Jarod Alper (University of Washington)

Jarod Alper

Professor of Mathematics
Victor Klee Faculty Fellow
Department of Mathematics
University of Washington
Box 354350
Seattle, WA 98195-4350

Office: PDL C-549
Email: jarod at uw dot edu

• eXperimental Lean Lab (XLL)

• UW Algebra and Algebraic Geometry Seminar

I am a Professor of Mathematics and a Victor Klee Faculty Fellow at the University of Washington. I am currently partially funded by NSF grants DMS-1801976 and DMS-2100088. From 2012-16, I was a lecturer/senior lecturer at Australian National University in Canberra, Australia where I was a recipient of an ARC DECRA grant. From 2011-12, I was a (tenure-track) assistant professor at Universidad de Los Andes in Bogotá, Colombia. From 2013-14 I was a Alexander von Humboldt fellow at Humboldt University in Berlin, Germany. Beforehand, I was an NSF postdoc from 2008-11 at Columbia University working with Johan de Jong. I completed my Ph.D. in 2008 under the supervision of Ravi Vakil at Stanford University.

Curriculum Vitae

Lecture notes

Notes on stacks and moduli, pdf (last updated: August 19, 2024), earlier drafts.

Preprints

Structure results for torus fixed loci (with F. Janda), pdf.
Coherently complete algebraic stacks in positive characteristic (with J. Hall and D. B. Lim), pdf.
The étale local structure of algebraic stacks (with J. Hall and D. Rydh), pdf.

Publications

Existence of moduli spaces for algebraic stacks (with D. Halpern-Leistner and J. Heinloth), pdf.
to appear in Inventiones mathematicae.
Artin algebraization for pairs with applications to the local structure of stacks and Ferrand pushouts (with J. Hall, D. Halpern-Leistner, and D. Rydh), pdf.
to appear in Forum of Mathematics, Sigma.
Projectivity of the moduli space of vector bundles on a curve (with P. Belmans, D. Bragg, J. Liang, and T. Tajakka), pdf.
to appear in Stacks Project Expository Collection published by Cambridge University Press, 2022.
Reductivity of the automorphism group of K-polystable Fano varieties (with H. Blum, D. Halpern-Leistner and C. Xu), pdf.
Inventiones mathematicae, 222 (2020), no. 3, 995-1032.
A Luna étale slice theorem for algebraic stacks (with J. Hall and D. Rydh), pdf.
Annals of Mathematics, (2) 191 (2020), no. 3, 675-738.
Cartan-Iwahori-Matsumoto decompositions for reductive groups (with D. Halpern-Leistner and J. Heinloth), pdf.
Pure and Applied Mathematics Quarterly, special issue in dedication to David Mumford's 80th birthday, 17 (2021), no. 2, 593-604.
Syzygies of the apolar ideals of the determinant and permanent (with R. Rowlands), pdf.
Journal of Algebraic Combinatorics, 51 (2020), no. 3, 419-454.
Associated forms and hypersurface singularities: The binary case (with A. Isaev), pdf.
Journal für die reine und angewandte Mathematik, 745 (2018), 83-104.
Second flip in the Hassett-Keel program: A local description (with M. Fedorchuk, D. Smyth, and F. van der Wyck), pdf.
Compositio Mathematica, 153 (2017), no. 8, 1547-1583.
Second flip in the Hassett-Keel program: Existence of good moduli spaces (with M. Fedorchuk and D. Smyth), pdf.
Compositio Mathematica, 153 (2017), no. 8, 1584-1609.
Second flip in the Hassett-Keel program: Projectivity (with M. Fedorchuk and D. Smyth), pdf.
International Mathematics Research Notices, no. 24, (2017), 7375-7419.

An integrated version of the above three papers, pdf.
A lower bound for the determinantal complexity of a hypersurface (with T. Bogart and M. Velasco), pdf.
Foundations of Computational Mathematics, 17 (2017), no. 3, 829-836.
Associated forms of binary quartics and ternary cubics (with A. Isaev and N.G. Kruzhilin), pdf.
Transformation Groups, 21 (2016), no. 2, 593-618.
Equivariant versal deformations of semistable curves (with A. Kresch), pdf.
Michigan Mathematical Journal, 65 (2016), no. 2, 227-250.
Singularities with G_m-action and the log minimal model program for M_g (with M. Fedorchuk and D. Smyth), pdf.
Journal für die reine und angewandte Mathematik, 721 (2016), 1-41.
Adequate moduli spaces and geometrically reductive group schemes, pdf.
Algebraic Geometry, 1 (2014), no. 4, 489-531.
Associated forms in classical invariant theory and their applications to hypersurface singularities (with A. Isaev), pdf.
Mathematische Annalen, 360 (2014), no. 3-4, 799-823.
Good moduli spaces for Artin stacks, pdf.
Annales de l'Institut Fourier, 63 (2013), no. 6, 2349-2402.
Invariant rings through categories (with J. de Jong), pdf.
Journal of Algebra, 375 (2013), 235-257.
Finite Hilbert stability of (bi)canonical curves (with M. Fedorchuk and D. Smyth), pdf.
Inventiones mathematicae, 191 (2013), no. 3, 671-718 (journal version).
Common left- and right-hand divisors of a quaternion integer (with M. Abouzaid, S. DiMauro, J. Grosslight, and D. Smith)
Journal of Pure and Applied Algebra, 27 (2013), no. 5, 779-785 (journal version).
Recasting results in equivariant geometry: affine cosets, observable subgroups, and existence of good quotients (with R. Easton), pdf.
Transformation Groups, 17 (2012), no. 1, 1-20.
GIT Constructions of Log Canonical Models of M_g (with D. Hyeon), pdf .
Compact Moduli and Vector Bundles, 87-106, Contemporary mathematics, 564, American Math Society, Providence, RI, 2012 (Proceedings of the 2010 conference at the University of Georgia, Athens) (journal version).
Local properties of Artin stacks, pdf (this version contains several corrections of the published version).
Tohoku Mathematical Journal, 64 (2012), no. 1, 105-123.
Computing invariants via slicing groupoids: Gel'fand MacPherson, Gale and positive characteristic stable maps, pdf.
Mathematische Nachrichten, 285 (2012), no. 5-6, 562-579.
On the local quotient structure of Artin stacks, pdf (this version contains several corrections of the published version).
Journal of Pure and Applied Algebra, 214 (2010), no. 9, 1576-1591.
On cosets of the unit loop of octonion integers, (with M. Abouzaid, S. DiMauro, J. Grosslight and D. Smith).
Communications in Algebra, 35 (2007), no. 1, 207-214 (journal version).
On the choice of random directions for stochastic approximation algorithms, (with J. Theiler).
IEEE Trans. Automat. Control, 51 (2006), no. 3, 476-481 (journal version).

Expository

A Guide to Organizing a Virtual Conference (with D. Litt and I. Vogt), pdf.
to appear in Notices Of The American Mathematical Society.
Artin algebraization and quotient stacks, pdf.
notes from the summer school Algebraic stacks and related topics in Mainz, Germany (Aug. 31 - Sept. 4, 2015).
The moduli stack of semistable curves
Oberwolfach Reports, Report No. 6 (2013), 373-376 (journal version).
Birational models of M_g
Oberwolfach Reports, Report No. 30 (2012), 22-25 (journal version).
Good moduli spaces for Artin stacks
Oberwolfach Reports, Report No. 26 (2008), 14-16 (journal version).

Conferences organized

Developments in moduli problems, February 27 to March 3, 2023.
AIM Workshop: Moduli Problems Beyond GIT, January 25 to January 29, 2021.
WAGON^2 (Western Algebraic Geometry ONline), November 13-14, 2020.
WAGON (Western Algebraic Geometry ONline), April 18-19, 2020.
Geometry at the ANU: graduate student workshop and conference, August 15-26, 2016.
Equivariant geometry and algebraic stacks at the ANU Kioloa campus, March 14-18, 2016.
Algebraic geometry and related fields at the ANU, May 29-31, 2013
Log minimal model program for moduli spaces at the American Institute of Mathematics (AIM), December 10-14, 2012
Moduli spaces and moduli stacks at Columbia University from May 23-27, 2011.

Teaching

Math 582A: Algebraic curves with a view toward moduli (Winter 2023)
Math 507: Advanced commutative algebra (Fall 2022)
Math 300: Introduction to Mathematical Reasoning (Spring 2022)
Math 567A: Algebraic Geometry (Fall 2021)
Math 581J: Topics in Scheme Theory (Fall 2021)
Math 404A: Introduction to Modern Algebra (Spring 2021)
Math 582C: Introduction to stacks and moduli (Winter 2021)
Math 582D: Recent Hits in Algebraic Geometry (Winter 2021)
Math 581B: Algebraic Groups I (Fall 2019)
Math 124A/B: Calculus I (Fall 2019)
Math 480A: Algebraic Complexity Theory (Spring 2019)
Math 124A: Calculus I (Spring 2019)
Math 427: Complex Analysis (Fall 2018)
Math 124B: Calculus I (Fall 2018)
Math 583D: Bridgeland stability (Spring 2018)
Math 582D: Moduli of Vector Bundles (Winter 2018)
Math 403B: Introduction to Modern Algebra (Winter 2018)
Math 504: Modern Algebra (Fall 2017)
Math 340: Abstract Linear Algebra (Spring 2017)
Math 508: Advanced Commutative Algebra (Winter quarter 2016-7)
Math 3345: Algebra 2 (Honors) -- Field Extensions and Galois Theory (Australian National University, Semester 1 2015)
Math 1013 (Calculus component) (Australian National University, Semester 1 2013)
Math 3346: Algebra 3 (Honors) -- Lie groups and algebras (Australian National University, Semester 2 2012)
Algebraic curves (Universidad de los Andes, Spring 2012)
Calculo diferencial (Universidad de los Andes, Spring 2012)
Calculo diferencial (Universidad de los Andes, Fall 2011)
Algebraic number theory (Columbia University, Fall 2010)
Calculus III (Columbia University, Fall 2010)
Calculus III (Columbia University, Fall 2008)