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.

**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. | |