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.

If you have any questions, contact Daniel McCormick at mccormic@math.utah.edu or Peter McDonald at mcdonald@math.utah.edu .

Fall 2020

This semester, join us for E-BIKES (the enchanted version of regular BIKES) on Tuesdays at 2pm. We'll be taking a tour through various areas of commutative algebra based on a very democratic ranked-choice election (learn more about ranked-choice voting here. Daniel and Peter are organizing.

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...

E.g. (knowledge of) commutative algebra (seminars)