The IPAC (Important Papers in Algebraic Combinatorics) Seminar Homepage

The 2020-2021 IPAC seminar is co-organized by
Jim Haglund of Penn, and Anna Pun of the University of Virginia,

The theme of the seminar is to work through articles/arXiv preprints which represent important current developments, at least initially in algebraic combinatorics. The seminar will meet (via zoom) on Tuesdays and Thursdays from 12-1pm Philadelphia time. Each seminar session will have a "host" who will be responsible for presenting material, but the degree to which the seminar will be a series of lectures or more of a group discussion may vary from week to week. If you wish to attend the talks email me to get the zoom link (jhaglund "at symbol" math.upenn.edu). recordings of the talks will be made. The first paper we will be working through is "A Proof of the Extended Delta Conjecture" by Blasiak, Haiman, Morse, Pun and Seelinger (BHMPS2), available on the arXiv. The seminar will run from the end of classes in the Spring to roughly the end of the summer break, i.e early May through sometime in late July or August. See the table below for our schedule for the 2021 Summer Season. (As of late August 2021 we have adjourned the seminar but plan to restart in May 2022 after the academic year ends),

The 2021 IPAC Seminar Schedule

Date                   Host                              Paper                              Seminar Lecture Notes                            
5/4 Anna Pun, Univ. of Virginia A Proof of the Extended Delta Conjecture Sections 3.1 and 3.2 on the Schiffman Algebra
5/6 Anna Pun, Univ. of Virginia A Proof of the Extended Delta Conjecture Sections 3.1 and 3.2 continued - see above link
5/11 Anna Pun, Univ. of Virginia A Proof of the Extended Delta Conjecture Sections 3.1 and 3.2 continued - see above link
5/13 Anna Pun, Univ. of Virginia A Proof of the Extended Delta Conjecture Section 3.3: Action of the Schiffman Algebra on Symmetric Functions
5/18 Anna Pun, Univ. of Virginia A Proof of the Extended Delta Conjecture Section 3.3 continued - see above link
5/20 Anna Pun, Univ. of Virginia A Proof of the Extended Delta Conjecture Section 3.4: GL characters and the shuffle algebra
5/25 Anna Pun, Univ. of Virginia A Proof of the Extended Delta Conjecture Section 4.1: Distinguished Negut Elements
5/27 Anna Pun, Univ. of Virginia A Proof of the Extended Delta Conjecture Section 4.2: Commutator Identity
6/1 Anna Pun, Univ. of Virginia A Proof of the Extended Delta Conjecture Section 4.3: Symmetry Identity for Db and Ea
6/3 Anna Pun, Univ. of Virginia A Proof of the Extended Delta Conjecture Section 4.3 continued - see above link
6/8 Anna Pun, Univ. of Virginia A Proof of the Extended Delta Conjecture Section 4.4: Shuffling the symmetric function side of the Extended Delta Conjecture
6/10 Anna Pun, Univ. of Virginia A Proof of the Extended Delta Conjecture Section 2: The Extended Delta Conjecture
Section 5.1: Reformulation of the combinatorial side
Section 5.2: Definition of N(Beta/Alpha)
Section 5.3: Transforming the Combinatorial Side
6/17 Jim Haglund, Penn A Proof of the Extended Delta Conjecture: Overview of Sections 2 and 5, continued.
See links above to Anna's notes, as well as
the following notes of Jim.
Part A of Review of Sections 2 and 5
Part B of Review of Sections 2 and 5
Part C of Review of Sections 2 and 5
7/1 Jim Haglund, Penn A Proof of the Extended Delta Conjecture: Overview of Section 6.
See the following notes of Jim on Section 6 and and supplementary notes of Anna on their 1st paper "A Shuffle Theorem for Paths under any Line" (BHMPS1) as well as Section 6 of BHMPS2
Section 6
Section 4.1 of BHMPS1 on Combinatorial LLT polys
Section 4.2 of BHMPS1 on Hecke algebras
Section 4.3 of BHMPS1 on Nonsymmetric Hall-Littlewood polys
Section 4.3 of BHMPS1 on LLT Series
Section 6.2 of BHMPS2 on LLT Series
Section 6.3 of BHMPS2 on the Extended Delta Thm
7/6 Jim Haglund, Penn A Proof of the Extended Delta Conjecture: Overview of proofs of the Cauchy formula and Pieri rules for nonsymmetric Hall-Littlewoods.
See the following notes of Jim on as well as notes of Anna above.
Cauchy Formula and Pieri Rules
7/8 Marino Romero, UCSD and Penn The Five Term Relation of Garsia and Mellit
7/13 Marino Romero, UCSD and Penn The Five Term Relation of Garsia and Mellit (continued)
7/15 Marino Romero, UCSD and Penn The Five Term Relation of Garsia and Mellit (continued)
7/20 Michele D'Adderio, Univ. of Pisa New Identities for Theta Operators (joint with Marino Romero)
7/22 Brendon Rhoades, UCSD Ordered Set Partitions, Generalized Coinvariant Algebras, and the Delta Conjecture Abstract: I will discuss the use of orbit harmonics in constructing coinvariant-type algebras related to the Delta Theorem, Hall-Littlewood polynomials, and more. Time permitting, I'll also discuss some varieties whose cohomology rings are presented by these algebras.