Lecture notes

Here are some lecture notes. I separate these from the talks below since these are more comprehensive.
  1. Some extensions of the Ananyan-Hochster principle (extended abstract), February 2019, Oberwolfach, "Singularities and Homological Aspects of Commutative Algebra" workshop
  2. Big polynomial rings and Stillman's conjecture (extended abstract), July 2018, Oberwolfach, "Classical algebraic geometry" workshop
  3. Mini-course on representation stability, August 2017, Texel, Summer school of the IRTG
  4. Using representation theory to calculate syzygies, November 2015, University of Illinois, Chicago, "Syzygies of Algebraic Varieties" workshop
  5. Twisted homological stability for groups via functor categories (extended abstract), May 2015, Oberwolfach, "Cohomology of Finite Groups" workshop
  6. Lectures on twisted commutative algebras (4 lectures), October 2014, Institut Henri Poincaré
  7. Infinite rank classical groups and specialization (extended abstract), April 2013, Oberwolfach, "Algebraic groups" workshop
  8. Free resolutions, degeneracy loci, and moduli spaces (notes), November 2011, Princeton University "Arithmetic invariant theory" seminar


Here is some material used in talks I have given. These are either in the form of slides or notes or a video of the talk.
Be careful of mistakes: when converting results into a conversational form or providing motivation, mistakes are easily introduced.
  1. Big polynomial rings and Stillman's conjecture, May 2020, UC San Diego RTG colloquium, notes, video
  2. Secants of Veronese embeddings and Hopf rings (video stream), April 2016, BIRS, "Free Resolutions, Representations, and Asymptotic Algebra"
  3. Twisted commutative algebras and related structures, April 2015, IMPANGA 15, Bedlewo
  4. Gröbner methods for representations of combinatorial categories, March 2015, Representation theory meeting, Bad Honnef
  5. Twisted commutative algebras (notes), February 2015, Caltech algebraic geometry seminar
  6. Gröbner bases: theory and applications, November 2014, Miller Institute lunch talk (This talk was aimed at a general scientist audience.)
  7. Representation stability and finite linear groups, November 2014, UC Berkeley, math department colloquium
  8. Gröbner methods for generic representation theory and the artinian conjecture, October 2014, GDR conference: algebraic topology and applications, Clermont-Ferrand
  9. Infinite-dimensional combinatorial commutative algebra, September 2014, Eau Claire AMS special session
  10. Gröbner bases, formal languages, and applications, September 2014, Eau Claire AMS special session
  11. Hyperplane arrangements and classical moduli spaces, September 2014, Eau Claire AMS special session
  12. Representations of Lie superalgebras and determinantal varieties (notes), July 2014, Representations of algebraic groups, Lyon
  13. Moduli spaces of Coble hypersurfaces (notes), June 2014, Macaulay2 research conference, UIUC
  14. Growth of ideals in subword posets (notes), June 2014, Stanley@70 conference, MIT
  15. Gröbner bases for twisted commutative algebras (notes), April 2014, UMichigan combinatorics seminar
  16. Twisted commutative algebras (notes), October 2013, Stony Brook algebraic geometry seminar
  17. Homology of Littlewood complexes (video stream), December 2012, MSRI, "Combinatorial commutative algebra and its applications"
  18. Combinatorics and geometry of E7 (slides), October 2012, University of South Carolina, math department colloquium (this is a less technical version of RTGC talk below)
  19. Combinatorics and geometry of E7 (slides), September 2012, Berkeley "Representation Theory, Geometry, Combinatorics" seminar
  20. Free resolutions, combinatorics, and geometry (slides), April 2012, my PhD thesis defense
  21. Koszul homology and classical invariant theory (notes), January 2012, University of Michigan commutative algebra seminar (Update: The conjecture in this talk is proved in the paper "Homology of Littlewood complexes")
  22. Free resolutions, degeneracy loci, and moduli spaces (notes), January 2012, University of Michigan algebraic geometry seminar (the topics of these notes overlap with those of the Sep. 2011 Princeton notes, but the content is different)
  23. Torus actions, multi-partitions, and crystals (slides), January 2012, Boston AMS-MAA joint meetings special session
  24. Sheaf cohomology and non-normal varieties (slides), December 2011, Toronto CMS special session
  25. Counting matrices over finite fields (slides), September 2011, University of Minnesota combinatorics seminar
  26. Geometric approach to Littlewood inversion formulas (slides), April 2011, College of the Holy Cross AMS special session
  27. Schubert complexes and degeneracy loci (slides), February 2011, UIUC Algebra-Geometry-Combinatorics seminar
  28. Some recent developments in Boij–Söderberg theory (slides), January 2011, Thunder Bay "Combinatorial algebra meets algebraic combinatorics"
  29. Saturation theorems for the classical groups (slides), October 2010, Notre Dame AMS special session
  30. Young tableaux and Betti tables (slides), October 2009, MIT combinatorics seminar