Eric Canton

Photo credit: Allison Beemer
Office: 312 Avery Hall
ecanton2 [at] math.unl.edu


Current students
I am a sixth year Ph.D. candidate at the University of Nebraska - Lincoln working in algebraic geometry and commutative algebra. My advisor is Wenliang Zhang. I study singularities and birational geometry in positive characteristic. Specific topics of interest include:
  1. F-singularities and their relation to MMP singularities
  2. Berkovich spaces
  3. tropical geometry and motivic integration
  4. positivity and vanishing theorems
  5. local cohomology
You can view my CV.
Preprints
  1. "Berkovich log discrepancies in positive characteristic"
  2. "A note on injectivity of Frobenius on local cohomology of hypersurfaces"
     Incorporated and expanded in the paper on complete intersections.
  3. "Relating F-signature and F-splitting ratio of pairs using left derivatives"
     Partially incorporated into the paper on behavior of singularities near the F-pure threshold.
Publications
  1. "A note on injectivity of Frobenius on local cohomology of global complete intersections"
     Journal of Pure and Applied Algebra, Vol. 220, Issue 8, August 2016. pp. 2879-2885
  2. "On the behavior of singularities near the F-pure threshold" Joint with Daniel J. Hernández, Karl Schwede, and Emily E. Witt.
     Illinois Journal of Mathematics, Vol. 60, No. 3-4, Fall and Winter 2016. pp. 669-685.

KUMUNUjr
I co-organized KUMUNUjr 2015, 2016, and 2017. The 2018 website is now up and registration is open (closes March 15).
Nebraska Conference for Undergraduate Women in Mathematics (NCUWM)
I am on the organizing committee for NCUWM 2018, which will take place January 26-28, 2018 in Lincoln, NE. Please look at our Sched site for the schedule of talks and events, as well as abstracts for all of the talks.
Code
I wrote some Macaulay2 code that can be used for exploration of F-signatures of pairs. It has essentially been incorporated into this excellent F-singularities package written by Daniel Hernández, Moty Katzman, Sara Malec, Karl Schwede, Pedro Teixeira, and Emily Witt.


Teaching
I am a recitation TA for calculus 2 for the Spring 2018 semester.
During my time at University of Nebraska, I have been an instructor for the following classes:
  1. Math 804T: Experimentation, conjecture, and reasoning. Masters in Arts for Teachers course.
  2. Landscapes in Mathematics Seminar
  3. Math 102: Trigonometry
  4. Math 101: College Algebra