Anne Fayolle

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BIKES

  • About
  • Spring 2024
  • Fall 2023
  • Spring 2023
  • Fall 2022
  • Spring 2022
  • Fall 2021
  • Spring 2021
  • Fall 2020
  • Summer 2020
  • Spring 2020
  • Fall 2019
  • Spring 2019
  • Fall 2018

    • About

    BIKES is the name of the Graduate student Commutative Algebra Seminar of the University of Utah.

    This seminar provides a relaxed environment, in which students can practice giving talks and learn about commutative algebra from other grad students and post docs.

    During the academic year 2024-2025, BIKES is organized by Brendan and Jenna. I organized it in 2023-2024.

    Spring 2024

    BIKES is held in LCB 222 (and online) on Fridays 3-4pm. This semester's BIKES is coorganized by Anne and Brendan (snacks suggestions go to Brendan).

    February 16 Aryaman Linear quotients of connected ideals of graphs
    February 23 Joseph Introduction to Gröbner bases
    March 1 Rahul Jet Bundles or Bundles of principal parts.
    March 22 Brendan Seeing Spec R inside of the derived category
    March 29 Debbie Minimal free resolutions of edge ideals of graphs
    April 5 Peter The McKay Correspondence: History and Generalizations
    April 12 Ethan Introduction to Determinantal Rings

    Fall 2023

    BIKES is held in LCB 222 (and online) on Fridays 3-4pm. This semester's BIKES is organized by Anne.

    September 1 Trung Morse resolutions
    September 8 Brendan The Lean Theorem Prover and Formal Mathematics
    September 15 Peter Singularities in characteristic zero: multiplier ideals, trace ideals, and closure operations
    September 22 Antonia Introduction to Local Duality
    September 29 Aryaman Invariant Theory of Commutative Rings
    October 6 Jenna Galois descent, cohomology, and conjugacy
    October 20 Rahul Hilbert-Kunz multiplicity, F-signature & a conjecture of Monsky
    October 27 Anne On tame ramification and compatible ideals
    December 1 Jorge Fusion invariant representations

    Spring 2023

    BIKES is held in JWB 208 (and online) on Fridays 3-4pm. This semester's BIKES is organized by Sandra.

    January 13 N/A Organizational Meeting
    January 20 Kriti Minkowski Inequality for Multiplicity of Ideals
    February 10 Seungsu F-Splittings and Strongly F-Regular Rings
    February 17 Peter The Test Ideal and The Multiplier Ideal Are Morally Equivalent
    February 24 Brendan The Lean Theorem Prover and Formal Mathematics
    March 3 Fellowship of the Ring
    March 17 Trevor F-Pure Threshold and Semi-quasi Homogeneous Singularities
    March 24 Fellowship of the Ring
    March 31 Trung Principal radical systems
    April 7 Anne An introduction to compatible ideals

    Fall 2022

    BIKES is held in LCB 323 (and online) on Thursdays 4-5pm. This semester's BIKES is organized by Sandra.

    August 24 N/A Organizational Meeting
    September 8 Josh Bounds on Loewy length via derived categories
    September 15 Antonia Examples and results on bounds on Loewy length via derived categories
    September 22 Trung Big Cohen-Macaulay Modules and Homological Conjectures (Theorems)
    September 29 Brendan Intersection Theorems in Local Algebra (part 1)
    October 20 Daniel The Improveder New Intersection Theorem

    Spring 2022

    BIKES was held in LCB 323 (and online) on Thursdays from 2-3pm. This semester's BIKES was organized by Trung.

    January 13 N/A Organizational Meeting
    January 27 Hanlin Splinters and derived splinters
    February 3 Peter Splinters and derived functors
    February 10 Eamon Unit F-modules and local cohomology
    February 17 Seungsu Discreteness and rationality of F-jumping numbers of hypersurfaces on regular rings
    February 24 Vaibhav Local cohomology modules of a polynomial ring over the integers have finitely many associated primes
    March 3 Trung Cellular resolutions and hull resolutions
    March 17 Trung Morse resolutions
    March 24 Peter An introduction to simplicial objects
    March 31 Antonia The Dold-Kan Correspondence
    April 7 Daniel Simplicial Rings and André-Quillen (Co)homology.
    April 14 Vaibhav About the job market

    Fall 2021

    BIKES was held in LCB 222 (and online) on Thursdays from 2-3pm. This semester's BIKES was organized by Trung.

    August 26 N/A Organizational Meeting
    September 9 Seungsu F-purity and F-regularity
    September 16 Vaibhav Introduction to differential operators
    September 23 Devlin Differential operators in characteristic p
    September 30 Trung A quick look at the singularity category
    October 7 Jack Derived categories and the singularity category
    October 21 Daniel Singularity category over a hypersurface ring
    October 28 Hanlin Stable homotopy category
    November 4 Peter D(R) and Ho(Mod-HR) are the same!
    November 18 Annie + Daniel Taylor resolution
    December 2 Sandra Simplicial resolution
    December 9 Trung Scarf complex and Lyubeznik resolution

    Spring 2021

    This semester, E-BIKES (the enchanted version of regular BIKES) met on Fridays at 3pm. Daniel and Peter organized.

    January 22 N/A Organizational Meeting
    February 5 Trung Peskine-Szpiro
    February 12 Sam Peskine-Szpiro
    February 19 Peter Complete and torsion modules
    February 26 Hanlin Complete and torsion modules
    March 12 Ben Golod rings and DGAs
    March 19 Daniel Golod rings and DGAs
    March 26 Josh Golod rings and DGAs
    April 2 Isaac F-signature in affine semigroup rings
    April 9 Vaibhav How bad are pinched Veronese rings?

    Fall 2020

    This semester, E-BIKES (the enchanted version of regular BIKES) met on Tuesdays at 2pm. Daniel and Peter organized.

    August 25 N/A Organizational Meeting
    September 1 Marcus Universally dendroidal quasi-images
    September 8 Aeolus Shallow root systems in desert landscapes
    September 15 Isaac Introduction to F-singularities
    September 22 Ruyi Kunz's Theorem
    September 29 Seungsu Geometric aspects of F-splitting
    October 6 Janina Introduction to group cohomology, Hochschild cohomology, and Hopf algebras
    October 13 Jian Kahler differentials and the Hoschild cohomology ring
    October 20 Daniel Hochschild cohomology and group cohomology
    October 27 Sandra D-modules and differential operators
    November 3 Trung D-modules and differential operators
    November 10 Vaibhav D-modules and differential operators
    November 17 Josh Rational homotopy theory
    November 24 Peter Rational homotopy theory
    December 1 Daniel Rational homotopy theory

    Summer 2020

    This summer, we decided to have virtual BIKES! As such, we temporarily rebranded as UNICYCLES (Utah's New International Commutative algebra You-Can-Learn-Electronically Seminar). We meet Mondays 10-11am MT on Zoom. Daniel and Peter organized.

    May 25 Peter Computing Rf_*F for coherent sheaves on projective space
    June 1 Vaibhav Finiteness properties of local cohomology modules: an extended example
    June 15 Jenny The depth of powers of an ideal
    June 22 Jian Classifying thick subcategories of the stable category of maximal Cohen-Macaulay modules over a hypersurface
    June 29 Sandra Some invariants in prime characteristic
    July 6 Trung Another proof of Kunz's theorem
    July 13 JJ Tilting equivalence: the key ingredient to perfectoid spaces
    July 20 Misc. Research chats
    July 27 Shalom Valuation domains and the Frobenius endomorphism
    August 3 Sudipta Quantifying singularities using differential signature
    August 10 Daniel TBD

    Spring 2020

    We meet Thursdays from 11:10 am to 12:00 noon in JWB 208. The plan this semester is to present one important and accessible paper in CA each week from February onwards. This semester BIKES was organized by Vaibhav.

    January 9 Josh Cohomology operators
    January 16 Thomas Basic elements theorem
    January 23 Ben Hochschild cohomology
    January 30 Eloísa An introduction to characteristic p
    February 6 Wei Support varieties and cohomology over CIs
    February 13 Janina Support varieties and cohomology over CIs
    February 20 Jian Support varieties and cohomology over CIs
    February 27 Daniel Total Betti numbers of modules of finite projective dimension
    March 5 Vaibhav Cohomological dimension of ideals defining Veronese subrings
    March 26 JJ Homology of Noetherian and local rings
    April 2 Peter Stability of associated primes
    April 9 Isaac A remark concerning multiplicities
    April 16 Jenny FI-modules
    April 23 Janina The dimension of an intersection in an ambient hypersurface

    Fall 2019

    We meet Wednesdays from 3:10pm to 4:00pm in JWB 108. This semester BIKES was organized by Vaibhav.

    August 30 Vaibhav Basics of homological algebra
    September 6 Janina Resolutions of modules and derived functors
    September 13 Sam Depth and projective dimension
    September 20 Wei Regular local rings
    September 27 Trung Cohen Macaulay rings
    October 4 Faith Injective modules and injective hulls
    October 18 Robert Introduction to representation staility
    October 25 Peter Matlis duality
    November 1 Pinches Gorenstein rings
    November 8 Daniel Introduction to local cohomology modules
    November 15 Jian Local cohomology modules- various definitions
    November 29 JJ Cohomological dimension
    December 6 Isaac Arithmetic rank

    Spring 2019

    We meet Thursdays from 11:00am to noon in JWB 335. This semester BIKES was organized by Janina.

    January 10 Sam Invariance under group action
    January 17 Vaibhav Invariance under group action
    January 24 Jenny Invariance under group action
    January 31 Ben Invariance under group action
    February 7 Patricia Klein
    February 14 Peter Characteristic p
    February 21 Dan Characteristic p
    February 28 Thomas Characteristic p
    March 7 Wei Local cohomology
    March 21 Jenny Local cohomology
    March 28 Thomas Local cohomology
    April 4 Daniel BGG
    April 11 Janina BGG
    April 25 Pinches BGG

    Fall 2018

    We meet Thursdays from 11:45am to 12:45pm in JWB 308. This semester BIKES was organized by Janina.

    August 30 Vaibhav An example of a ring of smooth functions
    September 6 Jenny Local Cohomology Modules
    September 13 Janina Derived Categories
    September 20 Thomas Divisor Class Groups of Noetherian domains
    September 27 Dan Symbolic powers
    October 4 John Koszul complex
    October 18 Marcus Tight closure and Hilbert-Kunz multiplicity
    October 25 Pinches Auslander-Buchsbaum formula
    November 1 Ben Matrix factorization
    November 8 Peter The Cohen structure theorem
    November 15 Organizational meeting
    November 29 Robert M. Walker A Mindfulness Meditation on Primary Decompositions
    December 6 Wei Example of an infinite dimensional Noetherian ring

    BIKES stands for...

    Bridges
    Into
    Knowledge
    E.g. (knowledge of) commutative algebra (seminars)
    Seminar

    © 2023 Anne Fayolle