Summer REU info- Vic Reiner

Vic Reiner

Some REU Summer 2019 info

Dates: Monday June 3 - Friday July 26, 2019
Room schedule and rough timetable
We 9:30am to noon in the first two weeks,
but will meet 10am Mon-Wed-Fri for the remainder.

First two weeks (June 3, June 10)
are in Vincent Hall 16 (basement auditorium)
meeting every day, with one mentor per day presenting background for an REU problem.
Exercises will also be posed, and student solutions presented.
Third, fourth weeks (June 17, June 24)
are in Vincent Hall 6 (a basement classroom).
Students will be presenting 20-minute talks on papers relevant for the REU problems.
Fifth, sixth weeks (July 1, July 8)
are still in Vincent Hall 6, mainly devoted to (brief) progress reports.
Seventh week (July 15) is still in Vincent Hall 6, mainly progress reporting and writing final reports.
Eighth week (July 22) is back in VinH 16, with last progress reports at 11am Mon,
then final presentations at 10am Wed and Thur, and Fri 9am debriefing.

Mentors (office number, weeks gone):
Christine Berkesch, Coordinator (VinH254, gone week 3),
Ben Brubaker (VinH352, gone week 6)
Sunita Chepuri (VinH552, gone weeks 3,4,5)
Sam Hopkins (VinH204, gone weeks 4,5),
Vic Reiner (VinH256, gone weeks 5,6)

TAs: Sarah Brauner (VinH556), Claire Frechette (VinH550), Andy Hardt (VinH524), Greg Michel (VinH524), Jorin Schug (VinH360), Katy Weber (VinH520)

Participants: Michael Curran, Quang Dao, Christopher Dowd, Nathan Kenshur, Feiyang Lin, Sean McNally, Christina Meng, Zachary Stier, Julian Wellman, Zixuan Xu, Calvin Yost-Wolff, Teresa Yu, Sylvester Zhang, Valerie Zhang.

Group photo

Touristic suggestions

Problems
No. (date) Mentor TAs Notes Sources
(asterisk ^* means priority
for student talks) Student talks
(date, TA for practice talk) Students
interested

1 (Mon 6/3)
Virtual syzygies of points Berkesch Michel
Schug Day 1 notes
Macaulay2 intro
Macaulay2 demo from lecture
Macaulay2 exercise solutions Cox lectures^*
Berkesch--Erman--Smith
Loper survey^*
Gao--Li--Loper--Mattoo
Almousa--Bruce--Loper--Sayrafi
Eisenbud book

Sean (Mon 6/24, Jorin/Greg)

CJ (Mon 6/24, Jorin/Greg) CJ
Sean

2 (Tues 6/4)
Brubaker Frechette
Weber Day 2 notes Zinn-Justin^* ("Six-vertex, loop, ...")
Brubaker--Bump--Friedberg^*
Lam^*
Zinn-Justin^* ("L-R coeffs ...") Valerie, Sylvester
(both Fri 6/21, Katy/Claire)

Calvin
Michael
Sylvester
Valerie

3 (Wed 6/5)
Chepuri Hardt
Michel Day 3 notes
Recurrence relations from lecture that defined a certain tau-sequence. Galashin--Pylyavskyy^*
Grinberg--Roby
Musiker--Roby
Reiner--Tseng (see Thm. 1.2) CJ
Sylvester
Valerie

4 (Thur 6/6)
Dihedral sieving Reiner Brauner
Hardt Day 4 notes from Sarah
Day 4 notes from Vic
worksheet for calculating (q,t)-Catalans, Schroeders in SAGE Rao--Suk^*
Eu-Fu^*
Haglund
Reiner--Stanton--White^* Zack, Michael (Mon 6/17, Sarah)
Zixuan (Mon 6/24, Greg)

Julian
Michael
Zack
Zixuan

5 (Fri 6/7)
Minuscule doppelgängers Hopkins Hardt Day 5 notes
SAGE code for testing the conjectures. Stanley^*
Hamaker-Patrias-Pechenik-Williams^*
Hopkins^*
Stanley's EC1 (see Chap. 3 on posets) Feiyang (Wed 6/19, Andy)
Julian (Wed 6/19, Andy)

Calvin
Julian
Quang
Sylvester

6 (Mon 6/10)
Virtual Stanley--Reisner theory Berkesch Schug Day 6 notes
Macaulay2 code Francisco--Mermin--Schweig^*
Hatcher Sec. 2.1^*
Miller--Sturmfels
Hochster
Eagon--Reiner^*
Yang^*

Nathan (Wed 6/26, Jorin) CJ
Feiyang
Nathan
Sean
Teresa
Zixuan

7 (Tues 6/11)
Directed graph associahedra Reiner Brauner Day 7 notes from Sarah
Day 7 notes from Vic Lam--Pylyavskyy^*
Carr--Devadoss
Postnikov--Reiner-Williams^*
Hersh
Björner
Christina (Fri 6/21, Andy)
Teresa (Wed 6/19, Sarah) Calvin
Christina
Julian
Quang
Teresa
Zixuan

8 (Wed 6/12)
Brubaker Weber Day 8 notes Steinberg^*
Rehmann^*
Piatetski-Shapiro^* Quang, Calvin
(both Wed 6/26, Katy/Claire) Calvin
Christina
Feiyang
Nathan
Quang
Zack

**Problems**
No. (date)	Mentor	TAs	Notes	Sources (asterisk ^* means priority for student talks)	Student talks (date, TA for practice talk)	Students interested
1 (Mon 6/3) Virtual syzygies of points	Berkesch	Michel Schug	Day 1 notes Macaulay2 intro Macaulay2 demo from lecture Macaulay2 exercise solutions	Cox lectures^* Berkesch--Erman--Smith Loper survey^* Gao--Li--Loper--Mattoo Almousa--Bruce--Loper--Sayrafi Eisenbud book	Sean (Mon 6/24, Jorin/Greg) CJ (Mon 6/24, Jorin/Greg)	CJ Sean
2 (Tues 6/4)	Brubaker	Frechette Weber	Day 2 notes	Zinn-Justin^* ("Six-vertex, loop, ...") Brubaker--Bump--Friedberg^* Lam^* Zinn-Justin^* ("L-R coeffs ...")	Valerie, Sylvester (both Fri 6/21, Katy/Claire)	Calvin Michael Sylvester Valerie
3 (Wed 6/5)	Chepuri	Hardt Michel	Day 3 notes Recurrence relations from lecture that defined a certain tau-sequence.	Galashin--Pylyavskyy^* Grinberg--Roby Musiker--Roby Reiner--Tseng (see Thm. 1.2)		CJ Sylvester Valerie
4 (Thur 6/6) Dihedral sieving	Reiner	Brauner Hardt	Day 4 notes from Sarah Day 4 notes from Vic worksheet for calculating (q,t)-Catalans, Schroeders in SAGE	Rao--Suk^* Eu-Fu^* Haglund Reiner--Stanton--White^*	Zack, Michael (Mon 6/17, Sarah) Zixuan (Mon 6/24, Greg)	Julian Michael Zack Zixuan
5 (Fri 6/7) Minuscule doppelgängers	Hopkins	Hardt	Day 5 notes SAGE code for testing the conjectures.	Stanley^* Hamaker-Patrias-Pechenik-Williams^* Hopkins^* Stanley's EC1 (see Chap. 3 on posets)	Feiyang (Wed 6/19, Andy) Julian (Wed 6/19, Andy)	Calvin Julian Quang Sylvester
6 (Mon 6/10) Virtual Stanley--Reisner theory	Berkesch	Schug	Day 6 notes Macaulay2 code	Francisco--Mermin--Schweig^* Hatcher Sec. 2.1^* Miller--Sturmfels Hochster Eagon--Reiner^* Yang^*	Nathan (Wed 6/26, Jorin)	CJ Feiyang Nathan Sean Teresa Zixuan
7 (Tues 6/11) Directed graph associahedra	Reiner	Brauner	Day 7 notes from Sarah Day 7 notes from Vic	Lam--Pylyavskyy^* Carr--Devadoss Postnikov--Reiner-Williams^* Hersh Björner	Christina (Fri 6/21, Andy) Teresa (Wed 6/19, Sarah)	Calvin Christina Julian Quang Teresa Zixuan
8 (Wed 6/12)	Brubaker	Weber	Day 8 notes	Steinberg^* Rehmann^* Piatetski-Shapiro^*	Quang, Calvin (both Wed 6/26, Katy/Claire)	Calvin Christina Feiyang Nathan Quang Zack

Final oral reports
Date Problem Talk titles and PDFs TA

Wed July 24
VinH 16
10am 1
2
6
7 Virtual Resolutions of General Points in SmoothFanoToricVariety(3,3)
Ribbon Lattices and Ribbon Function Identities
A Partial Characterization of Virtually Cohen-Macaulay Simplicial Complexes
Extended Nestohedra and their Face Numbers Jorin
Katy
Jorin/Greg
Sarah

Thur July 25
VinH 16
10am 3
4
5
8 Arborescences of Covering Graphs
Composite Sieving Techniques: Dihedral Action on Cluster Complexes
Rowmotion on the Trapezoid Poset
Metaplectic Analogues of Gelfand--Graev Models Greg
Andy/Sarah
Andy
Claire

**Final oral reports**
Date	Problem	Talk titles and PDFs	TA
Wed July 24 VinH 16 10am	1 2 6 7	Virtual Resolutions of General Points in SmoothFanoToricVariety(3,3) Ribbon Lattices and Ribbon Function Identities A Partial Characterization of Virtually Cohen-Macaulay Simplicial Complexes Extended Nestohedra and their Face Numbers	Jorin Katy Jorin/Greg Sarah
Thur July 25 VinH 16 10am	3 4 5 8	Arborescences of Covering Graphs Composite Sieving Techniques: Dihedral Action on Cluster Complexes Rowmotion on the Trapezoid Poset Metaplectic Analogues of Gelfand--Graev Models	Greg Andy/Sarah Andy Claire

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