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 Brendan Murphy at bsmurphy@math.utah.edu.
BIKES is held in JTB 310 (and online) on Wednesdays 2:15-3:30pm. This semester's BIKES is coorganized by Brendan and Jenna.
| August 21 | N/A | Organizational Meeting |
| August 26 | Aryaman | Very bad no-good evil rings |
| September 4 | Anne | F this and F that! |
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 | TBA |
| March 15 | Jenna & Antonia | TBA |
| March 22 | Jenna & Antonia | TBA |
| March 29 | Debbie | TBA |
| April 5 | Peter | TBA |
| April 12 | Ethan | TBA |
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 |
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 |
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 |
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 |
This semester, BIKES is being held in LCB 222 (and online) on Thursdays from 2-3pm. Trung is organizing.
| 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 |
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? |
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 |
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 |
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 |
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 |
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 |
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 |