Jack Jeffries

Jack Jeffries

Ph. D. Candidate
(Fifth year)
University of Utah
Department of Mathematics
Office: JWB 128

Advisor: Professor Anurag Singh

B.S.: The Ohio State University, 2010

Jack Jeffries
University of Utah
Department of Mathematics
155 S 1400 E RM 233
Salt Lake City, UT, 84112-0090

Email: jeffriesmath.utah.edu


My research is in Commutative Algebra. More particularly, my interests include local cohomology, Frobenius techniques in the study of singularities, invariant theory, generalized multiplicities, the convex Betti theory of Boij and Söderberg on free resolutions, and connections with statistics and neuroscience.

arXiv page

1. The j-multiplicity of Monomial Ideals, with Jonathan Montaño, Math. Res. Lett., 20 (2013) no. 4, 729-744.
2. Non-simplicial decompositions of Betti diagrams of complete intersections, with Courtney Gibbons, Sarah Mayes, Claudiu Raicu, Branden Stone, and Bryan White, to appear in J. Commut. Algebra
3. Multiplicities of Classical Varieties, with Jonathan Montaño and Matteo Varbaro, submitted
4. Separating Invariants and Local Cohomology, with Emilie Dufresne, submitted


Spring 2014: Linear Algebra 2270-002
Fall 2013: Intro to Statistical Inference 1070-004
Summer 2013: Applied Complex Variables 3160-001
Fall 2011: Calculus II 1220-005
Summer 2011: Intro to Statistical Inference 1070-001
Spring 2011: Intermediate Algebra 1010-001
Fall 2010: Quantitative Analysis 1100-005

Prof. Hochster's Homepage
Applications of Algebra

Seminars & Events

Algebra Seminar
Program Associate Seminar Series
Eisenbud's Seminar
Algebraic Geometry Seminar
Departmental Colloquium
Graduate Colloquium
Undergraduate Colloquium

Conferences & Workshops

WAGS Fall 2012
MSRI Special Year in Commutative Algebra
Discrete Morse Theory and Commutative Algebra
Computational Workshop on Frobenius Singularities and Invariants
PASI: Commutative Algebra and Its Interactions with Algebraic Geometry, Representation Theory, and Physics
AWM Utah What is Math? Day
AMS 2012 Spring Secional Lawrence
Oberwolfach Seminar: Cohen-Macaulay Modules, Surface Singularities and McKay Correspondence
AMS 2011 Fall Sectional Salt Lake City
MSRI Commutative Algebra SGW 2011


Lecture Notes from PASS Seminar Talk, 20 Nov 2012
Relations on Pure Betti Diagrams
Solutions to Hartshorne
\[\mathrm{Hom}_R(\mathrm{Ext}_R^{d-i}(M,\omega_R),E_R(R/\mathfrak{m}))\cong \mathrm{H}^i_{\mathfrak{m}}(M)\] \[\mathrm{\underline{Hom}}_{R/\mathfrak{m}}(\mathrm{Ext}_R^{d-i} (M,\omega_R),R/\mathfrak{m})\cong\mathrm{\underline{H}}^i_{\mathfrak{m}}(M)\]