Truls B. Raeder and Aaron M. Royer.

    Teaching

    I enjoy teaching. The UT Austin Mathematics Department recognized my teaching by awarding me with the Frank Gerth III Teaching Excellence Award in May 2014.

    I am not teaching this semester. In Spring 2016, I served as the coordinator for the undergraduate calculus learning assistant program at UT. In previous semesters, I served as a teaching assistant for the following classes:

  • M 408N with Prof. Anna Spice, Fall 2013.
  • M 408S with Prof. Mark M. Maxwell, Spring 2013.
  • M 408D with Prof. Alex Rand, Spring 2012.
  • M 408L with Prof. Diane Radin, Fall 2011.

    Service

    I am organizing no conferences currently.

    In the past, I helped organize the 2016 and 2015 texTAG conference and the 2014 Graduate Student Topology & Geometry Conference.

    Seminars and talks

    I have given the following talks outside of UT Austin:

  • "Weight structures and algebraic K-theory of stable ∞-categories" - Topology seminar, 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.

    This summer, I am running 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. You can find me on Facebook, Twitter, and even Instagram.

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