## General information

The Representation Stability group at Stanford University is run by Tom Church and Jenny Wilson.

During Winter 2015 the reading group is not meeting. In Fall 2014 we read three papers:

*Representation stability and finite linear groups*, by Andrew Putman and Steven Sam

*Gröbner methods for representations of combinatorial categories*, by Steven Sam and Andrew Snowden

*Noetherian property of infinite EI categories*, by Wee Liang Gan and Liping Li

Putman–Sam:

Friday 8/22: *Jenny Wilson*, overview of Noetherian theorem

Tuesday 9/2: *Jenny Wilson*, proof of Noetherian theorem

Friday 9/5: *Jenny Wilson*, proof of Noetherian theorem

Friday 9/12: *Thomas Church*, applications of Noetherian theorem

Sam–Snowden:

Friday 9/19: *Graham White*, regular languages and generating functions

Tuesday 9/30: *Evita Nestoridi*, Gröbner categories and Hilbert series

Tuesday 10/7: *Thomas Church*, Hilbert series of FI-modules and FI_{d}-modules

Tuesday 10/14: *Jennifer Wilson*, FI-, FI_{d}, FA-, and FS^{op}-modules are quasi-Gröbner

Tuesday 10/21 (**2:30–3:30pm**): *John Pardon*, Δ–modules, lecture 1

Tuesday 10/28 (**2:30–3:30pm**): *John Pardon*, Δ–modules, lecture 2

Tuesday 11/4: **No lecture**

Tuesday 11/11: *Thomas Church*, Categories of *G*-injections and *G*-surjections

Tuesday 11/18: No lecture

Tuesday 12/2 (1–2pm): *Patricia Hersh* (NC State), Representation stability and *S*_{n}-module structure in the partition lattice

##### 10/7: FI, FI_{d}, and FA are quasi-Gröbner

- Theorem 7.1.1 (with proof from Section 7.2)
- Theorem 7.1.2
- Corollary 7.1.3
- Corollary 7.1.5
- Remark 7.1.6 (explain why this is equivalent)
- Theorem 7.4.6
- Theorem 7.4.8
- Example 7.4.11 (configurations on disconnected manifold are f.g. as FI
_{d}-module)

##### 10/14: FS^{op} is quasi-Gröbner

- Definition of FS^op
- Remark 8.1.7 (just state equivalence)
- Theorem 8.1.1 (with proof from Section 8.2)
- Theorem 8.1.2
- Corollary 8.1.4
- Remark 8.1.5
- Theorem 8.3.1

##### 10/21 and 10/28: Δ–modules

- Example from Section 9.2 (connect with Segre embedding; make syzygies/Tor not forbidding)
- Theorem 9.2.2 as motiviation (perhaps read introduction of [Snowden])
- Definition of Δ-module (first two paragraphs of Section 9.1)
- Theorem 9.1.3 (give statement; proof occupies remainder of lectures)
- Section 9.3
- Lemma 9.3.1
- Proposition 9.3.2
- Lemma 9.4.1
- Proposition 9.4.2
- Proposition 9.4.3
- Proposition 9.4.4
- Corollary 9.4.5 (concludes first half of proof)
- Section 9.5 (concludes second half of proof)

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